The Spin Structure of the Nucleon

Christine A. Aidala∗
Physics Department,
University of Michigan,
450 Church Street,
Ann Arbor, MI 48109-1040,
U.S.A.

Steven D. Bass†
Institute for Theoretical Physics,
arXiv:1209.2803v2 [hep-ph] 1 Apr 2013

University of Innsbruck,
Technikerstrasse 25,
A-6020 Innsbruck,
Austria

Delia Hasch‡
INFN-Frascati, via E. Fermi 40,
00044 Frascati (Rm),
Italy

Gerhard K. Mallot§
CERN, CH-1211 Genève 23,
Switzerland

(Dated: 9 January 2013)

This article reviews our present understanding of QCD spin physics: the proton spin
puzzle and new developments aimed at understanding the transverse structure of the
nucleon. We discuss present experimental investigations of the nucleon’s internal spin
structure, the theoretical interpretation of the different measurements and the open
questions and challenges for future investigation.

CONTENTS V. Quark and Gluon Polarization from Data 16

A. Valence and sea polarization 16
I. Introduction 2 B. Gluon polarization 19
C. NLO QCD motivated fits to spin data 20
II. Spin Structure Functions and Parton Distributions 3
VI. Theoretical Understanding 22
III. Experiments 5
A. SLAC experiments 6 VII. Transverse Nucleon Structure and Orbital Angular
B. CERN experiments 7 Momentum 25
1. The EMC and SMC experiments 7 A. Generalized parton distributions 26
2. The COMPASS experiment 7 1. Deeply virtual Compton scattering 27
C. The HERMES experiment at DESY 8 2. The quest for orbital angular momentum and
D. JLab experiments 9 GPD parametrizations 29
E. Hadronic scattering experiments 10 B. Transversity, transverse-momentum-dependent
1. The Relativistic Heavy Ion Collider 10 distributions and fragmentation functions 30
2. RHIC as a polarized p + p collider 10 1. The Sivers and Boer-Mulders TMD distributions 32
3. RHIC experiments 11 2. The Collins TMD fragmentation function 34
3. Probing transversity 34
IV. The Proton Spin Puzzle 12 4. Current status and recent progress with TMD
A. Spin sum-rules 14 distributions 35
B. Proton spin puzzles 15 5. Proton-proton asymmetries and
C. Spin and the singlet axial-charge 15 TMD-factorization breaking 36

VIII. Future Projects 36

∗
IX. Conclusions and Outlook 37
caidala@umich.edu
† Steven.Bass@uibk.ac.at
‡
Acknowledgments 38
Delia.Hasch@lnf.infn.it
§ Gerhard.Mallot@cern.ch References 39
I. INTRODUCTION clusion of quark motion, quark spin contributes 100%
of the proton’s spin. Relativistic quark models without
There has been a vigorous and global program of ex- gluonic or pion cloud degrees of freedom generally pre-
periments and theoretical developments in the last 25 dict about 60% of the proton’s spin should be carried
years aimed at understanding the internal spin structure by the quarks, with the remaining 40% in quark orbital
of the proton. How is the proton’s spin built up from angular momentum. Today data and theory point to a
the spin and orbital angular momentum of the quarks consistent picture where the proton spin puzzle is a va-
(0)
and gluons inside? Tremendous progress has been made lence quark effect. Valence quark contributions to gA
with unraveling the proton’s spin structure with advances approximately saturate the measured value. While po-
in experimental techniques, theoretical models, pertur- larized glue may contribute a significant fraction of the
bative QCD, non-perturbative QCD and lattice calcula- proton’s spin (perhaps up to 50% at the scale of present
tions. experiments), sea quark and QCD gluon corrections to
This activity was inspired by the initial European the singlet axial-charge are small and within the expecta-
Muon Collaboration (EMC) data which suggested the tions of quark models. The pion cloud of the nucleon acts
puzzling result that quark intrinsic spin contributes little to shift angular momentum from spin to orbital angular
to the proton’s spin (Ashman et al., 1988). Today there momentum and induces SU(3) breaking in the nucleon’s
is good convergence of the theoretical and experimen- axial-charges. There is also a fascinating theoretical pos-
tal understanding the proton’s longitudinal spin struc- sibility that the valence quarks may polarize the QCD
ture. Further puzzling data in measurements of trans- vacuum in a nucleon through gluon topological effects so
verse single-spin asymmetries revealed up to 40% asym- that some fraction of the proton’s singlet axial-charge re-
metries in proton-proton collisions (and 5–10% in lepton- sides at zero parton momentum (or Bjorken x). Non-zero
nucleon collisions with unpolarized leptons and trans- orbital angular momentum of the valence quarks is ex-
versely polarized nucleons) which persist to high energies. pected, induced also by confinement which introduces a
These single-spin asymmetries indicate significant spin- transverse scale in the physics. This orbital angular mo-
orbit coupling in the nucleon associated with quark trans- mentum through spin-orbit coupling is a prime candidate
verse momentum and the bound state structure of the nu- to explain the large single spin asymmetries observed in
cleon. The study of transverse momentum and associated proton-proton collisions. Information about quark total
orbital angular-momentum processes has spawned new angular momentum in the proton can be extracted from
programs to map out the three-dimensional structure of deeply virtual Compton scattering and high-energy sin-
the nucleon. In this article we review these developments gle spin asymmetry data in model-dependent analyses.
highlighting the considerable and exciting developments The results are consistent with QCD lattice calculations.
in QCD spin physics in recent years, together with an This Review is organized as follows. In the first part
outlook to the future: What are the main open questions (Sections II–III) we give a brief introduction to nucleon
and the planned experiments to help answer them? spin physics and the experiments that have been per-
In 1988 EMC published their polarized deep inelastic formed to investigate it. Then, in Section IV, we discuss
(0)
measurement of the proton’s g1 spin dependent structure the proton spin puzzle and the small value of gA ex-
(0)
function and the flavor-singlet axial-charge gA (the nu- tracted from polarized deep inelastic scattering. In Sec-
cleon’s “quark spin content”) suggesting that quark spins tion V we give an overview of the present global pro-
summed over up, down and strange quark flavors con- gram aimed at disentangling the spin-flavor structure of
tribute only a small fraction of the proton’s spin. This the proton. Section VI covers the theoretical interpreta-
result inspired considerable theoretical activity and new tion of longitudinal spin data and understanding of the
experiments at CERN, SLAC, DESY, Jefferson Labo- proton spin puzzle. We next turn our attention to the
ratory (JLab) and the Relativistic Heavy Ion Collider transverse structure of the nucleon and manifestations
(RHIC) at Brookhaven National Laboratory (BNL) to of orbital angular momentum in the nucleon in Section
understand the spin structure of the nucleon. The first VII. This discussion introduces generalized parton dis-
task was to check the initial curious result from EMC and tributions (GPDs), which describe hard exclusive reac-
second to resolve the spin-flavor structure of the proton. tion processes, and transverse momentum dependent dis-
How is the spin content of the proton distributed among tributions (TMDs), which describe spin-momentum cor-
the valence and sea quarks and gluons? What about or- relations and spin-orbit couplings in the nucleon. The
bital angular momentum in the nucleon? TMDs are manifest in high-energy single-spin and az-
We now know that the nucleon’s flavor-singlet axial- imuthal asymmetries. A summary of key issues and chal-
charge measured in polarized deep inelastic scattering is lenging questions for the next generation of experiments
(0) is given in Section VIII and IX.
gA ∼ 0.35. This value was surprising from the view-
point of early quark models. In the static quark model Earlier review articles on the spin structure of
– the eightfold way picture of Gell-Mann – before in- the proton as well as complementary more recent

2
reviews, each with a different emphasis, are given functions g1 and g2 are defined through the imaginary
in Anselmino et al. (1995), Ellis and Karliner (1995), part of the forward Compton scattering amplitude. The
Cheng (1996), Altarelli et al. (1998), Shore (1998), structure functions contain all of the target-dependent
Lampe and Reya (2000), Filippone and Ji (2001), Jaffe information in the deep inelastic process. Consider the
(2001), Bass (2005), Kuhn et al. (2009), Barone et al. amplitude for forward scattering of a photon carrying
(2010a), Burkardt et al. (2010), Myhrer and Thomas momentum qµ (q 2 = −Q2 ≤ 0) from a polarized nucleon
(2010) and the monograph Bass (2007b). with momentum pµ , mass M and spin sµ . We work with
the kinematic Bjorken variable x = Q2 /2p · q = Q2 /2M ν
where ν = p · q/M = E − E ′ , and let y = p · q/p · k = ν/E.
II. SPIN STRUCTURE FUNCTIONS AND PARTON For a longitudinally polarized proton target (with spin
DISTRIBUTIONS denoted ⇑⇓) the unpolarized and polarized differential
cross-sections are
Our knowledge about the high-energy spin structure
d2 σ ↑⇓ d2 σ ↑⇑
of the nucleon comes from both polarized deep inelastic + =
scattering (DIS) experiments and high-energy polarized dxdy dxdy
  
proton-proton collisions. Polarized deep inelastic scat- 2πα2 M xy 2 2 2
1−y− F2 (x, Q ) + xy F1 (x, Q )
tering (pDIS) experiments involve scattering a longitu- M Ex2 y 2 2E
dinally polarized high-energy lepton beam from a longi- (1)
tudinally or transversely polarized nucleon at large mo-
mentum transfer. Inclusive measurements, where only and
the scattered lepton is observed in the final state, and
d2 σ ↑⇓ d2 σ ↑⇑
semi-inclusive measurements, where one tags on at least − =
one high-energy final state hadron in coincidence with the dxdy dxdy
  
scattered lepton, have been performed. The experiments 4α2 M xy 2 2M x 2
2−y− g1 (x, Q ) − g2 (x, Q )
were performed with an electron beam at SLAC and M Exy E E
JLAB, with electron and positron beams at DESY and (2)
with muon beams at CERN. In proton-proton scattering
the protons are either longitudinally or transversely po- where the mass of the lepton is neglected. The relation
larized. Polarized deep inelastic scattering experiments between the structure functions in deep inelastic lepton-
have so far all been performed using a fixed target. A fu- nucleon scattering and the virtual-photon nucleon cross-
ture polarized electron-ion collider is in planning. Details sections is discussed and derived in various textbooks,
of the experiments are given in Section III. Historically, e.g. Roberts (1990). One finds
information about the proton’s internal spin structure 2
came first from measuring the proton’s g1 and g2 spin σ 12 − σ 32 g1 − Q
ν 2 g2 g1
structure functions in inclusive deep inelastic scattering A1 = = → (3)
σ 12 + σ 32 F1 F1
and, more recently, from semi-inclusive reactions in both
lepton-nucleon and proton-proton collisions and hard ex- where σ 23 and σ 12 are the cross-sections for the absorption
clusive processes in lepton-nucleon scattering. of a transversely polarized photon with spin polarized
Measurements with longitudinally polarized targets parallel and anti-parallel to the spin of the longitudinally
and beams tell us about the helicity distributions of polarized nucleon. For a longitudinal polarized target the
quarks and gluons in the nucleon, which at leading or- g2 contribution to the differential cross-section and the
der can be thought of as the difference in probability of longitudinal spin asymmetry is suppressed relative to the
finding a parton with longitudinal polarization parallel g1 contribution by the kinematic factor M/E ≪ 1. For
or anti-parallel to that of the nucleon. Measurements a transverse polarized target this kinematic suppression
with transversely polarized targets are particularly sen- factor for g2 is missing implying that transverse polariza-
sitive to quark and gluon transverse and orbital angular tion is vital to measure g2 . We refer to Roberts (1990)
momentum. Studies of transverse degrees of freedom in and Windmolders (2002) for the procedure how the spin
the nucleon and in fragmentation processes are a current dependent structure functions are extracted from the
subject of experimental investigation with sensitivity to spin asymmetries measured in polarized deep inelastic
spin-orbit couplings in QCD. scattering.
For polarized lepton-proton scattering, specialize to In high-Q2 deep inelastic scattering the structure func-
the target rest frame and let E denote the energy of the tions F1 , F2 , g1 and g2 exhibit approximate scaling. They
incident lepton which is scattered through an angle θ to are to a very good approximation independent of Q2 and
emerge in the final state with energy E ′ . Let ↑↓ de- depend only on Bjorken x. (The small Q2 dependence
note the longitudinal polarization of the lepton beam. In which is present in these structure functions is logarith-
photon-nucleon scattering the spin dependent structure mic and determined by perturbative QCD evolution.)

3
 In the (pre-QCD) parton model the deep inelastic spin-dependent gluon distribution under Q2 evolution
structure functions F1 and F2 are written as (Altarelli and Parisi, 1977). This spin dependent gluon
distribution measures the momentum and spin depen-
1 1X 2
F1 (x) = F2 (x) = e {q + q̄}(x) (4) dence of glue in the proton. The second spin structure
2x 2 q q
function g2 vanishes without the effect of quark trans-
verse momentum and has a non-trivial parton interpre-
and the polarized structure function g1 is
tation (Jaffe, 1990; Roberts, 1990).
1X 2 The parton model description of polarized deep inelas-
g1 (x) = e ∆q(x). (5)
2 q q tic scattering involves writing the deep inelastic structure
functions as the sum over the convolution of “soft” quark
Here eq denotes the electric charge of the struck quark and gluon parton distributions with “hard” photon-
and parton scattering coefficients
( )
{q + q̄}(x) = (q ↑ + q ↑ )(x) + (q ↓ + q ↓ )(x) 1 1
g1p (x) = (∆u − ∆d) + (∆u + ∆d − 2∆s) ⊗ Cns q
∆q(x) = (q ↑ + q ↑ )(x) − (q ↓ + q ↓ )(x) (6) 12 36
( )
denote the spin-independent (unpolarized) and spin- 1 q g
+ (∆u + ∆d + ∆s) ⊗ Cs + f ∆g ⊗ C .
dependent quark parton distributions which measure the 9
distribution of quark momentum and spin in the proton.
(8)
For example, q ↑ (x) is interpreted as the probability to
find an anti-quark of flavor q with plus component of Here ∆q(x) and ∆g(x) denote the polarized quark and
momentum xp+ (p+ = p0 + p3 is the plus component gluon parton distributions, C q and C g denote the corre-
of the target proton’s momentum) and spin polarized sponding hard-scattering coefficients, and f is the num-
in the same direction as the spin of the target proton. ber of quark flavors liberated into the final state (f = 3
When we integrateR 1 out the momentum fraction x the below the charm production threshold). The parton dis-
quantity ∆q = 0 dx ∆q(x) is interpreted as the frac- tributions contain all the target-dependent information
tion of the proton’s spin which is carried by quarks (and and describe a flux of quark and gluon partons into the
anti-quarks) of flavor q. Hence summing over the up, (target independent) interaction between the hard pho-
down and strange quark ∆q contributions gives the total ton and the parton which is described by the coefficients
fraction of the proton’s spin carried by the spins of these C q and C g . These coefficients are calculated using per-
quarks. turbative QCD via the cross-section for the hard photon
What values should we expect for the ∆q? First, con- scattering from a quark or gluon parton “target”. They
sider the static quark model. The simple SU(6) proton are independent of infra-red mass singularities (terms in-
wavefunction volving the quark mass or virtuality of the parton in the
1 1 photon-parton collision) which are absorbed into the par-
|p ↑i = √ |u ↑ (ud)S=0 i + √ |u ↑ (ud)S=1 i ton distributions (and softened by confinement related
2 18
physics). If the same recipe (“factorization scheme”) for
1 1
− |u ↓ (ud)S=1 i − |d ↑ (uu)S=1 i separating hard and soft parts of the parton phase space
3
√ 3
is applied consistently to all hard processes then the fac-
2 torization theorem asserts that the parton distributions
+ |d ↓ (uu)S=1 i (7)
3 that one extracts from different experiments are process
yields the values ∆u − ∆d = 35 and ∆u + ∆d = 1. In rel- independent. In other words, the same polarized quark
ativistic quark models one has to take and gluon distributions should be obtained from experi-
 into
 account the
f
ments involving polarized hard QCD processes in polar-
four-component Dirac spinor ψ ∼ iσ·r̂g . The lower ized proton-proton collisions and polarized deep inelastic
component of the Dirac spinor is p-wave with intrinsic scattering experiments. For example, colliding longitudi-
spin primarily pointing in the opposite direction to the nally polarized proton beams provides sensitivity to the
spin of the proton (Jaffe and Manohar, 1990). Relativis- gluon-helicity distribution function at leading order. For
tic effects renormalize the axial charges by the depolar- hadron production with transverse momentum pT , the
ization factor 0.65 with a net transfer of angular momen- helicity-dependent difference in hadron production is de-
tum from intrinsic spin to orbital angular momentum. In fined as
QCD and in more sophisticated models further depolar-  
d∆σ 1 dσ ++ dσ +−
ization is induced by gluonic and pion-cloud degrees of ≡ − (9)
dpT 2 dpT dpT
freedom – see Section VI.
In QCD the flavor-singlet combination of the where the superscripts ++ and +− refer to same and
∆q(x) quark parton distributions mixes with the opposite helicity combinations of the colliding protons.

4
Factorization allows this to be written as a convolution boosts commute and a series of boosts and rotations can
of the long- and short-distance terms summed over all convert a longitudinally polarized nucleon into a trans-
possible flavors for the partonic interaction a + b → jet + versely polarized nucleon at infinite momentum. The
X difference between the transversity and helicity distribu-
d∆σ XZ tions reflects the relativistic character of quark motion in
= dxa dxb ∆fa (xa , µ)∆fb (xb , µ) the nucleon.
dpT
ab
Following the discovery that the quark spin contribu-
d∆σ̂ ab→jet+X tion to the proton’s spin is small, there has been a vig-
× (xa Pa , xb Pb , µ).
dpT orous program to measure the separate contributions of
(10) up, down and strange quark flavors as well as the gluon
spin and the orbital contributions. This has inspired
Here Pa and Pb denote the momenta of the incident pro- dedicated spin programs in semi-inclusive deep inelas-
tons; ∆fa (xa , µ) are the polarized parton distributions tic scattering (SIDIS) and polarized proton-proton col-
of the colliding partons carrying light-cone momentum lisions to measure the separate valence and sea quark
fraction x evaluated at factorization and renormalization as well as gluon polarization. As efforts to investigate
scale µ. The helicity-dependent difference in the cross- nucleon spin in more detail intensified and various ex-
section of the hard partonic scattering a + b → jet + X is perimental programs were being developed in the 1990s,
denoted by d∆σ̂ and is calculable in perturbative QCD. new theoretical ideas arose as well. TMD distributions,
Partonic cross-section calculations are carried out to fi- describing spin-momentum correlations in the nucleon,
nite order in αs and have a dependence on factoriza- were initially proposed (Sivers, 1990) to explain the very
tion and renormalization scales, denoted µ. The final large transverse single spin asymmetries involved in po-
hadronic cross-section is independent of the factorization larized hadronic scattering that were first observed in the
and renormalization scales and the scheme used. The 1970s by Klem et al. (1976) and Dragoset et al. (1978).
QCD parton model treatment readily generalizes to the The GPDs introduced in Mueller et al. (1994), Ji (1997b)
production of high-energy hadrons in the final state, with and Radyushkin (1997) to describe hard exclusive reac-
the produced “fast” hadron carrying a significant fraction tions provided for the first time a means of describing
of the momentum of a “parent” parton. The parton-to- the radial position distributions of partons at a specific
hadron process is parametrized by fragmentation func- longitudinal momentum within the nucleon. Both TMD
tions which also obey process-independent factorization distributions and GPDs offer links to the orbital angu-
in perturbative QCD calculations. lar momentum contributions to the nucleon’s spin. These
Analogous to the helicity distributions measured with processes and the present status of experimental and the-
longitudinal polarization, transversity distributions de- oretical investigation are described in Section VII.
scribe the density of transversely polarized quarks inside
a transversely polarized proton, see e.g. Barone et al.
(2002). The transversity distributions, which were in-
troduced in Ralston and Soper (1979), Artru and Mekhfi III. EXPERIMENTS
(1990), Jaffe and Ji (1992) and Cortes et al. (1992), are
interpreted in parton language as follows. Consider a Experiments that have probed the nucleon spin struc-
nucleon moving with (infinite) momentum in the ê3 - ture are outlined in Table I. This includes both polar-
direction, but polarized transverse to ê3 . Then δq(x) ized deep inelastic lepton-nucleon scattering and proton-
(also denoted ∆T q(x) and hq1 (x) in the literature) counts proton collision experiments. Considerable effort was in-
the quarks with flavor q, momentum fraction x and their vested in developing polarized beam and target technol-
spin parallel to the spin of a nucleon minus the num- ogy, yielding physics results with ever increasing preci-
ber anti-parallel. That is, in analogy with Eq. (6), δq(x) sion. The first experiments focused on inclusive deep
measures the distribution of partons with transverse po- inelastic measurements of nucleon spin structure. More
larization in a transversely polarized nucleon, viz. recent experiments, described in detail below, were able
δq(x) = q ↑ (x) + q̄ ↑ (x) − q ↓ (x) − q̄ ↓ (x). (11) to detect and identify hadrons in the final state lead-
ing to new probes of the nucleon in semi-inclusive and
In a helicity basis transversity corresponds to helicity-flip hard exclusive reactions. Future experimental programs
making it a probe of chiral symmetry breaking (Collins, (COMPASS-II, the 12 GeV upgrade of JLab and experi-
1993). There is no gluon analogue of transversity in ments at Fermilab and RHIC) with high luminosity and
the nucleon so δq evolves in Q2 like a valence or non- acceptance are planned to explore the three-dimensional
singlet quark distribution, without mixing with glue. structure of the nucleon in spatial and transverse mo-
If quarks moved non-relativistically in the nucleon δq mentum degrees of freedom. We discuss these future
and ∆q would be identical since rotations and Euclidean programs in Section VIII.

5
TABLE I High energy spin experiments: the kinematic ranges in x and Q2 correspond to the average kinematic values of the
highest statistics measurement of each experiment, which is typically the inclusive spin asymmetry; x denotes Bjorken x unless
specified.

Experiment Year
Beam Target Energy (GeV) Q2 (GeV2 ) x
Completed experiments
SLAC – E80, E130 1976–1983 e− H-butanol <23 1–10 0.1–0.6
∼
SLAC – E142/3 1992–1993 e −
NH3 , ND3 < 30 1–10 0.03–0.8
∼
SLAC – E154/5 1995–1999 e− NH3 , 6 LiD, 3 He < 50 1–35 0.01–0.8
∼
+
CERN – EMC 1985 µ NH3 100, 190 1–30 0.01–0.5
CERN – SMC 1992–1996 µ+ H/D-butanol, NH3 100, 190 1–60 0.004–0.5
FNAL E581/E704 1988–1997 p p 200 ∼1 0.1 < xF < 0.8
Analyzing and/or Running
DESY – HERMES 1995–2007 e+ , e− H, D, 3 He ∼ 30 1–15 0.02–0.7
+
CERN – COMPASS 2002–2012 µ NH3 , 6 LiD 160, 200 1–70 0.003–0.6
JLab6 – Hall A 1999–2012 e− 3
He <6 1–2.5 0.1–0.6
∼
JLab6 – Hall B 1999–2012 e −
NH3 , ND3 <6 1.-5 0.05–0.6
∼
RHIC – BRAHMS 2002–2006 p p (beam) 2× (31–100) ∼ 1–6 −0.6 < xF < 0.6
RHIC – PHENIX, STAR 2002+ p p (beam) 2× (31–250) ∼ 1–400 ∼ 0.02–0.4
Approved future experiments (in preparation)
CERN – COMPASS–II 2014+ µ+ , µ− unpolarized H2 160 ∼ 1–15 ∼ 0.005–0.2
π− NH3 190 −0.2 < xF < 0.8
JLab12 – HallA/B/C 2014+ e− HD, NH3 , ND3 , 3 He <12 ∼ 1–10 ∼ 0.05–0.8
∼

A. SLAC experiments namic nuclear polarization, which requires temperatures

of about 1 K and strong magnetic holding fields. Such
SLAC experiments pioneered polarized DIS measure- targets contain a considerable amount of non-polarizable
ments and set many standards in polarized beam and nucleons, which is parametrized by the so-called dilution
target technologies. Their spin program focused on factor. This factor depends on all kinematic variables rel-
high statistics measurements of the inclusive asymme- evant for the process under study and needs, in principle,
tries. The first measurements of the proton spin structure to be determined for each type of measurement. Typi-
were performed by the experiments E80 (Alguard et al., cal values for polarized solid state targets range between
1976, 1978) and E130 (Baum et al., 1980, 1983), fol- 0.1 and 0.2 with the exception of 6 LiD (0.4-0.5) and rep-
lowed by a series of high precision experiments E142 resent an important factor in the extraction of physical
(Anthony et al., 1996), E143 (Abe et al., 1998), E154 observables from the measured ones. Information on the
(Abe et al., 1997) and E155 (Anthony et al., 1999, 2000) neutron structure was obtained either from the combina-
a decade later. These experiments utilized polarized elec- tion of measurements with proton and deuteron targets
trons which were produced by laser photoemission and or by using a polarized 3 He target which is dominated by
subsequently accelerated. The longitudinal polarization the neutron since the two proton spins in 3 He are anti-
of the beam was frequently inverted and the polarization aligned. Here, polarization was obtained from optical
measured using Møller scattering. A rapid cycling of the pumping and adiabatic spin exchange. The target polar-
beam and/or target polarization reduces systematic un- ization was measured using the NMR technique. Scat-
certainties in the measured spin asymmetries related to tered electrons were detected with magnetic spectrome-
the stability of the experimental setup. Polarized tar- ters optimized for high-momentum-resolution and good
get materials involved solid-state butanol and ammonia electron identification.
(NH3 ) for the proton and D-butanol, ND3 as well as 6 LiD
for the deuteron (Crabb and Meyer, 1997; Meyer, 2004).
For the most recent E154 and E155 experiments the tar-
get polarization was typically 38% for 3 He, 90% for NH3
and 22% for LiD with beam polarization about 80%. The
target material, doped with a paramagnetic substance or
irradiated with electron beams, was polarized using dy-

6
B. CERN experiments on a solid-state polarized target consisting of two or three
cells with proton or deuteron target material polarized in
1. The EMC and SMC experiments opposite directions. The usable beam intensity is typi-
cally 2 × 107 /s during a 9.6 s long spill. The repetition
Following the early measurements at SLAC, the Euro- rate varies and is typically about 1/40 s. The muon po-
pean Muon Collaboration (EMC) experiment performed larization arises naturally from the weak decay of the
at CERN in 1985 the first polarized DIS measurements at parent pions produced by the primary proton beam of
x < 0.1 down to x = 0.01 after a series of measurements 400 GeV. The momentum of each beam muon is mea-
of unpolarized nucleon and nuclear structure functions. sured in the beam momentum station. Downstream of
The experiment used the polarized CERN muon beam up the target, the scattered muon and produced hadrons
to momenta of 200 GeV and a solid-state irradiated am- are detected in a two-stage magnetic spectrometer with
monia target. Their low-x measurements, accessible due the two dipole magnets (SM1, SM2).
to the high energy of the muons, suggested the break- Charged particles are tracked in the beam regions by
down of the naive parton picture that quarks provide scintillating fiber stations (SciFi) and by silicon detec-
essentially all of the spin of the nucleon (Ashman et al., tors. In the inner region close to the beam, gaseous detec-
1988, 1989). tors of the micromegas and gas-electron-multiplier (Gem)
This triggered more detailed and precise measurements types with high rate capabilities are deployed. The back-
by the Spin Muon Collaboration (SMC) in 1992–1996, bone of tracking in the intermediate region is multiwire
and by COMPASS (since 2002). The beam line and proportional chambers (MWPCs). Finally, the large area
the principal ideas of the CERN muon experiments are tracking away from the beam region is covered by drift
described in the COMPASS Section III.B.2. The EMC chambers (DC, W45) and drift tubes (Straws, RW, MW).
Spectrometer is described in Aubert et al. (1981). The The velocity of charged particles is measured in a ring-
polarization of the CERN muon beam was measured by imaging Cherenkov detector (RICH), which can separate
SMC Adeva et al. (1994b). A detailed description of the pions and kaons from 9 GeV up to 50 GeV. The inner
SMC deuteron target polarization is given in Adeva et al. quarter of the photon detector is made of multianode-
(1994a). The COMPASS experiment used the SMC tar- photomultiplier tubes, while the outer part relies on MW-
get in the initial period of data taking up to 2005 as PCs with a photosensitive CsI cathode.
reported in Ball et al. (2003). A new target is used since The energy of charged particles is measured in sam-
2006 (Gautheron, 2007). pling hadron calorimeters (HCAL), while neutral par-
After 1987 the focus was on the region x < 0.1 and ticles, in particular high-energy photons, are detected
the flavor-singlet axial-charge (Ellis–Jaffe sum-rule) for in electromagnetic calorimeters (ECAL). They comprise
the neutron. The latter must deviate from the naive pre- lead glass modules as well as scintillator/lead “shashlik”
diction in a similar way as for the proton in order to modules in the inner high-radiation region.
preserve the fundamental isovector Bjorken sum-rule for Event recording is triggered by the scattered muon,
g1p −g1n . (These sum-rules are discussed below.) The SMC which is “identified” by its ability to traverse thick
experiment could extend the measured x-range down to hadron absorbers, located just upstream of the Muon
x = 0.004 (for Q2 > 1 GeV2 ) and established the va- Wall detectors (MW). The event selection is based on
lidity of the Bjorken sum-rule with measurements using various systems of scintillator hodoscopes and logic mod-
polarized proton (butanol and ammonia) and deuteron
(D-butanol) targets (Adeva et al., 1993, 1998b). The
MW2, MWPC
large acceptance of the SMC spectrometer in the for-
Length: 60 m
ward direction allowed them to present the first deter- Hodoscopes
mination of individual quark distributions for different
flavors (Adeva et al., 1996, 1998a) from semi-inclusive SM2
DIS. A dedicated polarimeter confirmed the validity of E/HCAL1
RICH
the beam polarization obtained from Monte Carlo simu- E/HCAL2
lations (Adams et al., 2000; Adeva et al., 1994b) used in SM1
the EMC, SMC and COMPASS analyses. Polarized
Target MWPC, Gems, Scifi,
W45
MW1
2. The COMPASS experiment RW
Straws, Gems
Micromegas, DC, Scifi
The COMPASS spectrometer (Abbon et al. (2007), μ beam Scifi, Silicon
Fig. 1) is installed at the muon beam line of the CERN
SPS accelerator. A polarized muon beam of energy 160–
200 GeV and with a polarization of about 80% impinges FIG. 1 The Compass spectrometer, for a description see text.

7
ules applying selection criteria like target pointing and (E’, k’)
energy loss in the scattering. The patterns causing a
trigger were optimized by Monte Carlo simulations. The
spectrometer has about 250k read-out channels, which
(E, k) θ
e
can be recorded with a frequency of 20 kHz for an event µ
size of the order of 40 kByte. (ν, q)
The heart of the experiment is the polarized target sys- γ*
tem. While the muon beam comes naturally polarized p
due to the parity violation in the decay of the parent u
pions, polarizing protons and deuterons is very difficult. d π
Gas targets can not be used with the muon beam due u
to the low beam intensity compared to electron beams. N π
An advantage of muon beams is the high muon energy,
which presently can not be reached by electron beams.
The polarized target system comprises a 2.5 T solenoid +
magnet, a 0.6 T dipole magnet, a 3 He/4 He dilution refrig- π
erator, a 70 GHz microwave system and an NMR system
to measure the target polarization. The target material FIG. 2 Semi-inclusive DIS studied at COMPASS, HERMES
is cooled down to about 60 mK in frozen spin mode. The and JLab.
nucleons/nuclei are polarized by dynamic nuclear polar-
ization which only is applicable for particular materials.
In COMPASS irradiated ammonia (NH3 ) and lithium-6 and scattered lepton. The years 2008–2009 were dedi-
deuteride (6 LiD) were selected as proton and deuteron cated to the hadron spectroscopy program of COMPASS
targets, respectively. Lithium-6 is very close to a system with pion, kaon and proton beams. In 2012 the pion po-
of a free deuteron and a helium-4 core and has essen- larizability is being measured using a negative pion beam
tially the same magnetic moment as the deuteron. Thus and a thin nickel target. A pilot run for deeply virtual
6 Compton scattering and hard exclusive meson produc-
LiD corresponds to two deuterons plus a helium nucleus.
Typically, polarizations of 85% for protons and 50% for tion has been successfully completed in 2012.
deuterons were reached. A key feature of COMPASS is
that both target polarizations are present simultaneously
in separate target cells along the beam, e.g. “→, ←” for C. The HERMES experiment at DESY
the two-cell configuration until 2004 and “→, ←, →” for
the three-cell configuration from 2006 onward. In the The HERMES experiment employed an innovative
former configuration the length of the cells was twice technique for the polarized target, which is very different
60 cm while in the latter it was 30 cm, 60 cm, 30 cm, from all other polarized DIS experiments. Gas targets of
respectively. Thus in an asymmetry measurement most pure nuclear-polarized atoms of hydrogen or deuterium
systematic uncertainties cancel. Using the dipole and were used, which permit essentially background-free mea-
solenoid magnet, the magnetic field can be rotated from surements from highly polarized nucleons with little or
e.g. pointing downstream to transverse to upstream. The no dilution of the signal from unpolarized nucleons in
spin follows the magnetic field adiabatically and thus the the target. This choice eliminates one of the main sys-
spin orientations can be changed within 30 min. Such tematic sources in polarized DIS, the uncertainty in the
a field rotation is performed typically once per day for determination of the dilution factor.
the longitudinal polarization in order to cancel poten- The HERMES gas targets were highly longitudinally
tially remaining systematic effects. The field can also be (∼ 85%) or transversely (75%) polarized with the abil-
kept transverse for measurements with transverse target ity to invert the direction of the spin of the nucleons
polarization. Here the polarization is inverted by repo- within milliseconds. Due to the low densities, however,
larizing typically once per week. In the shutdown year such targets are only practicable in the high currents
2005 the superconducting target magnet was replaced of storage rings. HERMES was operating from 1995
by a new one, increasing the angular acceptance from to 2007 at the HERA lepton storage ring, which pro-
±70 mrad to ±180 mrad. vided electron or positron beams of typically 40 mA
The experiment is taking data since 2002. The main and with an energy of 27.5 GeV. In order to enhance
focus has been on inclusive and semi-inclusive polarized the target density, the novel technique of a storage cell
deep inelastic scattering. As schematically depicted in was used (Airapetian et al., 2004b; Baumgarten et al.,
Fig. 2, the detection of a hadron in the final state provides 2003a,c, 2002). Here, the gas was fed into a T-shaped
information about the flavor of the struck quark, while open-ended elliptical cell coaxial to the lepton beam. The
the kinematics of the DIS event is fixed by the incoming gas atoms underwent several hundred wall bounces be-

8
fore escaping from the ends where they were differentially a ring-imaging Cherenkov provided lepton identification
pumped away by a large system of turbo-pumps. This with very high efficiency and purity better than 99% as
increased the density by a factor of about 100 compared well as pion, kaon and proton separation over almost the
to free gas jet targets. whole momentum range of 2–15 GeV. All components
The polarized atoms were injected into the cell from an are described in detail in Ackerstaff et al. (1999a).
atomic beam source based on Stern-Gerlach polarization A recoil detector was installed in the target region for
filtering and radio-frequency transitions between atomic the last 1.5 years of HERMES data taking with unpolar-
substates in a magnetic field (Airapetian et al., 2005c). ized hydrogen and deuterium targets in order to enhance
A small sample gas diffused from the middle of the cell access to hard exclusive processes, in particular to deeply
into a Breit-Rabi polarimeter which measured the atomic virtual Compton scattering.
polarization (Baumgarten et al., 2002), or into a target
gas analyzer which measured the atomic and the molec-
ular content of the sample (Baumgarten et al., 2003b). D. JLab experiments
A magnet surrounding the storage cell provided a hold-
ing field defining the polarization axis and prevented spin Experiments at Jefferson Lab utilized the highest po-
relaxation via spin exchange or wall collisions. The cell larization electron beams (85%) with energy ranging
temperature was kept at about 100 K, the value for which from 0.8 GeV close to 6 GeV. The technologies of polar-
atomic recombination and spin relaxation during wall col- izing beam and target follow those pioneered and further
lisions are minimal. developed at SLAC.
Stored high energy electron beams may become spon- The beam was provided by the Continuous Electron
taneously transversely polarized via a small polariza- Beam Accelerator Facility (CEBAF) (Leemann et al.,
tion asymmetry in the emission of synchrotron radi- 2001), which used polarized electron guns based on a
ation by the beam particles as they are deflected by “superlattice” of a thin gallium arsenide (GaAs) layer
the magnetic fields of the ring (Sokolov-Ternov ef- on top of GaAs-phosphide bulk matter illuminated by
fect) (Sokolov and Ternov, 1964). The beam polariza- circularly polarized photons from high intensity lasers
tion grows and approaches asymptotically an equilibrium (Sinclair et al., 2007; Stutzman et al., 2007). Subse-
value with a time constant depending on the characteris- quently, the polarized electrons passed up to five times
tics of the ring, for HERA typically 1/2 hour. Polariza- the two linear accelerators based on superconducting ra-
tions as large as 60% were achieved. Spin rotators and dio frequency technology and connected by two recircula-
polarimeters were essential components of the HERA lep- tion arcs. The spin direction of the electrons was manip-
ton beam (Barber et al., 1994, 1993; Beckmann et al., ulated using the crossed electric and magnetic fields of
2002; Buon and Steffen, 1986). Spin rotators in front of Wien filters, which allow for rapid spin rotation. Their
and behind the experiment provided longitudinal polar- direction was inverted every about 30 ms. Beam po-
ization at the interaction point and at one of the two larimetry was employed at several stages of the accel-
beam polarimeters. The two beam polarimeters were eration process. CEBAF delivered polarized beams si-
based on Compton back-scattering of circularly polarized multaneously to the three experimental halls (Hall A, B
laser light. They continuously monitored the transverse and C) with the option to independently dial the energy
and longitudinal polarization of the lepton beam. and intensity. Typical beam intensities ranged from a
The HERMES spectrometer was designed to detect the few nA in Hall B to over 100 µA in the other two halls
scattered lepton and produced hadrons within a wide an- (Kazimi et al., 2004).
gular acceptance and with good momentum resolution. Longitudinal polarized solid state ammonia (NH3 ) tar-
Particular emphasis was given to the particle identifica- gets for the proton and ND3 for the deuteron were em-
tion capabilities which allowed for pion, kaon and pro- ployed at Hall B (Keith et al., 2003). These targets are
ton separation over almost the whole momentum range based on similar techniques as discussed before for the
(Akopov et al., 2002). The HERA beam lines passed SLAC and CERN experiments for both polarization and
through the non-instrumented horizontal mid-plane of polarimetry. Hall A used a polarized 3 He target. The
the spectrometer. A horizontal iron plate shielded the target polarization was measured by both the NMR tech-
beam lines from the 1.5 Tm dipole field of the spectrom- nique of adiabatic fast passage and a technique based on
eter magnet, thus dividing the spectrometer in two iden- electron paramagnetic resonance (Romalis et al., 1998).
tical halves. The geometrical acceptance of ±170 mrad Average target polarizations of about 55% were obtained.
horizontally and ±(40 − 140) mrad vertically resulted in Hall A and C were both instrumented with small accep-
detected scattering angles ranging from 40 to 220 mrad. tance but high resolution spectrometers that could cope
Tracking was provided by several stages of drift cham- with the highest beam intensities but measured at fixed
bers before and after the spectrometer magnet. The scattering angles. These spectrometers are equipped
combination of signals from a lead-glass calorimeter, a for high resolution tracking, precise time-of-flight mea-
preshower detector, a transition radiation detector and surements and lepton/hadron separation (Alcorn et al.,

9
2004). for 255 GeV beams have been achieved. The maximum
31
Hall B was instrumented with the CEBAF Large Ac- luminosities
√ achieved thus far are 5 × 10√ cm−2 s−1 at
32 −2 −1
ceptance Spectrometer (CLAS) (Mecking et al., 2003). s = 200 GeV and 2 × 10 cm s at s = 510 GeV.
The CLAS design was based on a toroidal field, generated Three experiments have studied polarized proton
by six superconducting coils arranged around the beam collisions at RHIC. There are two ongoing large
line. The six coils naturally divided the detector into six experiments, STAR (Ackermann et al., 2003) and
independent spectrometers, each of them containing a set PHENIX (Adcox et al., 2003), each of which have more
of drift chambers for tracking, a gas Cerenkov counter for than 500 collaborators total working on both the heavy
electron/pion separation, an array of scintillator counters ion and polarized proton programs, and the smaller
for particle identification using time of flight measure- BRAHMS (Adamczyk et al., 2003) experiment, with
ments, and electromagnetic calorimeters for neutral par- fewer than 100 collaborators, which took data through
ticle identification. For charged particles, CLAS covered 2006. In additional to the program of proton spin struc-
polar angles between 8◦ and 142◦ in the laboratory frame ture measurements, the transverse single-spin asymmetry
and between 60% and 80% of the azimuthal angles. in elastic proton-proton scattering has also been mea-
sured to constrain the hadronic spin-flip amplitude in
this reaction (Adamczyk et al., 2012b).
E. Hadronic scattering experiments

While deep inelastic lepton-nucleon scattering has long 2. RHIC as a polarized p + p collider
been a standard tool of the trade in the study of unpo-
larized and polarized nucleon structure, much has been RHIC is the first and only high-energy polarized
learned from polarized hadronic scattering as well. The proton-proton collider in the world. A number of techno-
first high-energy primary polarized proton beams were logical developments and advances over the past several
achieved at the Zero-Gradient Synchrotron at Argonne decades have made it possible to create a high-current
National Laboratory in 1973. Proton beams there were polarized proton source, maintain the beam polarization
initially accelerated to 6 GeV with a polarization of throughout acceleration and storage, and obtain accurate
about 60%, and shortly thereafter polarized beams up measurements of the degree of beam polarization at vari-
to 12 GeV were achieved. In the 1990s at Fermilab, sec- ous stages from the source to full-energy beams in RHIC.
ondary beams of polarized protons or antiprotons from For an overview of RHIC as a polarized-proton collider
lambda or antilambda decays opened up new kinematic see Alekseev et al. (2003). In the case of polarized-proton
regions for polarized hadronic scattering,
√ with polar- running at RHIC, a pulse of polarized H− ions from
ized beams of up to 200 GeV ( s = 19 GeV). Polar- the source is accelerated to 200 MeV in the linac, then
ized hadronic scattering experiments at center-of-mass stripped of its electrons as it is injected and captured
energies more than an order of magnitude higher were as a single bunch of polarized protons in the Booster,
achieved with the inauguration of the Relativistic Heavy which accelerates the protons to 1.5 GeV. The bunch of
Ion Collider for polarized protons in 2001. polarized protons is then transferred to the Alternating
Gradient Synchrotron (AGS) and accelerated to 24 GeV
before injection into RHIC. Each bunch is accelerated in
1. The Relativistic Heavy Ion Collider the AGS and injected into RHIC independently, with the
two RHIC rings being filled one bunch at a time. The
RHIC is located at Brookhaven National Laboratory direction of the spin vector is selected for each bunch
in New York. RHIC was built to collide heavy ions at separately. The nominal fill duration is eight hours, af-
center-of-mass energies of up to 200 GeV per colliding ter which the beams are dumped and fresh beams are
nucleon pair and polarized protons at center-of-mass en- injected into RHIC. The bunch-by-bunch spin patterns
ergies ranging from 50 to 500 GeV. Collision of asym- in consecutive fills are varied in order to reduce potential
metric species, i.e. different species in the two beams, is systematic effects.
also possible due to independent rings with independent Polarized proton injection uses an optically-pumped
steering magnets. The first polarized proton collisions polarized H− ion source (OPPIS) (Zelenski et al., 2002).
were achieved at a center-of-mass energy of 200 GeV in H− polarization at the source of 85% has been achieved.
December 2001. Siberian snakes (Derbenev et al., 1978), a series of
The RHIC storage ring is 3.83 km in circumference spin-rotating dipoles, so named because of the beam tra-
and is designed with six interaction points (IPs) at which jectory through the magnets and the fact that they were
beam collisions are possible. Up to 112 particle bunches developed at Novosibirsk in Russia, are used to overcome
per ring can be injected, in which case the time between both imperfection and intrinsic depolarizing resonances
bunch crossings at the IPs is 106 ns. Polarizations of in RHIC. There are two snakes installed in each RHIC
up to 65% for 100 GeV proton beams and about 60% ring at diametrically opposite points along the rings. The

10
two snakes in each ring rotate the spin vector 180◦ about 2012 PHENIX Detector
PC3
perpendicular horizontal axes, without perturbing the PC3 Central
Magnet TEC
PbSc PC2 PbSc
stable spin direction and with only local distortion of the
beam orbit. In this way, all additive depolarizing effects
from resonances are avoided. PbSc
DC DC
PbSc

TOF-W BBC

7.9 m = 26 ft
For RHIC to provide full-energy polarized beams, the RICH RICH
PbSc BB PbGl
polarization must be measurable at various stages of ac-
celeration in order to identify and address possible ori- MPC (F)VTX
gins of depolarization at each step. Only RHIC po-
PbSc PC1 PC1 PbGl
larimetry will be discussed here. There are two types of
polarimeters installed in RHIC. The fast proton-carbon Aerogel
TOF-E
(pC) polarimeter (Nakagawa et al., 2008) takes advan-
West Beam View East
tage of a known analyzing power, ApC N ≈ 0.01, in the RPC3 RPC3
et
elastic scattering of polarized protons with carbon atoms So
uth
Central Magnet ag
n
M nM
(p↑ + C → p↑ + C), which originates from interference uo
nM M
uo
ag rth
between electromagnetic and hadronic elastic scattering net No

amplitudes. The pC polarimeter can make measure- MPC

10.9 m = 36 ft
ments in less than ten seconds and provide immediate BBC

information on the stability or decay of the beam po- ZDC South ZDC North

larization from a few data points taken over the sev- MuID
(F)VTX
MuID

eral hours of a fill. Calibration of the pC polarimeter MuTr

to within an absolute beam polarization of less than 5%
can then be provided by measuring polarized elastic p+ p
scattering with a polarized hydrogen-jet-target polarime-
South Side View North
ter (Zelenski et al., 2005). With the hydrogen-jet-target
18.5 m = 60 ft
polarization of greater than 90% known to better than 2%
in absolute polarization (Okada et al., 2006), the abso-
lute beam polarization can be determined by exploiting FIG. 3 The PHENIX detector at RHIC as configured for data
the symmetry of the process. taking in 2012.

The naturally stable spin direction through accelera-

tion and storage in RHIC is transverse to the proton’s 3. RHIC experiments
momentum, in the vertical direction. Spin rotator dipole
magnets have been used to achieve both radial and longi- a. The PHENIX detector PHENIX was designed as a
tudinal spin (MacKay et al., 2003). The rotators are lo- large, multi-purpose experiment with fast data acquisi-
cated outside the interaction regions of the PHENIX and tion and high granularity over a limited acceptance. See
STAR experiments, giving both experiments the ability Fig. 3 for beam and side views of the PHENIX detec-
to choose independently whether they want longitudi- tor as configured for data taking in 2012. There are two
nally or transversely polarized collisions. The BRAHMS central arms with an acceptance covering a pseudora-
experiment, having no spin rotators available, focused pidity range |η| < 0.35 and ∆φ = π2 each in azimuth.
on transverse spin measurements. The local nature of the The central arms include drift and pad chambers (DC,
spin rotator magnets means that the STAR and PHENIX PC1, PC2, PC3) for momentum and position measure-
experiments must each have their own way of checking ments, a ring-imaging Cherenkov detector (RICH) pri-
the direction of the spin vector at their respective inter- marily for electron identification, small-acceptance time-
action regions. of-flight and aerogel counters (TOF-E, TOF-W, Aero-
gel) for charged hadron identification, and electromag-
Observed azimuthal transverse single spin asymmetries netic calorimetry (PbSc, PbGl). Electronics-level trig-
in the production of forward neutrons (Bazilevsky et al., gering in the central arms uses information from the
2003) and forward charged particles can be used to calorimetry and ring-imaging Cherenkov detector. There
provide local polarimetry. These asymmetries are ex- are two muon spectrometers covering a pseudorapidity
ploited by the experiments to measure the degree to of 1.2 < |η| < 2.4, consisting of tracking chambers and
which the beam polarization is vertically transverse, ra- muon identifier panels (MuTr, MuID). Resistive plate
dially transverse, or longitudinal. More information on chambers (RPC3) were added in 2011 and 2012 to im-
local polarimetry at PHENIX and STAR can be found prove triggering on high-momentum muons for W bo-
in Adare et al. (2007) and Kiryluk (2005). son measurements. Forward electromagnetic calorimetry

11
(MPC) covering 3.0 < |η| < 3.9 was added in 2006 and well as luminosity measurements, and ZDCs identical to
2007, and silicon vertex detectors ((F)VTX) for heavy those used by PHENIX and STAR.
flavor measurements over |η| < 2.4 were added in 2011
and 2012.
For luminosity measurements, identical zero-degree IV. THE PROTON SPIN PUZZLE
hadronic calorimeters (ZDC) are located in the RHIC
tunnel at ±18 m from the nominal IP for all RHIC We begin our discussion of physics results by first de-
experiments. PHENIX also uses quartz Cherenkov scribing how the small value of the “quark spin content”
(0)
beam-beam counters (BBC) positioned around the beam gA is obtained from polarized deep inelastic scattering
pipe at ±1.44 m from the nominal interaction point as and the first moment of the g1 spin structure function.
a minimum-bias trigger detector and for polarization- In QCD the first moment of g1 is determined from the
averaged as well as spin-dependent luminosity measure- dispersion relation for polarized photon-nucleon scatter-
ments. Collision rates for 500 GeV p + p running reach ing and the light-cone operator product expansion. One
∼3 MHz, and the electronics-level triggers select events finds that the first moment of g1 is related to the scale-
to reduce this rate to approximately 7 kHz of recorded invariant axial charges of the target nucleon by
data. Z 1
dx g1p (x, Q2 )
0
!
b. The STAR detector The Solenoidal Tracker at RHIC 1 (3) 1 (8) n X o
= gA + gA 1+ cNSℓ αℓs (Q)
(STAR) was designed as a large, multi-purpose detec- 12 36
ℓ≥1
tor with wide acceptance, making it well suited for cor- n X o
1 (0) 1
relation measurements. The core of STAR is a time- + gA |inv 1 + cSℓ αℓs (Q) + O( 2 ) + β∞ .
projection chamber, which covers 2π in azimuth and 9 Q
ℓ≥1
has tracking capabilities over |η| < 1.3 and good parti- (12)
cle identification for |η| < 1. There is electromagnetic
(3) (8) (0)
calorimetry for −1 < η < 2. In the forward direc- Here gA , gA and gA |inv are the isovector, SU(3)
tion, there is additional electromagnetic calorimetry for octet and scale-invariant flavor-singlet axial-charges re-
2.5 < η < 4.0. Recent upgrades include a time-of-flight spectively. The flavor non-singlet cNSℓ and singlet cSℓ
detector with 100 ps resolution for additional particle Wilson coefficients are calculable in ℓ-loop perturba-
identification, and tracking based on Gem detectors for tive QCD. These perturbative QCD coefficients have
1 < η < 2 was partially installed for 2012 data-taking been calculated to O(α3s ) precision (Larin et al., 1997).
to enable charge-sign discrimination of forward electrons For αs = 0.3 n typical of the deepoinelastic experiments
n
from W boson decays. P3
one finds 1 + ℓ=1 cNSℓ αℓs (Q) = 0.85 and 1 +
In addition to the zero-degree hadronic calorimeters P3 o
ℓ
identical among the RHIC experiments, STAR has scin- ℓ=1 c Sℓ αs (Q) = 0.96. The term β∞ represents a pos-
tillator beam-beam counters positioned around the beam sible leading-twist subtraction constant from the circle at
pipe covering 3.4 < |η| < 5.0, which provide a minimum- infinity when one closes the contour in the complex plane
bias trigger as well as spin-averaged and spin-dependent in the dispersion relation (Bass, 2005). The subtraction
luminosity measurements along with the ZDCs. constant affects just the first moment and corresponds to
a contribution at Bjorken x equal to zero.
In terms of the flavor-dependent axial-charges
c. The BRAHMS detector The BRAHMS detector was a
smaller experiment at RHIC designed for excellent mo- 2M sµ ∆q = hp, s|qγµ γ5 q|p, si (13)
mentum measurement and charged particle identification
the isovector, octet and singlet axial charges are
over a very broad range of rapidities. It consisted of two
movable spectrometer arms covering small solid angles, (3)
gA = ∆u − ∆d
the Forward Spectrometer, which could be positioned as (8)
close as 2.3◦ from the beam pipe, and the Midrapidity gA = ∆u + ∆d − 2∆s
(0) (0)
Spectrometer, which could be moved to cover an angu- gA |inv /E(αs ) ≡ gA = ∆u + ∆d + ∆s. (14)
lar range from 30◦ < θ < 95◦ . The spectrometer arms
included five dipole magnets, time-projection chambers, Here
multi-wire drift chambers, time-of-flight hodoscopes, and Z αs
threshold as well as ring-imaging Cherenkov detectors. E(αs ) = exp dα̃s γ(α̃s )/β(α̃s ) (15)
0
Global detectors consisted of a silicon array for multi-
plicity measurements, threshold Cherenkov beam-beam is a renormalization group factor which corrects for the
counters for event vertex and timing determination as (two loop) non-zero anomalous dimension γ(αs ) of the

12
singlet axial-vector current 0.08

xg p
1
EMC

¯ µ γ5 d + s̄γµ γ5 s
Jµ5 = ūγµ γ5 u + dγ (16)
SMC
E143
0.06
E155
which is close to one and which goes to one in the limit HERMES

Q2 → ∞. The  symbol βdenotes the QCD beta func- 0.04

CLAS
COMPASS
tion β(αs ) = − 11 − 23 f (α2s /2π) + ... and γ is given
0.02
by γ(αs ) = f (αs /π)2 + ... where f (=3) is the num-
ber of active flavors (Kodaira, 1980). The singlet ax-
(0) 0
ial charge, gA |inv , is independent of the renormaliza-
(0)
tion scale µ and corresponds to gA (Q2 ) evaluated in the

xg d
1
SMC
(3)
limit Q2 → ∞. The flavor non-singlet axial-charges gA E143
(8) 0.03 E155
and gA are renormalization group invariants. We are HERMES
free to choose the QCD coupling αs (µ) at either a hard CLAS
0.02
or a soft scale µ. The perturbative QCD expansion of COMPASS

E(αs ) remains close to one – even for large values of

0.01
αs . If we take αs ∼ 0.6 as typical of the infra-red then
E(αs ) ≃ 1 − 0.13 − 0.03 + ... = 0.84 + ... where −0.13 and
0
−0.03 are the O(αs ) and O(α2s ) corrections respectively.
(0)
In the naive parton model gA is interpreted as the
fraction of the proton’s spin which is carried by the in- JLAB Hall A
xg n
1
trinsic spin of its quark and anti-quark constituents. The 0.02 E142
(0)
experimental value of gA is obtained through measuring E154

g1 and combining the first moment integral in Eq.(12) 0.01 HERMES

(3) (8)
with knowledge of gA and gA from other processes plus
0
theoretical calculation of the perturbative QCD Wilson
coefficients. −0.01
The isovector axial-charge is measured independently
(3)
in neutron β-decays (gA = 1.270±0.003 (Beringer et al., −0.02
2012)) and the octet axial charge is commonly taken
−0.03
to be the value extracted from hyperon β-decays as-
(8)
suming a 2-parameter SU(3) fit (gA = 0.58 ± 0.03 10 −2 10 −1 1

(Close and Roberts, 1993)). However, it should be noted

x
(8)
the uncertainty quoted for gA has been a matter of FIG. 4 World data on xg1 as a function of x for the proton
some debate (Jaffe and Manohar, 1990; Ratcliffe, 2004). (top), the deuteron (middle) and the neutron (bottom) at the
SU(3) symmetry may be badly broken and some have Q2 of the measurement. Only data points for Q2 > 1 GeV 2
(8) and W > 2.5 GeV are shown. Error bars are statistical errors
suggested that the error on gA should be as large as
only.
25% (Jaffe and Manohar, 1990). A recent re-evaluation
of the nucleon’s axial-charges in the Cloudy Bag model
taking into account the effect of the one-gluon-exchange
hyperfine interaction and the pion cloud plus kaon loops
(8) 1999), HERMES (Airapetian et al., 2007a), JLab
led to the value gA = 0.46 ± 0.05 (Bass and Thomas, (Dharmawardane et al., 2006; Zheng et al., 2004), and
(8)
2010). The model reduction of gA from the SU(3) value COMPASS (Alekseev et al., 2010d; Alexakhin et al.,
(3)
comes primarily from the pion cloud with gA taking its 2007). There is a general consistency among all data
physical value. sets. The kinematic reach of the different experiments is
Deep inelastic measurements of g1 have been per- visible in Fig. 5. COMPASS have the smallest-x data,
formed in experiments at CERN, DESY, JLab and down to x ∼ 0.004.
SLAC. An overview of the world data on the nu- There are several striking features in the data. COM-
cleon’s g1 spin structure function is shown in Fig. 4. PASS measurements of the deuteron spin structure func-
This data is published in EMC (Ashman et al., 1989), tion g1d show the remarkable feature that g1d is consis-
SMC (Adeva et al., 1998b), E142 (Anthony et al., 1996), tent with zero in the small-x region between 0.004 and
E143 (Abe et al., 1998), E154 (Abe et al., 1997), 0.02 (Alexakhin et al., 2007). In contrast, the isovec-
E155 (Anthony et al., 2000), E155 (Anthony et al., tor part of g1 is observed to rise at small x as g1p−n ∼

13
 (This deep inelastic quantity misses any contribution to
EMC (0)
4
gp(x,Q 2)+c i

x=0.006
SMC
gA |inv from a possible delta function at x = 0). When
(8) (0)
E143 combined with gA = 0.58 ± 0.03, the value of gA |pDIS
3.5 E155
x=0.015 in Eq.(17) corresponds to a negative strange-quark po-
HERMES
1

x=0.025 CL A S
larization
3
x=0.035
COMPASS 1 (0) (8)
LSS 05 ∆sQ2 →∞ = (g |pDIS,Q2 →∞ − gA )
3 A
x=0.049
2.5 = −0.08 ± 0.01(stat.) ± 0.02(syst.) (18)
x=0.077
– that is, polarized in the opposite direction to the spin
2 x=0.120
of the proton. With this ∆s, the following values for the
x=0.170 up and down quark polarizations are obtained
1.5
x=0.240 ∆uQ2 →∞ = 0.84 ± 0.01(stat.) ± 0.02(syst.)
1 x=0.340
∆dQ2 →∞ = −0.43 ± 0.01(stat.) ± 0.02(syst.) (19)

x=0.480
The non-zero value of ∆sQ2 →∞ in Eq.(18) is known as
0.5
the violation of the Ellis-Jaffe sum-rule (Ellis and Jaffe,
x=0.740 1974).
(0)
0 2 The extracted value of gA |pDIS required to be un-
1 10 10
Q (GeV 2)
2 derstood by theory, and the corresponding polarized
(8)
strangeness, depend on the value of gA . If we in-
FIG. 5 World data for g1 (x, Q2 ) for the proton with Q2 > (8)
stead use the value gA = 0.46 ± 0.05 the correspond-
1 GeV2 and W > 2.5 GeV. For clarity a constant ci = (0)
0.28(11.6 − i) has been added to the g1 values within a par- ing experimental value of gA |pDIS would increase to
(0)
ticular x bin starting with i = 0 for x = 0.006. Error bars gA |pDIS = 0.36 ± 0.03 ± 0.05 with
are statistical errors only. (Also shown is the QCD fit of
Leader et al. (2006).) ∆s ∼ −0.03 ± 0.03. (20)

We shall discuss the value of ∆s in more detail in Sections

V and VI in connection with more direct measurements
x−0.22±0.07 (Alekseev et al., 2010d) and is much bigger from semi-inclusive deep inelastic scattering plus global
than the isoscalar g1d . This compares to the situation in fits to spin data, models and recent lattice calculations
the unpolarized structure function F2 where the small-x with disconnected diagrams (quark sea contributions) in-
region is dominated by isoscalar gluonic exchanges. cluded.
The Bjorken sum-rule (Bjorken, 1966, 1970) for the
isovector part of g1 follows from current algebra and is
A. Spin sum-rules
a fundamental prediction of QCD. The first moment of
the isovector part of g1 is determined by the nucleon’s
To test deep inelastic sum-rules it is necessary to have
isovector axial-charge
all data points at the same value of Q2 . Next-to-leading
order (NLO) QCD-motivated fits taking into account the Z 1
1 (3) n X o
scaling violations associated with perturbative QCD are dxg1p−n = gA 1 + cNSℓ αℓs (Q) . (21)
6
used to evolve all the data points to the same Q2 . First 0 ℓ≥1
moment sum-rules are then evaluated by extrapolating
these fits to x = 0 and to x = 1, or using a Regge- up to a 1% correction from charge symmetry violation
motivated extrapolation of the data. Next-to-leading or- suggested by a recent lattice calculation (Cloet et al.,
der (NLO) QCD-motivated fits discussed in Section V.C 2012). It has been confirmed in polarized deep inelas-
(3)
are used to extract from these scaling violations the par- tic scattering at the level of 5%. The value of gA ex-
ton distributions and in particular the gluon polarization. tracted from the most recent COMPASS data is 1.28 ±
Polarized deep inelastic scattering experiments are in- 0.07(stat.) ± 0.010(syst.) (Alekseev et al., 2010d) and
terpreted in terms of a small value for the flavor-singlet compares well with the Particle Data Group value 1.270±
axial-charge. For example, COMPASS found using the 0.003 deduced from neutron beta-decays (Beringer et al.,
(8)
SU(3) value for gA (Alexakhin et al., 2007) and no lead- 2012).
R1
ing twist subtraction constant The evolution of the Bjorken integral xmin dxg1p−n
as a function of xmin as well as the isosinglet integral
(0) R1 p+n
gA |pDIS,Q2 →∞ = 0.33 ± 0.03(stat.) ± 0.05(syst.). (17) xmin dxg1 are shown in Fig. 6. The Bjorken sum-rule

14
∫ g (x) dx • Can we extract information about the quark and
Bjorken COMPASS data
p
g1 = g1 − g n1 gluon orbital angular momentum contributions
1
x min

p
g1 = g1 + g n1 from experiments, and with minimal model depen-
1

0.15
Ellis−Jaffe dence?

We next discuss the theoretical development and exper-

0.1
imental work that has been performed to address these
questions and the physics interpretation of present mea-
0.05 surements.

0 C. Spin and the singlet axial-charge

10−2 10−1
x min 1
There are two key issues involved in understanding the
FIG. 6 Convergence of the first moment integral of g1 as a (0)
function of the lower integration limit xmin for the Bjorken small value of gA |pDIS : the physics interpretation of the
(0)
integral (isospin non-singlet) and the Ellis–Jaffe integral (iso- flavor-singlet axial-charge gA and possible SU(3) break-
singlet) from the COMPASS proton and deuteron data at (8)
ing in the extraction of gA from hyperon β-decays. How
Q2 = 3 GeV2 . The arrows indicate the theoretical expecta- (0) (8)
tions. Error bars are statistical errors only. big really is the OZI violation ∆s = 13 (gA |pDIS − gA )?
Theoretical QCD analysis based on the axial anomaly
leads to the formula
and isosinglet integral converges in the measured x re- X 
gion. Note that a large contribution, about 50%, of the (0) αs
gA = ∆q − 3 ∆g + C∞ (22)
Bjorken sum-rule comes from x < ∼ 0.15. The integral for 2π partons
q
the first moment of g1p+n saturates at x ∼ 0.05: the isos-
inglet part of g1 is close to zero in this measured range – see Altarelli and Ross (1988), Efremov and Teryaev
of small Bjorken x. (1988), Carlitz et al. (1988), Bass et al. (1991) and Bass
The nucleon’s second spin structure function g2 is (2005). Here ∆gpartons is the amount of spin carried
believed
R1 to satisfy the Burkhardt-Cottingham sum-rule by polarized gluon partons in the polarized proton with
0
dxg 2 = 0 (Burkhardt and Cottingham, 1970). The αs ∆g ∼ constant as Q2 → ∞ (Altarelli and Ross, 1988;
most precise measurements to date in polarized deep in- Efremov and Teryaev, 1988)); ∆qpartons measures the
elastic scattering come from the SLAC E155 and E143
R 0.8 spin carried by quarks and anti-quarks carrying “soft”
experiments, which report 0.02 dx g2p = −0.042 ± 0.008 transverse momentum kt2 ∼ O(P 2 , m2 ) where P 2 is a
R 0.8 typical gluon virtuality in the nucleon and m is the
for the proton and 0.02 dx g2d = −0.006 ± 0.011 for the
deuteron at Q2 = 5 GeV2 (Anthony et al., 2003). E155 light quark mass. The polarized gluon term is associ-
estimate a contribution about 0.02 to the first moment ated with events in polarized deep inelastic scattering
of the proton g2 come from the x range between 0 and where the hard photon strikes a quark or anti-quark gen-
0.02 from the twist-two (Wandzura-Wilczek) part of g2 : erated from photon-gluon fusion and carrying kt2 ∼ Q2
R1 (Carlitz et al., 1988). It is associated with the QCD ax-
g2WW (x) = x dy y g1 (y) − g1 (x).
ial anomaly in perturbative QCD. C∞ denotes a poten-
tial non-perturbative gluon topological contribution with
B. Proton spin puzzles support only at Bjorken x = 0 (Bass, 2005). This term is
discussed in Section VI on theoretical understanding. It
The results from polarized deep inelastic scattering is associated with the possible subtraction constant in the
pose the following questions: dispersion
R 1 relation for g1 . If non-zero it would mean that
limǫ→0 ǫ dxg1 will measure the difference of the singlet
• How is the spin 12 of the proton built up from the
axial-charge and the subtraction constant contribution;
spin and orbital angular momentum of the quarks
that is, polarized deep inelastic scattering measures the
and gluons inside? (0) (0)
combination gA |pDIS = gA − C∞ .
(0) (0)
• Why is the quark spin content gA |pDIS so small? Possible explanations for the small value of gA |pDIS
(0) (8) extracted from polarized deep inelastic experiments that
• How about gA 6= gA ? What separates the values have been suggested in the theoretical literature in-
of the octet and singlet axial-charges? How reliable clude screening from positive gluon polarization, possible
(8)
is the SU(3) value of gA ? SU(3) breaking in the isosinglet axial-charges gA and
(8)

(0)
• Is the proton spin puzzle a valence quark or gA , negative strangeness polarization in the nucleon, a
sea/glue effect? possible topological contribution at x = 0 plus connec-

15
tions to axial U(1) dynamics discussed in Fritzsch (1989), ton.
Narison et al. (1995), Shore (2008) and Bass (1999b).
The two-loop QCD evolution factor E(αs ) in Eq.(15)
is associated with the polarized gluon term which car- V. QUARK AND GLUON POLARIZATION FROM DATA
ries all the scale dependence. The quark spin contribu-
tion ∆qpartons and the subtraction constant in Eq.(22) Key observables needed to understand the small value
are QCD scale invariant. The quark spin term ∆qpartons (0)
of the singlet axial-charge gA |pDIS are the polarized
is also known as the JET and chiral scheme (Cheng, strangeness and polarized glue in the nucleon. The
1996; Leader et al., 1998) and AB scheme (Ball et al., search for polarized strangeness has inspired a dedi-
1996) version of quark polarization – see Section V.C. cated experimental program with semi-inclusive deep in-
In an alternative approach,P called the MS scheme elastic scattering. Further, much activity was moti-
(Bodwin and Qiu, 1990), q ∆qMS , is defined as the to- vated by the discovery of Altarelli and Ross (1988) and
tal matrix element of the flavor-singlet axial-current (in- Efremov and Teryaev (1988) that polarized glue makes a
cluding the gluonic terms in Eq.(22)). We return to this scaling contribution to the first moment of g1 , αs ∆g ∼
issue in Section V.C with discussion of QCD fits to ex- constant. If there were a large negative contribution
perimental data. The growth in the gluon polarization αs
−3 2π ∆g with e.g. gluon polarization of the order of
∆g ∼ 1/αs at large Q2 is compensated by growth with
∆g ≃ 2.5 at Q2 = 10 GeV2 , then this could reconcile
opposite sign in the gluon orbital angular momentum. (0)
One would like to understand the dynamics which yield the small measured value of gA |pDIS with the naive par-
a small value of the singlet axial-charge extracted from ton model expectation of about 0.6 through Eq. (22).
This suggestion sparked a vigorous and ambitious pro-
polarized deep inelastic scattering and also the sum-rule
for the longitudinal spin structure of the nucleon gram to measure ∆g. Interesting channels include gluon
mediated processes in semi-inclusive polarized deep in-
1 1X elastic scattering (COMPASS and HERMES) and hard
= ∆q + ∆g + Lq + Lg (23) QCD processes in high-energy polarized proton-proton
2 2 q
collisions at RHIC.
where Lq and Lg denote the orbital angular momentum
contributions. Operator definitions of the different terms
or combinations of terms in this equation are discussed in A. Valence and sea polarization
Jaffe and Manohar (1990), Ji (1997b), Shore and White
(2000), Bakker et al. (2004), Bass (2005), Chen et al. Semi-inclusive measurements of fast pions and kaons in
(2008), Wakamatsu (2010), Leader (2011) and most re- the current fragmentation region with final state particle
cently in Hatta (2012), Ji et al. (2012) and Lorce (2012). identification can be used to reconstruct the individual
We discuss orbital angular momentum and attempts to up, down and strange quark contributions to the pro-
measure it in Sections VI–VII. ton’s spin. In contrast to inclusive polarized deep inelas-
There is presently a vigorous global program to dis- tic scattering where the g1 structure function is deduced
entangle the different contributions. Key experiments by detecting only the scattered lepton, the detected par-
include semi-inclusive polarized deep inelastic scattering ticles in the semi-inclusive experiments are high-energy
(COMPASS and HERMES) and polarized proton-proton (greater than 20% of the energy of the incident photon)
collisions (PHENIX and STAR), as well as deeply vir- charged pions and kaons in coincidence with the scat-
tual Compton scattering and hard exclusive meson pro- tered lepton. For large energy fraction z = Eh /Eγ → 1
duction to learn about total angular momentum (COM- the most probable occurrence is that the detected π ±
PASS, HERMES and JLab). Single spin observables in and K ± contain the struck quark or anti-quark in their
semi-inclusive scattering from transversely polarized tar- valence Fock state. They therefore act as a tag of the
gets is sensitive to orbital angular momentum in the pro- flavor of the struck quark (Close, 1979).

In leading order the virtual-photon–proton double-spin where zmin ∼ 0.2. Here ∆fq (x, Q2 ) is the quark (or
(cross-section) asymmetry is anti-quark) polarized parton distribution, fq (x, Q2 ) the
unpolarized distribution
R 2 h and eq is the quark charge;
Dfh (z, Q2 ) = dpt Dq (z, p2t , Q2 ) is the fragmentation
P 2 2
R1 h 2 function for the struck quark or anti-quark to produce
q,h eq ∆fq (x, Q ) zmin dzDf (z, Q )
Ah1p (x, Q2 ) ≃ P R1 a hadron h (= π ± , K ± ) carrying energy fraction z =
2 2 h 2
q,h eq fq (x, Q ) zmin dzDf (z, Q ) Eh /Eγ in the target rest frame; Note the integration over
(24)

16
TABLE II First moments for valence quark and light-sea polarization from SMC, HERMES, and COMPASS. For each ex-
periment the integrated sea is evaluated from data up to x = 0.3 and, for SMC, assuming an isospin symmetric polarized
sea.
Experiment x-range Q2 (GeV2 ) ∆uv ∆dv ∆ū ∆d¯
SMC 0.003–0.7 10 0.73 ± 0.10 ± 0.07 −0.47 ± 0.14 ± 0.08 0.01 ± 0.04 ± 0.03 0.01 ± 0.04 ± 0.03
HERMES 0.023–0.6 2.5 0.60 ± 0.07 ± 0.04 −0.17 ± 0.07 ± 0.05 0.00 ± 0.04 ± 0.02 −0.05 ± 0.03 ± 0.01
COMPASS 0.006–0.7 10 0.67 ± 0.03 ± 0.03 −0.28 ± 0.06 ± 0.03 0.02 ± 0.02 ± 0.01 −0.05 ± 0.03 ± 0.02

π+
0.8 A 1,p 0.8 A K+
1,p
0.4 A π1,d+ AK+
1,d
0.6 0.6
0.2
0.4 0.4
0.2 0.2
0
0 0
−0.2 −0.2 −0.2
π− π−
0.8 A 1,p A K−
1,p
0.4 A 1,d AK−
1,d
0.6
COMPASS 0.2
0.4
HERMES
0.2
0
0
−0.2 −0.2
10−2 10−1 10−2 10−1 10−2 10−1 10−2 10 −1
x x
FIG. 7 Semi-inclusive longitudinal double-spin asymmetries for identified pions and kaons from COMPASS (Alekseev et al.,
2009b, 2010c) and HERMES (Airapetian et al., 2005a) for the proton (left) and the deuteron (right) as function of x at the
Q2 of the measurements. The error bars and bands indicate the statistical and systematic uncertainties, respectively. Figure
adapted from Alekseev et al. (2009b) (left, proton target) and Alekseev et al. (2010c) (right, deuteron target).

the transverse momentum pt (Close and Milner, 1991). arated charged pion and kaon production from proton
Since pions and kaons have spin zero, the fragmentation and deuteron targets. There is good agreement between
functions are the same for both polarized and unpolar- the COMPASS and HERMES data in the kinematic re-
ized leptoproduction. The fragmentation functions for gion of overlap – see Fig. 7. Flavor-separated polarized
u → π + and d → π − are known as “favored” (where the quark distributions for valence and sea quarks are then
fragmenting quark has the same flavor as a valence quark extracted from the data using fragmentation functions
in the final state hadron); the fragmentation functions for that have been fitted to previous hadron production data,
u → π − and d → π + are known as “unfavored”. with the most accurate taken to be those from the DSS
This program for polarized deep inelastic scatter- group (de Florian et al., 2007) from a global fit to single-
ing was pioneered by the SMC (Adeva et al., 1996, hadron production in e+ e− , ep and pp collisions.
1998a) and the HERMES (Ackerstaff et al., 1999b;
Airapetian et al., 2004a, 2005a) experiments. The The polarizations of the up and down quarks are pos-
most recent measurements from HERMES are reported itive and negative respectively, while the extracted sea
in Airapetian et al. (2008c) and from COMPASS in polarization data are consistent with zero – see Ta-
Alekseev et al. (2010c). ble II which includes measurements from COMPASS
The experimental strategy has been to measure the (Alekseev et al., 2010c), HERMES (Airapetian et al.,
asymmetries Ah1 for charged hadron production and sep- 2005a) and SMC (Adeva et al., 1998a).

The COMPASS and HERMES determinations of the x∆s(x). There is no evidence in the semi-inclusive data
sum of strange and anti-strange polarisation ∆s(x) are for large negative strange quark polarization in the nu-
shown together in Fig. 8, plotted in the combination cleon. The HERMES data covers the region 0.02 <

17
 (Bourrely et al., 2002) and chiral quark soliton models
x∆s
COMPASS
HERMES
(Wakamatsu, 2003) predict positive values. The COM-
PASS and HERMES results are consistent with these pre-
0.1 dictions within uncertainties.

The W -boson production program at

RHIC (Bunce et al., 2000) will provide additional
0 flavor-separated measurements of polarized up and down
quarks and anti-quarks. At RHIC the polarization of
the u, ū, d, and d¯ quarks in the proton is being measured
−2 −1
directly using W boson production in ud¯ → W + and
10 10
x dū → W − . The charged weak boson is produced through
a pure V−A coupling and the chirality of the quark and
FIG. 8 COMPASS (Alekseev et al., 2010c) and HERMES anti-quark in the reaction is fixed. The W is observed
(Airapetian et al., 2008c) results for the strangeness polar-
through its leptonic decay W → lν, and the charged
ization x∆s(x) as function of x. The data are obtained in a
leading-order analysis of SIDIS asymmetries (including those lepton is measured. Measurement of the flavor-separated
for charged kaons) and using the DSS fragmentation func- anti-quark helicity distributions via W production in
tions (de Florian et al., 2007). The inner error bar represents p + p collisions is complementary to measurements via
the statistical uncertainty; the full bar the quadratic sum of SIDIS in that there is no dependence on details of the
statistical and systematic uncertainties. fragmentation process, and the process scale, Q2 ≈ MW 2

is significantly higher than any data from existing fixed-

target polarized DIS experiments. A parity-violating
x < 0.6, where the extracted ∆s is consistent with a asymmetry for W + production in p + p collisions at
zero or small positive value. This data integrates to √
R 0.6 s = 500 GeV consistent with predictions based on anti-
0.02
dx∆s = 0.037 ± 0.019 ± 0.027 (Airapetian et al., quark helicity distributions extracted from SIDIS has
2008c) in contrast with the negative value for polarized already been observed by both PHENIX (Adare et al.,
strangeness, Eq.(18), extracted from inclusive measure- 2011b) and STAR (Aggarwal et al., 2011) based on data
ments of g1 . COMPASS measurements (Alekseev et al., collected in 2009. Considerably improved results are
2009b, 2010c) show no evidence of strangeness polar- expected from data taken in 2011 and 2012 with higher
ization in the region x > 0.004 with the integrated luminosities and polarization. Preliminary results for
∆s = −0.02 ± 0.02 ± 0.02. both W + and W − asymmetries from STAR, based on
The precise value of ∆s extracted from semi-inclusive data taken at the beginning of 2012, are consistent with
scattering may be affected by any possible future im- results from SIDIS and suggest the possible asymmetry
provement in the accuracy of the kaon fragmentation ∆ū > ∆d¯ for x from 0.05–1 (Aschenauer et al., 2012b).
functions DqK (z). However a drastic change in the ratio
R + R +
dzDs̄K / dzDuK would be needed to bring the first An independent measurement of the strange-quark
moment of ∆s extracted from semi-inclusive scattering in axial-charge could be made through neutrino-proton elas-
agreement with the inclusive value, Eq.(18), obtained us- tic scattering. This process measures the combination
(8) 1 (0)
ing the SU(3) value of gA (Alekseev et al., 2010c). More 2 (∆u − ∆d − ∆s)inv − 0.01gA |inv , where the small last
experimental data, especially on kaon fragmentation pro- term is a correction from heavy-quarks which has been
cesses, are needed for improved precision on strangeness calculated to LO (Kaplan and Manohar, 1988) and NLO
polarization in the nucleon. (Bass et al., 2002) accuracy. The axial-charge measured
Semi-inclusive data are consistent with a small pos- in νp elastic scattering is independent of any assumptions
itive or zero isospin asymmetry in the polarized sea about possible SU(3) breaking, the presence or absence
∆ū ¯ 2
R 0.3− ∆d. For the COMPASS data at 3 GeV one finds of a subtraction at infinity in the dispersion relation for
dx(∆ū − ∆ ¯ = 0.06 ± 0.04(stat.) ± 0.02(syst.).
d) g1 and the x ∼ 0 behavior of g1 . A recent suggestion for
0.004 R 0.3
For HERMES data at 2.5 GeV2 0.023 dx(∆ū − ∆d) ¯ = an experiment using low-energy neutrinos produced from
0.048 ± 0.057(stat.) ± 0.028(syst.) (Airapetian et al., pion decay at rest is discussed in Pagliaroli et al. (2012).
2005a). These values compare with the unpolarized
R1
sea measurement 0 dx(ū − d) ¯ = −0.118 ± 0.012 from In a recent analysis (Pate et al., 2008) of parity vio-
the E866 experiment at FNAL (Towell et al., 2001). A lating quasi-elastic electron and neutrino scattering data
compilation of theoretical predictions is given in Peng between 0.45 and 1 GeV2 (from the JLab experiments G0
(2003). Meson cloud models predict small negative and HAPPEx and the Brookhaven experiment E734), the
isospin asymmetries in the polarized sea (Cao and Signal, axial form-factor was extrapolated to Q2 = 0 and favored
2001; Kumano and Miyama, 2002) whereas statistical negative or zero values of ∆s with large uncertainty.

18
 polarization by HERMES (Airapetian et al., 2000a) and
p↑
SMC (Adeva et al., 2004) and the most recent HERMES
determination (Airapetian et al., 2010c) and COMPASS
q q
measurement (Adolph et al., 2012e).
These measurements in lepton-nucleon scattering are
g g listed in Table III for the ratio of the polarized to un-
polarized glue ∆g/g and shown in Fig. 11 for leading-
p↑ order (LO) analyses of the data. The data cluster around
xg ∼ 0.1 with the exception of the COMPASS NLO point
from open charm. There is no evidence in the data for
non-zero gluon polarization at this value of xg .
FIG. 9 Jet production from quark-gluon scattering in The chance to measure ∆g was a main physics drive
polarized proton-proton collisions. for polarized RHIC. Experiments using the PHENIX
µ µ
B. Gluon polarization
q
γ
*
Polarized proton-proton scattering is sensitive to the c
ratio of polarized to unpolarized glue, ∆g/g, via leading-
order interactions of gluons, as illustrated in Fig. 9. The
first experimental attempt to look at gluon polariza- g c
tion was made by the FNAL E581/704 Collaboration us-
ing a 200 GeV polarized proton beam and a polarized k
proton target. They measured a longitudinal double-
spin asymmetry ALL for inclusive multi-γ and π 0 π 0 pro- p
duction consistent with zero within their sensitivities,
suggesting that ∆g/g is not so large in the region of FIG. 10 Production of a cc̄ pair in polarized photon gluon
fusion is being used to measure gluon polarization in the po-
0.05 < <
∼ xg ∼ 0.35 (Adams et al., 1994). larized proton.
COMPASS was conceived to measure ∆g via the study
of the photon-gluon fusion process, as shown in Fig. 10.
The cross-section for this process is directly related to
the (polarized) gluon distribution at the Born level. The and STAR detectors are investigating polarized glue in
experimental technique consists of the reconstruction of the proton. Measurements of ∆g/g from RHIC are
charmed mesons (Adolph et al., 2012d; Alekseev et al., sensitive to √gluon polarization in the range 0.02 < ∼
2009c) or high-pT hadrons (Ageev et al., 2006) in the <
g ∼ 0.3 ( s = 200 GeV) and 0.06 ∼ xg ∼ 0.4
x√ < <
final state to access ∆g. For the charmed meson case ( s = 62.4 GeV) for the neutral pion ALL measured by
COMPASS also performed a NLO analysis which shifts PHENIX (Adare et al., 2009a,b) and inclusive jet pro-
probed xg to larger values. The high-pT particle method duction measured by STAR at 200 GeV center-of-mass
leads to samples with larger statistics, but these have energy (Abelev et al., 2008b; Adamczyk et al., 2012a).
higher background contributions from QCD Compton Additional channels sensitive to ∆g at RHIC have
processes and fragmentation. High-pT hadron produc- been published as well (Abelev et al., 2009; Adare et al.,
tion was also used in early attempts to access gluon 2011a, 2012).

Combined preliminary results from PHENIX and (Djawotho, 2011), providing the first evidence for non-
STAR using more recent 200 GeV data than those pub- zero gluon polarization in the proton. The relationship
lished in Adare et al. (2009b) and Abelev et al. (2008b) between the pion and jet pT scales is given by the mean
are shown in Fig. 12. The longitudinal double spin asym- z value of ∼ 0.5 (Adler et al., 2006). The data are shown
metry in neutral pion production measured by PHENIX with a calculation using helicity distributions extracted
based on combined data from 2005, 2006, and 2009 is from a global fit to polarized world data from DIS,
shown as a function of pion pT (upper scale) (Manion, semi-inclusive DIS, and proton-proton collisions (DSSV)
2011). Figure 12 also shows the asymmetry in single- (de Florian et al., 2008, 2009) that was updated to in-
inclusive jet production as a function of jet pT (lower clude these results (Aschenauer et al., 2012b). See the
scale) measured by STAR based on data taken in 2009 following section for more details about fits to helicity

19
TABLE III Polarized gluon measurements from deep inelastic experiments.

Experiment process hxg i hµ2 i (GeV2 ) ∆g/g

HERMES (Airapetian et al., 2000a) hadron pairs 0.17 ∼2 0.41 ± 0.18 ± 0.03
HERMES (Airapetian et al., 2010c) inclusive hadrons 0.22 1.35 0.049 ± 0.034 ± 0.010+0.125
−0.099
SMC (Adeva et al., 2004) hadron pairs 0.07 −0.20 ± 0.28 ± 0.10
COMPASS (Ageev et al., 2006; Procureur, 2006) hadron pairs, Q2 < 1 0.085 3 0.016 ± 0.058 ± 0.054
COMPASS (Adolph et al., 2012e) hadron pairs, Q2 > 1 0.09 3 0.125 ± 0.060 ± 0.063
COMPASS (Adolph et al., 2012d) open charm (LO) 0.11 13 −0.06 ± 0.21 ± 0.08
COMPASS (Adolph et al., 2012d) open charm (NLO) 0.20 13 −0.13 ± 0.15 ± 0.15

0.8 π0 pT (GeV)
∆g/g

New COMPASS, high p , Q2>1 GeV 2, 2002−2006

T
2 2
COMPASS, high p , Q <1 GeV , 2002−2003
0.6 T
0 5 10 15
COMPASS, open charm, 2002−2007
SMC, high p , Q2>1 GeV2
0.4 T
HERMES, high p , all Q2
T
PHENIX Prelim. π 0 , Run 2005-2009
0.2 PHENIX shift uncertainty
DSSV++ for π 0
0 0.04 STAR Prelim. jet, Run 2009
STAR shift uncertainty
−0.2 DSSV++ for jet
A LL
−0.4
DSSV fit, µ 2=3 GeV 2 0.02
−0.6 LSS fit with ∆G>0, µ 2=2.5 GeV 2
LSS fit with ∆G changing sign, µ 2=2.5 GeV 2

−0.8
10−2 10−1 xg
0

FIG. 11 Gluon polarization ∆g/g from leading-order anal- PHENIX / STAR scale uncertainty 6.7% / 8.8% from pol. not shown
yses of hadron or hadron-pair production as function of the
probed gluon momentum fraction xg . Also shown are NLO 0 10 20 30
fits from de Florian et al. (2009) and Leader et al. (2010). Jet p (GeV)
(Figure adapted from Adolph et al. (2012e).) The inner er- T
ror bar represents the statistical uncertainty; the full bar the
quadratic sum of statistical and systematic uncertainties. The FIG. 12 The longitudinal double-spin asymmetry in π 0 pro-
horizontal bar indicates the xg range of the measurement. duction measured by PHENIX (Manion, 2011) and in jet pro-
duction measured by STAR (Djawotho, 2011), shown with
calculations based on the DSSV polarized parton distribu-
tions that were updated to include these results; Figure
from Aschenauer et al. (2012b). The relationship between
the pion and jet pT scales is given by the mean z value of
distributions. A given pT bin for single inclusive jet or ∼ 0.5 (Adler et al., 2006). Error bars represent the statistical
hadron production generally samples a wide range of xg uncertainty.
values. However, dijet measurements in p + p collisions
provide better constraints on the xg values probed. Pre-
liminary STAR results for dijet production have also been C. NLO QCD motivated fits to spin data
released (Walker, 2011) and confirm the non-zero double-
spin asymmetry seen in single jet production. Global NLO perturbative QCD analysis are performed
on polarization data sets including both lepton-nucleon
While there is now evidence in the RHIC data that and proton-proton collision data. The aim is to ex-
gluon polarization in the proton is non-zero, the mea- tract the polarized quark and gluon parton distribu-
surements indicate that polarized glue, by itself, is not tions. These analysis, starting from Ball et al. (1996) and
sufficient to resolve the difference between the small value Altarelli et al. (1997), frequently use DGLAP evolution
(0)
of gA |pDIS and the naive constituent quark model pre- and are performed in a given factorization scheme. This
αs
diction, ∼ 0.6, through the polarized glue term −3 2π ∆g. QCD fit approach has more recently been extended to a
Note however that gluon polarization ∆g ∼ 0.2 − 0.3 global analysis of data from polarized DIS, semi-inclusive
would still make a significant contribution to the spin of polarized DIS and high-energy polarized proton-proton
the proton in Eq.(23). collisions (de Florian et al., 2008, 2009).

20
 The separation of g1 into “hard” and “soft” contribu- ing order by Altarelli and Parisi (1977) and at next-
tions is not unique and depends on the choice of “factor- to-leading order by Zijlstra and van Neerven (1994),
ization scheme”. For example, one might use a kinematic Mertig and van Neerven (1996) and Vogelsang (1996).
cut-off on the partons’ transverse momentum squared The largest uncertainties in the QCD fits are associ-
(kt2 > µ2 ) to define the factorization scheme and thus ated with the ansatz chosen for the shape of the spin-
separate the hard and soft parts of the phase space for the dependent quark and gluon distributions at a given in-
photon-parton collision. The cut-off µ2 is called the fac- (8)
put scale. Further, the SU(3) value of gA (= 0.58 ±
torization scale. The coefficients in Eq.(8) have the per- 0.03) is assumed in present fits though no significant
turbative expansion C q = δ(1 − x) + α s q 2 2
2π f (x, Q /µ ) and change in the χ2 quality of the fits should be ex-
Cg = α 2π
s
f g
(x, Q 2
/µ 2
) where the strongest singularities in (8)
pected if one instead took a value of gA with pos-
the functions f q and f g as x → 1 are ln(1 − x)/(1 − x)+ sible 20% SU(3) breaking included.1 The values for
and ln(1 − x) respectively, see e.g. Lampe and Reya the quark and gluon spin contents (∆Σ and ∆g) ob-
(2000). The deep inelastic structure functions are depen- tained in recent NLO fits are listed in Table IV with re-
dent on Q2 and independent of the factorization scale µ2 sults quoted from Blümlein and Böttcher (2010) (BB10:
and the “scheme” used to separate the γ ∗ -parton cross- DIS data), Nocera et al. (2012) (NFRR12: DIS data),
section into “hard” and “soft” contributions. Leader et al. (2010) (LLS10: DIS and SIDIS data) and
Examples of different “schemes” used in the lit- Hirai and Kumano (2009) (AAC08: DIS and RHIC data)
erature are the modified minimal subtraction (MS) and de Florian et al. (2008, 2009) (DSSV08: DIS, SIDIS
(Bodwin and Qiu, 1990; ’t Hooft and Veltman, 1972) to and proton-proton collision data).
regulate the mass singularities which arise in scatter-
The most complete fits in terms of maximum included
ing from massless partons, the “AB” (Ball et al., 1996)
and “CI” (chiral invariant) (Cheng, 1996) or “JET” data are from the DSSV group, which take the SU(3)
(8)
(Leader et al., 1998) schemes. In the MS scheme the po- value for gA . One finds need for a large negative con-
larized gluon distribution does not contribute explicitly tribution to ∆s from small x, outside the measured x
to the first moment of g1 . In the AB, CI and JET schemes range when SIDIS dataR is included. The values obtained
1
on the other hand the polarized gluon (axial anomaly in this approach for xmin dx∆s(x) are ∆s = −0.057
contribution) αs ∆g does contribute explicitly to the first with xmin = 0 and about −0.001 with xmin = 0.001.
R1 That is, to reproduce the SU(3) value of the octet axial-
moment since 0 dx C (g) = − α 2π – see the spin decom-
s

position in Eq.(22). charge, the negative polarized strangeness obtained from

The µ2 dependence of the parton distributions is given inclusive g1 measurements gets pushed into the unmea-
by the DGLAP equations (Altarelli and Parisi, 1977) sured small-x range, x < 0.004. It is interesting here to
Z 1 note that, historically (before COMPASS, HERMES and
d dy x RHIC Spin), the proton spin puzzle was assumed to be
∆Σ(x, t) = ∆Pqq ( , αs (t))∆Σ(y, t)
dt x y y associated with strangeness/sea/glue polarization in the
Z 1  newly opened kinematics of EMC, SLAC and SMC, x be-
dy x
+ 2f ∆Pqg ( , αs (t))∆g(y, t) tween 0.1 and 0.01. We now have accurate SIDIS mea-
x y y
surements down to x ∼ 0.004 which show no evidence
Z 1
d dy x for large sea/glue polarization effects. With the SIDIS
∆g(x, t) = ∆Pgq ( , αs (t))∆Σ(y, t)
dt x y y measurements of ∆s, either one needs SU(3) breaking in
Z 1  the octet axial-charge or strangeness/glue effects at very
dy x
+ ∆Pgg ( , αs (t))∆g(y, t) small x. Without including the most recent data from
x y y
2009 or later, de Florian et al. (2008, 2009) find a best-fit
(25) R1
full first moment 0 dx∆g(x) = −0.084 at Q2 = 10 GeV2 .
P
where ∆Σ(x, t) = q ∆q(x, t), t = ln µ
2
and f is With a very large ∆χ2 /χ2 = 2% allowed range, the trun-
R1
the number of active flavors. The splitting func- cated first moment 0.001 dx∆g = 0.013+0.702 −0.314 was ob-
tions Pij in Eq.(25) have been calculated at lead- tained. With these errors ∆g is still not precise.

A recent attempt to extract polarized parton distri- ing neural network techniques is reported in Nocera et al.
butions from inclusive polarized deep inelastic data us- (2012). In this approach no assumption is made about
the functional form of the input distributions, greatly
reducing the primary (and notoriously difficult to quan-
1
tify) systematic uncertainty on parton distribution fits.
We thank S. Taneja and R. Windmolders for discussion on this
The neural network method has already been used
issue.

21
TABLE IV First moments of the polarized singlet-quark and gluon distributions at the scale 4 GeV2 in the MS scheme; values
quoted from Nocera et al. (2012).

DSSV08 BB10 LSS10 AAC08 NFRR12

∆Σ(Q2 ) 0.25 ± 0.02 0.19 ± 0.08 0.21 ± 0.03 0.24 ± 0.07 0.31 ± 0.10
∆g(Q2 ) −0.10 ± 0.16 0.46 ± 0.43 0.32 ± 0.19 0.63 ± 0.19 −0.2 ± 1.4

(3) (8)
quite successfully in the parametrization of the unpo- axial-charges gA and gA , corresponding to the matrix
larized parton distributions, with results published at elements of partially conserved currents, the model is
NLO in 2010 (Ball et al., 2010) and now NNLO in well designed to make a solid prediction.
2012 (Ball et al., 2012). However, in the case of the ap- The effective color-hyperfine interaction has the quan-
plication of the neural network method in the extraction tum numbers of one-gluon exchange (OGE). In models of
of polarized parton distributions, thus far only inclusive hadron spectroscopy this interaction plays an important
polarized DIS data has been incorporated, similar to the role in the nucleon-∆ and Σ − Λ mass differences, as well
BB10 fit (Blümlein and Böttcher, 2010). as the nucleon magnetic moments (Close, 1979) and the
spin and flavor dependence of parton distribution func-
tions (Close and Thomas, 1988). It shifts total angular-
VI. THEORETICAL UNDERSTANDING momentum between spin and orbital contributions and,
therefore, also contributes to model calculations of the
In relativistic quark models some of the proton’s spin octet axial-charges (Myhrer and Thomas, 1988). With
is carried by quark orbital angular momentum. One has OGE included (together with a phenomenological wave-
(3)
to take into accountthe four-component
 Dirac spinor for function renormalization to ensure gA takes the physi-
f cal value), the model is in very good agreement with the
the quarks ψ = √N , where f and g are functions
4π iσ·r̂g SU(3) fit to the nucleon and hyperon axial-charges ex-
of the spatial coordinates and N is a normalization fac- (8)
tracted from β-decays with gA predicted to be around
tor. The lower component of the Dirac spinor is p-wave 0.6.
with intrinsic spin primarily pointing in the opposite di- Next, the pion cloud induces SU(3) breaking in
rection to spin of the nucleon. In the MIT Bag model, the nucleon’s axial-charges. The pion cloud fur-
where quarks are confined in an infinite square well po- ther shifts intrinsic spin into orbital angular mo-
tential with radius R, one finds the depolarization factor mentum (Schreiber and Thomas, 1988; Tsushima et al.,
RR
N 2 0 drr2 (f 2 − 31 g 2 ) = 0.65 for ∆q in the proton with 1988). Including pion and kaon cloud corrections gives
all quarks in the (1s) ground-state (Jaffe and Manohar, (8)
the model result gA = 0.46 ± 0.05 (with the corre-
1990). That is, 35% of the proton’s spin content is shifted sponding semi-classical singlet axial-charge or spin frac-
into orbital angular momentum through the confinement tion being 0.42 ± 0.07 before inclusion of gluonic effects)
potential. (Bass and Thomas, 2010). With this Cloudy Bag value
More detailed calculations of non-singlet axial-charges (8) (0)
for gA the corresponding experimental value of gA |pDIS
in relativistic constituent quark models are sensitive to (0)
would increase to gA |pDIS = 0.36 ± 0.03 ± 0.05, consid-
the confinement potential, effective color-hyperfine inter- (0)
action, pion and kaon clouds plus additional wavefunc- erably reducing the apparent OZI violation 31 (gA |pDIS −
(8)
tion corrections (associated with center of mass motion) gA ) that one needs to explain.
(3)
chosen to reproduce the physical value of gA . A recent lattice calculation with disconnected dia-
This physics was recently investigated within grams included (Bali et al., 2012) gave ∆s = −0.02±0.01
the Cloudy Bag model (Bass and Thomas, 2010; in the MS scheme at 7.4 GeV2 . This value compares with
Myhrer and Thomas, 2008; Thomas, 2008). The Cloudy the Cloudy Bag prediction ∆s ∼ −0.01 before gluonic
Bag was designed to model confinement and sponta- degrees of freedom are included. These numbers are in
neous chiral symmetry breaking, taking into account good agreement with the values extracted from polarized
pion physics and the manifest breakdown of chiral SIDIS data by COMPASS and HERMES with the DSS
symmetry at the bag surface in the MIT bag. If we fragmentation functions.
wish to describe proton spin data including matrix Gluon polarization has been investigated in bag and
3 8
elements of Jµ5 , Jµ5 and Jµ5 , then we would like to light-cone models and in studies of heavy-quark axial-
know that the model versions of these currents satisfy charges. The nucleon’s charm-quark axial-charge was
the relevant Ward identities (the divergence equations interpreted to give an estimate of gluon polarization
for these currents). For the scale-invariant non-singlet |∆g(m2c )| < 2
∼ 0.3 with αs (mc ) = 0.4 (Bass et al., 2011).

22
This upper bound corresponds to |3 2π αs
∆g| <
∼ 0.06. Val- and sea quark contributions is suppressed at small x.
2
ues of ∆g ∼ 0.3 and ∼ 0.5 at 1 GeV were obtained in the Neither the SU(3) flavor-singlet nor octet contribution
MIT Bag model (Chen and Ji, 2008) and in a light-cone breaks free in the measured small x region. Hence, the
model (Brodsky et al., 1995) respectively. These theo- suppression of g1p+n at small x should be either an isos-
retical values are consistent with the extractions of gluon inglet effect or a delicate cancellation between octet and
polarization from COMPASS, HERMES and RHIC Spin singlet contributions over an order of magnitude in small
data. Bjorken x.
To understand C∞ ,2 deep inelastic sum-rules are de- The g1p−n data are consistent with quark model and
rived using the operator product expansion and the dis- perturbative QCD counting rules predictions in the va-
persion relation for deeply-virtual photon-nucleon scat- (3)
lence region x > 0.2 (Bass, 1999a). The size of gA
tering. Two important issues with the dispersion are forces us to accept a large contribution from small x (a
the convergence of the first moment integral at the high- non-perturbative constraint) and the rise in g1p−n is in
est energies and any contribution from closing the circle excellent agreement with the prediction g1p−n ∼ x−0.22
in the complex momentum plane. The subtraction con- of hard Regge exchange (Bass, 2007a) – in particu-
stant, if finite, corresponds to a constant real term in the lar a possible a1 hard-pomeron cut involving the hard-
forward Compton scattering amplitude. It affects just pomeron which seems to play an important role in un-
the first moment integral and thus behaves like a δ(x) polarized deep inelastic scattering (Cudell et al., 1999)
term with support only at x = 0. A subtraction constant and in the proton-proton total cross-section measured
yields a finite correction to the sum-rule obtained from at LHC (Donnachie and Landshoff, 2011). (Soft) Regge
integrating only over finite non-zero values of Bjorken x. theory predicts that the singlet term should behave as
One can show (Bass, 2005) that non-local gluon topo- ∼ N ln x in the small x limit, with the coefficient N to be
logical structure requires consideration of a possible δ(x) determined from experiment (Bass and Landshoff, 1994;
subtraction constant. Whether it has finite value or not is Close and Roberts, 1994). From the data, this normal-
sensitive to the realization of axial U(1) symmetry break- ization seems to be close to zero.
ing by instantons (Crewther, 1978; ’t Hooft, 1986) and Where are we in our understanding of the spin struc-
the importance of topological structure in the proton. (0)
ture of the proton and the small value of gA |pDIS ? Mea-
The QCD vacuum is a Bloch superposition of states char-
surements of valence, gluon and sea polarization suggest
acterized by non-vanishing topological winding number
that the polarized glue term −3 α 2π ∆g and the strange
s
and non-trivial chiral properties. When we put a valence
quark contribution ∆spartons in Eq.(22) are unable to re-
quark into this vacuum it can act as a source which po- (0)
larizes the QCD vacuum with net result that the spin solve the small value of gA |pDIS . Two explanations are
“dissolves”. Some fraction of the spin of the constituent suggested within the theoretical and experimental uncer-
quark is shifted from moving partons into the vacuum at tainties depending upon the magnitude of SU(3) break-
x = 0. This spin contribution becomes associated with ing in the nucleon and hyperon axial-charges. One is a
(8)
non-local gluon topology with support only at Bjorken value of gA ∼ 0.5 plus an axial U(1) topological effect at
x = 0. x = 0 associated with a finite subtraction constant in the
Valuable information about the spin puzzle also follows g1 dispersion relation. The second is a much larger pion
(8)
from looking at the x dependence of g1 . The small value cloud reduction of gA to a value ∼ 0.4. Combining the
(0) theoretical error on the pion cloud chiral corrections em-
of gA or “missing spin” is associated with a “collapse” in
the isosinglet part of g1 to something close to zero instead braces both possibilities. The proton spin puzzle seems
of a valence-like rise at x less than about 0.05 to be telling us about the interplay of valence quarks
R 1 – see e.g. with chiral dynamics and the complex vacuum structure
the g1 data in Fig. 4 and the convergence of xmin dxg1p+n
R1 of QCD.
and xmin dxg1p−n in Fig. 6. This isosinglet part is the sum
Orbital angular momentum (OAM) in relativistic
of SU(3)-flavor singlet and octet contributions. If there quark models (for example the MIT and Cloudy bag
were a large positive polarized gluon contribution to the models) without explicit gluon degrees of freedom has
proton’s spin, this would act to drive the small x part of the usual interpretation of relativistic quantum mechan-
the singlet part of g1 negative (Bass and Thomas, 1993) ics. For QCD dynamics the definition of OAM is more
– that is, acting in the opposite direction to any valence- subtle because of the gauge covariant derivative, meaning
like rise at small x. However, gluon polarization mea- that quark orbital momentum is in principle sensitive to
surements constrain this spin contribution to be small in the gluon fields in the nucleon that the quarks interact
measured kinematics meaning that the sum of valence with.
Going beyond spin and helicity to consider also orbital
and total angular momentum, several operator decom-
n o positions have been proposed. Starting from the relation
2 In the notation of Eq.(12): β∞ = − 91 C∞ 1 + ℓ≥1 cSℓ αℓs (Q) .
P
between angular momentum and the energy-momentum

23
tensor, Ji (1997b) takes observable – for example, in SIDIS the largest kt events
Z are included in the MS version of ∆q whereas they are
J~q = d3 x ~x × T~q omitted in the JET scheme version (Bass, 2003).
Z " # There are some theoretical subtleties when dealing
~
Σ ~
= d3 x ψ † ψ + ψ † ~x × (−iD)ψ , with gluon angular momentum. In the parton model
2 the gluon polarization ∆g has a clean interpretation in
Z light-cone gauge as the forward matrix element of the
J~g = d3 x ~x × (E~ × B).
~ (26) local Chern-Simons current K+ (appearing in the QCD
axial anomaly) up to a surface term which has support
The gauge covariant derivative Dµ = ∂µ + igAµ with
only at x = 0 (Bass, 2005; Manohar, 1990). In light-
Aµ the gluon field means that Lq is a priori sensitive
cone gauge K+ coincides with the gluon spin operator
to gluonic degrees of freedom. The Jq and Jg quantities
(Jaffe, 1996). In general, Ji’s Jg in Eq.(26) is not readily
here are amenable to QCD lattice calculations and, in
separable into spin and orbital components. New ideas
principle, measurable through deeply virtual Compton
have recently been investigated where one separates the
scattering. In an alternative approach, taking the + light
gluon field into a “physical” transverse part and “pure”
cone component of the QCD angular momentum tensor
gauge part, with different conventions how to deal with
in A+ = 0 gauge Jaffe and Manohar (1990) proposed the
the gauge part (Chen et al., 2008; Hatta, 2012; Lorce,
operator decomposition
 3 2012; Wakamatsu, 2010). Discussion of total orbital an-
1 † gular momentum involving gluonic degrees of freedom
M +12 = q+ †
γ5 q+ + q+ ~x × i∂~ q+ should be labelled with respect to the scheme or conven-
2
  tion used.
+2TrF +j ~x × i∂~ Aj + Trǫ+−ij F +i Aj To connect quark model predictions with lattice cal-
culations and fits to data it is necessary to use QCD
(27) evolution of the model results from the low-energy scale
where the gluon term in the gauge covariant derivative is where the model applies up to the hard scale of deep
no longer present through the gauge fixing. inelastic scattering. Model calculations (and also lat-
The connection between the quark and gluon total an- tice calculations without disconnected diagrams) of ∆q
gular momentum contributions J q and J g and the QCD are commonly understood to refer to the scale invari-
energy-momentum tensor allows us to write down their ant version of this quantity, e. g. the chiral/JET or
LO QCD evolution equations (Ji et al., 1996). The quark AB scheme quark spin contributions in Eq. (22). One
and gluon total angular momenta in the infinite scal- chooses a model ansatz for the gluon polarization and
ing limit are given by Jq (∞) = 12 {3f /(16 + 3f )} and total angular momentum, typically ∆g = Jg = 0 at the
Jg (∞) = 21 {16/(16 + 3f )}, with f the number of active model input scale. For illustration, Fig. 13 shows the
flavors – that is, the same scaling limit as the quark and evolution of total and orbital angular momentum con-
gluon momentum contributions at infinite Q2 . The Ji tributions in the Cloudy Bag from the model scale up
and Jaffe-Manohar definitions of orbital angular momen- to Q2 = 4 GeV2 . Various phenomenological investi-
tum satisfy the same (LO) QCD evolution equation, so, gations (Mattingly and Stevenson, 1994; Steffens et al.,
at LO, are equal in a model calculation if the glue con- 1995) found that by going beyond leading order QCD
tribution can be set equal to zero at a low-energy input (and including pions in the nucleon wavefunction), the
scale. optimal fit to high-energy scattering data involved taking
To obtain information about the quark “orbital angu- the running coupling αs about 0.6–0.8 at the low energy
lar momentum” Lq we need to subtract the value of the input scale. For this range of αs the scale dependence of
“intrinsic spin” Sq = 21 ∆q measured in polarized deep ∆Σ (in full QCD) through Eq.(15) converges well. (Go-
inelastic scattering from the total quark angular momen- ing to higher orders in the model fits to data and putting
tum Jq . This means that Lq is scheme dependent with in pions raises the model input scale µ0 needed for the cal-
different schemes corresponding to different physics con- culations.) Table V compares the results of lattice calcu-
tent depending on how the scheme handles information lations (Hägler et al., 2008) for up- and down-quark spin
about the axial anomaly, large-kt physics and any possi- and total angular momentum with the Cloudy Bag model
ble “subtraction at infinity” in the dispersion relation for results and the values extracted from QCD fits to hard
g1 . The quark total angular momentum Jq is anomaly exclusive reaction data, GPDs (Goloskokov and Kroll,
free in QCD so that axial anomaly effects occur with 2009), and transverse single spin asymmetries, TMDs
equal magnitude and opposite sign in Lq and Sq . When (Bacchetta and Radici, 2011). The lattice calculation in-
looking at physical observables that are sensitive to OAM volves connected diagrams only (no axial-anomaly con-
and quark spin (with possible axial-anomaly contribu- tribution) plus chiral extrapolation. The QCD fit num-
tion) it will be important to identify which OAM defini- bers are central values modulo (possibly large) system-
tion and which scheme quantity is most relevant to the atic errors from the model functional forms of distribu-

24
 momentum and finite spin-orbit couplings which can be
probed in experiments. The search for orbital angular
momentum has motivated new theoretical and experi-
mental investigations of the three dimensional structure
of the nucleon. Key observables in deeply virtual Comp-
ton scattering (DVCS) and transverse single spin asym-
metries in lepton-nucleon and proton-proton scattering,
and also the large x limit of the down quark helicity dis-
tribution are sensitive to orbital angular momentum in
the nucleon.
Hard exclusive reactions such as DVCS are described
theoretically using the formalism of generalized parton
distributions (GPDs) and probe the three-dimensional
spatial structure of the nucleon, as reviewed in Ji (1998),
FIG. 13 Calculation of the NLO QCD evolution of Ju , Ld , Jd , Goeke et al. (2001) and Diehl (2003). Ji has derived a
Lu in the Cloudy Bag with model input scale Q0 = 0.4 GeV. sum-rule connecting the forward limit of GPDs to infor-
Figure from Thomas et al. (2010), copyright 2010 WSPC. mation about the quark and gluon total angular momen-
tum in the proton (Ji, 1997b). Considerable experimen-
tal and theoretical effort has and continues to be invested
tions used in the fits. There is good convergence of the
aimed at accessing this information.
different theoretical values with “data”. Here, one has
Studies of single spin asymmetries for semi-inclusive
Lu ∼ −Ld ∼ 15% at the scale of typical deep inelastic
meson production in high-energy lepton-nucleon and
measurements.
proton-proton collisions are sensitive to possible spin-
In an alternative approach, the proton spin puzzle has
orbit coupling both in the nucleon and in the final-
also been addressed in the Skyrme model, where baryons
state hadronization process; for a recent review see
emerge as topological solitons in the meson fields at large
Barone et al. (2010a). One studies correlations between
number of colors Nc , and in the chiral quark soliton
the transverse momentum (orbital motion) of partons,
model (ChQSM), where explicit quark degrees of free-
their spin and the spin polarization of the nucleon.
dom are also present in the model. The nucleon’s axial
The theoretical tools are transverse momentum depen-
charges in these models are sensitive to which mesons are
dent (TMD) distributions and fragmentation functions.
included in the model and the relative contribution of a
TMDs probe the three-dimensional transverse momen-
quark source and pure meson component. In an early cal-
(0) tum structure of the nucleon and are associated, in part,
culation Brodsky et al. (1988) found that gA vanishes in
with finite orbital angular momentum.
a particular version of the Skyrme model with just pseu-
Experimental studies of three-dimensional nucleon
doscalar mesons. Finite values of ∆s ∼ −0.08, close to
structure have been pioneered at HERMES and JLab for
the value obtained from inclusive g1 measurements with
(8) GPDs and at COMPASS, HERMES and RHIC for TMDs
good SU(3) assumed for gA are found in the ChQSM in single spin asymmetry measurements. There has also
(Wakamatsu, 2007). been considerable theoretical effort aimed at model and
lattice calculations of these observables.
TABLE V Model, lattice and fit extractions of angular mo- In the rest of this Section we present the theory and
mentum contributions in the proton, quoted for 4 GeV2 (ex- present status of these new GPDs and TMD distribu-
cept GPD at 2 GeV2 ). tions plus spin-orbit coupling in fragmentation and the
prospects for future experiments including key observ-
Cloudy Bag Lattice GPD TMD
ables that will be studied. The aim for experiments
∆u 0.85 ± 0.06 0.82 ± 0.07
should be to focus on observables that have the clean-
∆d −0.42 ± 0.06 −0.41 ± 0.07 est theoretical interpretation with minimal model depen-
Ju 0.30 0.24 ± 0.05 0.24 0.24 dence.
Jd −0.04 0.00 ± 0.05 0.02 0.02 Quark orbital angular momentum in the nucleon may
also be manifest in future measurements of the large x
behavior of the polarized down-quark distribution ∆d/d
and in the ratio of the proton’s spin-flip Pauli form-factor
VII. TRANSVERSE NUCLEON STRUCTURE AND to the Dirac form-factor at large Q2 . These observables
ORBITAL ANGULAR MOMENTUM can be studied with the 12 GeV upgrade of JLab. Va-
lence Fock states with non-zero orbital angular momen-
Confinement induces transverse hadronic scales in the tum induce a logarithmic correction to the QCD count-
nucleon with accompanying finite quark orbital angular ing rules predictions for these observables. Perturbative

25
QCD calculations which take into account orbital angular ement3
momentum give
Z
P+ + −
dy − e−ixP y hp′ |ψ̄α (y)ψβ (0)|piy+ =y⊥ =0
2π
F2 /F1 ∼ (log2 Q2 /Λ2 )/Q2 (28) 
1 −
= γαβ H(x, ξ, t)ū(p′ )γ + u(p)
4

for the ratio of Pauli to Dirac form-factors at large Q2 ′ +µ ∆µ
+E(x, ξ, t)ū(p )σ u(p)
(Belitsky et al., 2003). Form-factor measurements at 2M
JLab (Gayou et al., 2002; Jones et al., 2000) are consis- 
p 1 e
tent with this behavior and also with F2 /F1 ∼ 1/ Q2 + (γ5 γ − )αβ H(x, ξ, t)ū(p′ )γ + γ5 u(p)
4
for Q2 between 4 and 6 GeV2 , in contrast to the count- 
e ′ ∆+
ing rules prediction without orbital angular momentum +E(x, ξ, t)ū(p )γ5 u(p) .
F2 /F1 ∼ 1/Q2 (Lepage and Brodsky, 1980). One also 2M
finds a logarithmic correction to the leading large-x be- (29)
havior of the negative-helicity spin-dependent quark dis-
tributions ∼ (1 − x)5 log2 (1 − x) (Avakian et al., 2007).
An interesting prediction here is that ∆d/d should cross The physical interpretation of the generalized parton
zero and become positive at a value x ∼ 0.75 when this distributions (before worrying about possible renormal-
term is included, in contrast to the model expectation ization effects and higher order corrections) is the follow-
that crossing occurs at x ∼ 0.5 when this orbital an- ing. Expanding out the quark field operators in Eq. (29)
gular momentum effect is neglected. An accurate mea- in terms of light-cone quantized creation and annihilation
surement of ∆d/d at x close to unity would be very in- operators one finds that for x > ξ (x < ξ) the GPD is
teresting if this quantity can be extracted free of uncer- the amplitude to take a quark (anti-quark) of momen-
tainties from nuclear effects (Kulagin and Melnitchouk, tum k − ∆/2 out of the proton and reinsert a quark
2008a,b) in the neutron structure functions measured (anti-quark) of momentum k + ∆/2 into the proton some
from deuteron or 3 He targets. distance along the light-cone to reform the recoiling pro-
ton. In this region the GPD is a simple generalization
of the usual parton distributions studied in inclusive and
semi-inclusive scattering which are formally defined via
light-cone correlation functions – see e.g. Bass (2005). In
the remaining region −ξ < x < ξ the GPD involves tak-
A. Generalized parton distributions ing out (or inserting) a q q̄ pair with momentum k − ∆/2
and −k − ∆/2 (or k + ∆/2 and −k + ∆/2) respectively.
Note that the GPDs are interpreted as probability am-
Observables in deeply virtual Compton scattering and plitudes rather than densities. The non-forward matrix
deeply virtual meson production are sensitive to infor- elements give access to transverse degrees of freedom in
mation about total angular momentum in the nucleon. the nucleon.
In these hard exclusive reactions a deeply virtual pho-
ton impacts on a nucleon target and a real photon or In the forward limit the GPDs H and H̃ are related to
a meson is liberated from the struck nucleon into the the parton distributions studied in deep inelastic scatter-
final state, leaving the target nucleon intact. These pro- ing
cesses can be described using the formalism of general-
ized parton distributions (GPDs), involving the Fourier
H(x, ξ, t)|ξ=t=0 = q(x)
transforms of off-diagonal nucleon matrix elements (Ji,
1997a,b; Mueller et al., 1994; Radyushkin, 1997). e
H(x, ξ, t)|ξ=t=0 = ∆q(x) (30)

The important kinematic variables are the virtuality of

the hard photon Q2 , the momenta p−∆/2 of the incident whereas the GPDs E and Ẽ have no such analogue. Inte-
proton and p + ∆/2 of the outgoing proton, the invari- grating over x the first moments of the GPDs are related
ant four-momentum transferred to the target t = ∆2 , the
average nucleon momentum P , the generalized Bjorken
variable k + = xP + and the light-cone momentum trans-
ferred to the target proton ξ = −∆+ /2p+. In the Bjorken
limit, ξ is related to Bjorken xB via ξ = xB /(2 − xB ). 3 We work in the light-cone gauge A+ = 0 (so the path-ordered
The generalized parton distributions are defined as the gauge-link needed for gauge-invariance in the correlation function
light-cone Fourier transform of the point-split matrix el- becomes trivial and set equal to one).

26
 electron
to the nucleon form-factors k k'
Z +1 q'
dxH(x, ξ, t) = F1 (t) + +
−1 p p'
proton
Z +1
DVCS Bethe-Heitler
dxE(x, ξ, t) = F2 (t)
−1
Z +1 FIG. 14 The leading DVCS and Bethe-Heitler processes.
e
dxH(x, ξ, t) = GA (t)
−1
Z +1
e ξ, t) = GP (t). quarks, while the neutron (via a deuteron or 3 He target)
dxE(x, (31) is most sensitive to Jd . The experiments require high
−1
luminosity to measure the small exclusive cross-section,
Here F1 and F2 are the Dirac and Pauli form-factors of plus measurements over a wide range of kinematics in
the nucleon, and GA and GP are the axial and induced- Q2 , x and t (since sum-rule tests and evaluations depend
pseudoscalar form-factors respectively. (The dependence on making reliable extrapolations into unmeasured kine-
on ξ drops out after integration over x.) matics). In particular, one has to extrapolate the GPDs
GPDs contain vital information about quark total an- to t = 0. One also needs reliable theoretical technology
gular momentum in the nucleon. Ji’s sum-rule (Ji, 1997b) to extract the GPDs from the measured cross-sections.
relates Jq to the forward limit of the second moment in GPDs appear in the amplitudes for DVCS and hard ex-
x of the spin-independent quark GPDs clusive meson production as convolutions with the hard
Z   scattering coefficient and only these so-called Comp-
1 +1
Jq = dxx H q (x, ξ, t = 0)+E q (x, ξ, t = 0) . (32) ton form factors (CFF) are experimentally accessible.
2 −1 Measuring photon and also meson production in the fi-
nal state gives access to different flavor combinations of
The gluon “total angular momentum” could then be ob-
GPDs, like in semi-inclusive DIS. However, meson pro-
tained through the equation
duction is more sensitive to QCD radiative corrections
X 1 and power corrections in 1/Q, and reliable theoretical de-
Jq + Jg = . (33) scription requires larger values of Q2 compared to DVCS.
q
2
Channels particularly sensitive to gluons in the proton
In principle, it could be extracted from precision are hard exclusive vector meson production where both
measurements of the Q2 dependence of DVCS at quark and gluon GPDs appear at lowest order in the
next-to-leading-order accuracy where the quark GPDs strong coupling constant. There is a challenging program
mix with glue under QCD evolution or via Jg = to disentangle the GPDs from the formalism and to undo
R
1 +1 g g the convolution integrals which relate the GPDs to mea-
2 −1 dxx{H (x, ξ, t = 0) + E (x, ξ, t = 0)} if the gluon sured cross-sections. In practice, the approach used is to
GPD can be accurately measured in more direct ex-
constrain models of GPDs against experimental data in
periments. In these equations Jq and Jg are defined
measured kinematics. These models are then integrated
through the proton matrix elements of the angular mo-
to obtain the Ji moments of Ju and Jd , which may then
mentum operators in Eq.(26). If information about Jq
be compared to the predictions of QCD inspired model
can be extracted from experiments, then the correspond-
plus lattice calculations – see Table V.
ing quark “orbital angular momentum” can be deduced
by subtracting the value of the quark spin content ∆q In the rest of this discussion we focus on deeply virtual
extracted from deep inelastic scattering and polarized Compton scattering.
proton-proton collisions. 4
Experimental attempts to access Jq via Eq.(32) require
accurate determination of the two unpolarized GPDs H 1. Deeply virtual Compton scattering
and E. Measurements from a proton target are more sen-
sitive to Ju , the total angular momentum carried by up Measurements of hard exclusive processes are much
more challenging than traditional inclusive and semi-
inclusive scattering experiments. These exclusive pro-
cesses require a difficult full reconstruction of final state
4 We note recent discussion of a J=0 fixed pole contribution to particles and their cross-sections are usually small, de-
DVCS (Brodsky et al., 2009a,b), which corresponds to a xδ(x) manding high luminosity machines.
term in the GPD H and affects the 1/x moment of this GPD
though not the sum-rules in Eqs.(31) and (32). The same
DVCS experiments have to be careful to choose the
fixed pole also contributes to the Schwinger term sum-rule kinematics so as not to be saturated by a large Bethe-
for the 1/x moment of the longitudinal structure function FL Heitler (BH) background where the emitted real photon
(Broadhurst et al., 1973). is radiated from the incident lepton rather than from the

27
proton target – see Fig. 14.
Most of the DVCS program so far has focused on the ZEUS
W = 104 GeV
DVCS-BH interference term. Use of different combina- Q2 = 3.2 GeV2
tions of beam and target polarization plus changing the 10
electric charge of the incident lepton beam gives maxi-

dσDVCS/dt (nb/GeV2)
mum access to most combinations of DVCS observables.
Measurement of the DVCS-BH interference term – see
Eq.(34) below – allows one to measure not only the size 1
of the DVCS amplitude but also its phase – that is, it
gives separate information about the real and imaginary
H1
parts of the Compton form factors.
−1 W = 82 GeV
Pioneering measurements of DVCS have been per- 10 Q2 = 8 GeV2
formed at DESY (HERMES, H1 and ZEUS) and JLab Q2 = 15.5 GeV2
(Hall A and Hall B), which complement each other in the Q2 = 25 GeV2
covered kinematic phase space and the extracted observ-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ables. −t (GeV2)
The experiments use different measurement techniques
to access exclusive reactions. The HERA collider experi- FIG. 15 The t dependence of the DVCS cross-section for sev-
ments at DESY, H1 and ZEUS, as well as CLAS (Hall B eral values of Q2 as measured by H1 and ZEUS. The curves
at JLab) have the advantage of nearly hermetic spectrom- are results of fits of the form e−b|t| with b being related to the
transverse extension of partons in the proton at a given x and
eters, whereas the fixed target experiments HERMES
Q2 (see text). The inner error bar represents the statistical
and JLab Hall A had to deal with the restrictions caused uncertainty; the full bar the quadratic sum of statistical and
by incomplete event reconstruction due to their forward systematic uncertainties.
spectrometers. Hall A and HERMES successfully em-
ployed the so-called missing mass technique together
with careful background subtraction (Airapetian et al.,
2008b; Camacho et al., 2006). For Hall A the low beam transverse
R 2 momentum
p shift in Eq. (29)) F (b, x, Q2 ) ∝
−ib∆T
energy and high resolution spectrometer allowed one to d ∆T exp dσ/dt (Burkardt, 2003; Diehl, 2002).
resolve pure elastic scattering from associated produc- The impact parameter provides an estimate of the trans-
tion with an excited nucleon in the final state. The verse extension of the partons probed during the hard
latter contribution was treated as part of the signal in process. While DVCS data provide information about
HERMES results. Very recently, beam-spin asymme- the transverse distribution of quarks in the proton, data
tries for a pure DVCS sample have also been reported on exclusive heavy vector meson production (J/Ψ or Υ)
by HERMES (Airapetian et al., 2012c). In the fixed tar- describe the transverse distribution of glue at specific val-
get experiments the spin-dependent DVCS cross-sections ues of x.
have been explored using longitudinally polarized lep- The full DVCS cross-section reads (Diehl and Sapeta,
ton beams with longitudinally (JLab and HERMES) 2005)
and transversely (HERMES) polarized targets. HER-
MES also took advantage of the available different beam dσ(ℓp → ℓγp) ∼
charges. BH I DV CS
dσUU + eℓ dσUU + dσUU
JLab experiments focus on kinematics dominated by BH I DV CS
+ Pℓ SL dσLL + eℓ Pℓ SL dσLL + Pℓ SL dσLL
valence quarks. Data from Hall A suggest leading twist-
BH I DV CS
2 dominance of DVCS even at the relatively low Q2 of + Pℓ ST dσLT + eℓ Pℓ ST dσLT + Pℓ ST dσLT
1.5–2.3 GeV2 (Camacho et al., 2006). I
+ eℓ Pℓ dσLU DV CS
+ Pℓ dσLU
The HERA collider experiments H1 and ZEUS mea- I DV CS
+ eℓ SL dσUL + SL dσUL
sured the DVCS cross-section close to the forward direc-
I DV CS
tion with ξ < 10−2 , integrated over its azimuthal depen- + eℓ ST dσUT + ST dσUT .
dence, in an xB range where two-gluon exchange plays a (34)
major role in addition to the leading order quark-photon
scattering process. Figure 15 shows the cross-section Here the first subscript U, L on dσ indicates an unpo-
differential in t for different ranges in Q2 measured larized or longitudinally polarized lepton beam and the
by H1 (Aaron et al., 2008) and ZEUS (Chekanov et al., second subscript U, L, T denotes an unpolarized, longitu-
2009). The data are well described by the exponential dinally or transversely polarized proton target; Pℓ is the
behavior dσ/dt ∝ e−b|t| . The distribution of partons in lepton beam polarization; SL and ST denote longitudinal
the transverse plane is then obtained from this depen- and transverse proton polarization. Of particular inter-
dence by a Fourier transform with respect to ∆T (the est is also the dependence on the sign of the charge of the

28
 the charge asymmetry and AXY are the polarization-
TABLE VI Linear combinations of Compton form factors
(CFF) in the DVCS-BH interference terms. Here, F1 and
dependent asymmetries with X and Y indicating the
F2 are the electromagnetic form factors. Subleading terms beam and target polarization, respectively, which could
not shown are suppressed in a wide range of kinematics. be longitudinal (L) or transverse (T ). The subscript I in-
dicates an extraction of the pure interference term. The
Target polarization CFF combination measured asymmetries are subject to a harmonic expan-
unpolarized / charge e − t 2 F2 E
F1 H + ξ(F1 + F2 )H sion with respect to the azimuthal angle(s) as given by
4m
e + ξ(F1 + F2 )H − . . . the superscript of AXY in the Figure. These data de-
longitudinal F1 H
noted by squares in Fig. 16 show results extracted from
transverse ∝ sin(φ − φS ) F2 H − F1 E + . . . a DVCS sample with kinematically complete event re-
e − F1 ξ E
transverse ∝ cos(φ − φS ) F2 H e + ... construction (Airapetian et al., 2012c). The dependence
on the kinematic variables t, Q2 , and xB was explored
for each observable.
An example of the high statistics data from JLab is
beam lepton eℓ , which allows one to disentangle contribu-
shown in Fig. 17 for the beam-spin asymmetry ALU
tions from the pure interference term and the DVCS term
measured fully differentially by CLAS (Girod et al.,
as pioneered in Airapetian et al. (2007b, 2008b). The
2008). The presented data contain an admixture of the
various cross-section terms depend on the azimuthal an-
Asin φ sin φ
LU,I and ALU,DV CS contributions from the interfer-
gle φ between the lepton scattering plane and the photon
ence and pure DVCS terms, which cannot be separated
production plane, and, in case of a transversely polarized
here. CLAS also provides measurements of Asin φ
UL and
proton target, also on the azimuthal angle φS between sin 2φ
the lepton plane and the transverse target spin vector. AUL (Chen et al., 2006).
Equation (34) indicates the large variety of observables
accessible with polarized beams and/or targets.
As an example for the azimuthal dependence of the 2. The quest for orbital angular momentum and GPD
parametrizations
cross-section we give the expression for the interference
term for the case of an unpolarized target and polarized
beam (Belitsky et al., 2002) Of the two GPDs H and E entering Ji’s sum-rule,
! Eq.(32), measurements with unpolarized targets but
X3 X2
I I
longitudinally polarized beams and also beam-charge
I∝ −eℓ cn cos(nφ) + λ sn sin(nφ) . (35) asymmetries are mainly sensitive to H. As indicated
n=0 n=1 in Table VI, transverse target polarization provides
The proportionality involves a kinematic factor and the kinematics-wise unsuppressed access to E. The GPD
lepton propagators of the BH process; λ is the helicity of E is essentially unknown. In contrast to H, it is not
the incoming lepton. The Fourier coefficients cIn provide related to a deep inelastic parton distribution in the for-
an experimental constraint on the real part of the Comp- ward limit; E describes helicity flip at the proton ver-
ton form factor and sIn on the imaginary part. Their tex and requires finite orbital angular momentum in the
relation to linear combinations of Compton form factors nucleon. Contributions from E to most DVCS observ-
and hence to the respective GPDs is listed in Table VI. ables are damped by kinematic factors ∼ |t|/Mp2 , with
A specific Fourier coefficient can be accessed experimen- the average |t| value generally much smaller than 1 GeV2
tally by weighting the cross-section with the respective in the experiments. To access E requires DVCS and/or
azimuthal modulation. vector meson production asymmetry measurements with
The DVCS-BH interference term was extracted by transversely polarized nucleon targets. It may also be
varying the electric charge of the incident lepton (HER- accessed through the beam polarization dependence of
MES) and studying polarization observables, varying the DVCS with a neutron target because of the different
beam or target helicity (JLab and HERMES). JLab ex- size of the form-factors for the neutron (Belitsky et al.,
periments have focused on studying their accessible ob- 2002). Measurements have been performed already for all
servables fully differentially. HERMES explored the ad- channels (Adolph et al., 2012a; Airapetian et al., 2008b,
vantages of using simultaneously polarization and charge 2009a; Mazouz et al., 2007). Despite the lack of pre-
observables to cleanly isolate the interference term and cision for these observables, attempts to extract in-
obtained the most complete set of DVCS observables formation about quark total angular momentum have
measured so far providing access to all interference terms been performed by fitting theoretical models of GPDs
listed in Eq. (34). to the DVCS measurements (Airapetian et al., 2008b;
Figure 16 shows a summary of the HERMES DVCS Mazouz et al., 2007). Although this analysis is very
measurements with polarized proton and deuterium tar- model dependent, the results agree (surprisingly) well
gets at their average kinematics (Airapetian et al., with model and lattice expectations, e.g. the calcu-
2008b, 2009c, 2010b,d, 2011a,b, 2012b,c). Here, AC is lations reported in Table V. For example, within the

29
 Hydrogen
a(t) Q2 = 2.8 Q2 = 3.3
HERMES DVCS Deuterium 0.3 0.3
x B = 0.45 0.3
x B = 0.46
Hydrogen Pure 0.2 0.2 0.2
cos(0 φ)
AC 0.1 0.1 0.1 Q2 = 3.7
cos φ
x B = 0.46
AC 0 0 0
cos(2 φ) 2 2
AC Q = 2.3 Q = 2.7 Q2 = 3.0
0.3 0.3
x B = 0.35 0.3
x B = 0.36 x B = 0.36
cos(3 φ)
AC 0.2 0.2 0.2
sin φ
A LU 0.1 0.1 0.1
sin (2 φ)
A LU 0 0 0
sin φ
A LU,I Q2 = 1.7 Q2 = 1.9 Q2 = 2.2
0.3 0.3
x B = 0.25 0.3
x B = 0.25 x B = 0.25
sin φ
A LU,DVCS 0.2 0.2 0.2
sin(2 φ)
A LU,I 0.1 0.1 0.1
sin( φ − φs )
A UT,I 0 0 0
sin( φ − φs)
A UT,DVCS Q2 = 1.2 Q2 = 1.4 Q2 = 1.6
0.3 0.3
x B = 0.13 0.3
x B = 0.17 x B = 0.18
sin( φ − φs) cos φ
A UT,I 0.2 0.2 0.2
cos( φ − φs) sin φ
A UT,I 0.1 0.1 0.1
cos( φ − φs ) 0 0 0
A LT,I
0 0.5 1 1.5 0 0.5 1 1.5 0 0.5
cos( φ − φs )
A LT,BH+DVCS
−t1(GeV
1.5 2
)
sin( φ − φs) sin φ
A LT,I FIG. 17 The leading beam-spin asymmetry amplitude
cos( φ − φs) cos φ
A LT,I a(t) = Asin
LU
φ
differential in t, x and Q2 as measured by
sin φ CLAS, from Girod et al. (2008). An earlier CLAS mea-
A UL
sin(2 φ)
surement (Stepanyan et al., 2001) is indicated by the square.
A UL The open triangles represent the cross-section data from Hall
cos(0 φ)
A LL A (Camacho et al., 2006). Error bars are statistical errors
cos φ
A LL
only.
cos(2 φ)
A LL

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3

Amplitude Value not directly accessible, as x represents a mute variable
which is integrated over. In the interpretation of DVCS
FIG. 16 Overview of all DVCS azimuthal asymmetry ampli- observables one has to deal with complex amplitudes;
tudes measured at HERMES with proton and deuterium tar- the GPDs are embedded in the Compton form factors
gets, given at the average kinematics. The inner error bar rep- which relate to the measured cross-sections. Despite
resents the statistical uncertainty; the full bar the quadratic these complications and the early stage of global fitting
sum of statistical and systematic uncertainties.
for GPDs, many results have been obtained in recent
years fitting to different hard exclusive scattering data.
Interested readers are referred to the original literature
in Vanderhaeghen et al. (1999), Goloskokov and Kroll
model of Vanderhaeghen et al. (1999) JLab Hall A DVCS (2008), Guidal (2010) Kumericki and Mueller (2010) and
measurements from the neutron were interpreted to give Goldstein et al. (2011). This phenomenology is comple-
Jd + Ju /5.0 = 0.18 ± 0.14(expt.) (Mazouz et al., 2007) mented by progress in lattice QCD calculations of GPD
whereas HERMES results from the proton gave Ju + moments (Brommel et al., 2007; Göckeler et al., 2007;
Jd /2.8 = 0.49 ± 0.17(expt.) (Airapetian et al., 2008b) in Hägler et al., 2008).
the same model.
To go further and perform global fits of GPDs to hard
exclusive observables one faces several challenging theo- B. Transversity, transverse-momentum-dependent
retical issues. Parameterizations of GPDs have to deal distributions and fragmentation functions
with two longitudinal variables instead of one plus the t
dependence of DVCS. It is also not yet known whether Striking single spin asymmetries associated with spin-
relatively simple and smooth functions like those used momentum correlations (expected with parton orbital
in QCD fits to deep inelastic data are sufficient to de- angular momentum) were first observed in the 1970s.
scribe GPDs. A reliable parameterization of GPDs might Using a 12 GeV polarized proton beam from the Ar-
therefore require a larger number of moments than em- gonne National Laboratory Zero Gradient Synchrotron
ployed in usual QCD parton descriptions. In addition, on a fixed target, up to 40% more positive pions
the dependence of the functions on the variable x is were produced left of the beam when the beam was

30
polarized up, and up to 20% more negative pions tributions do not survive integration over kt . They de-
were produced to the right of the beam (Klem et al., scribe correlations between the quark transverse momen-
1976). These measurements were confirmed by simi- tum with the spin of the quark and/or the spin of the
lar experiments (Antille et al., 1980; Apokin et al., 1990; parent nucleon, viz. spin-orbit correlations. The three
Dragoset et al., 1978; Saroff et al., 1990), but it was not TMDs denoted by h describe the distribution of trans-
until the 1990s that a theoretical framework was devel- versely polarized partons. They are chiral-odd distribu-
oped to attempt interpreting them. tions and appear only in observables involving two chiral-
Single-spin asymmetries have now also been observed odd partners, such as Drell-Yan processes (two chiral-odd
in proton-proton collisions at RHIC, where they reach parton distributions) or SIDIS (chiral-odd parton distri-
up to ∼ 40%, and in lepton-nucleon collisions at COM- bution and the Collins fragmentation function discussed
⊥
PASS, HERMES and JLab, where they are typically below). The three distributions f1T (the Sivers distri-
5 − 10%. Single-spin asymmetries for hadron produc- bution), h⊥ 1 (the Boer-Mulders distribution) and h⊥ 1T
tion from transversely polarized targets tell us about (pretzelosity) require orbital angular momentum in the
spin-orbit coupling in the nucleon and/or in the fragmen- nucleon since they involve a transition between initial
tation process. Transverse-momentum-dependent distri- and final nucleon states whose orbital angular momen-
butions simultaneously describe the dependence on lon- tum differ by ∆Lqz = ±1 (Sivers and Boer-Mulders) or
gitudinal momentum fraction of the parton within the ∆Lqz = ±2 (pretzelosity). The “worm-gear” functions
parent hadron as well as the parton’s transverse momen- h⊥ ⊥
1L and g1T link two perpendicular spin directions and
tum. Similarly, transverse-momentum-dependent frag- are also connected to quark orbital motion inside nucle-
mentation functions describe the dependence on longitu- ons.
dinal momentum fraction of the produced hadron with Transverse momentum distributions have been stud-
respect to the scattering parton as well as the hadronic ied most in semi-inclusive DIS experiments where they
transverse momentum with respect to the jet axis. appear in combination with the usual unpolarized frag-
mentation function D(z, pt ) or, in case of the chiral-odd
TMD distributions, with a chiral-odd Collins fragmen-
TABLE VII Leading-twist transverse-momentum dependent tation function H1⊥ (z, pt ) discussed in Section VII.B.2.
parton distributions. U , L, and T stand for unpolarized, One measures the azimuthal distribution of the produced
longitudinally polarized, and transversely polarized nucleons
(rows) and quarks (columns) respectively.
final-state hadron with respect to the virtual-photon axis.
Each species of TMD comes with a different angular mod-
ulation in the semi-inclusive cross-section allowing it to
❅ q U L T be projected out to yield information about the differ-
N❅
U f1 h⊥
ent spin-momentum correlations (Bacchetta et al., 2004).
1
All these leading-twist TMDs have been measured in
L g1 h⊥
1L
⊥ ⊥
semi-inclusive DIS over the last decade. However, sev-
T f1T g1T h1 h⊥ 1T
eral have been the focus of more intense studies and we
focus on those here.
The different modulation combinations are listed in
We next introduce these distributions and frag- Table VIII together with present
√ experimental measure-
mentation functions, and discuss their phenomenol- ments. Results quoted at s = 18 GeV are from COM-
ogy. In QCD there are eight leading-twist quark PASS, 7.4 GeV from HERMES and 3.5 GeV from JLab.
TMDs. These are listed in Table VII and discussed Here φ is the angle between the lepton direction and the
in Mulders and Tangerman (1996) and Bacchetta et al. plane spanned by the exchanged photon and tagged final-
(2007). The three distributions highlighted in boldface state hadron, e.g. a high-energy meson; φS is the angle
survive integration over transverse momentum kt . These between the lepton direction and the transverse nucleon
yield the unpolarized parton distribution, f1 (x, kt ), the target spin. The convolution is taken over the involved
spin-dependent parton distribution g1 (x, kt ) and the transverse momenta of the quark and the hadron pro-
transversity distribution h1 (x, kt ). The other five dis- duced in the fragmentation process.

When one projects out the terms with different az- from CLAS reveal a clear signal for the worm-gear-1 dis-
imuthal angular dependence summarized in Table VIII, tribution; there is some hint for a non-zero worm-gear-2
the COMPASS, HERMES and JLab data suggest that distribution (with low significance) and (so far) no sig-
the Sivers, Collins and Boer-Mulders effects are all nificant signal for pretzolosity in the proton. For the
present in the proton target data – see below. JLab data deuteron target, there is evidence for a Boer-Mulders ef-

31
TABLE VIII Experimental access to the leading twist TMD distributions in SIDIS with unpolarized (U), longitudinally (L)
or transversely polarized (T) beam (modulation first subscript) and/or target (modulation second subscript).
√
Modulation Combination s Target Observed Measurement
Distribution name GeV type hadron types
sin(φ + φS )U T h1 ⊗ H1⊥ 18 d h± , π ± , K ± , K 0 Ageev et al. (2007) and Alekseev et al. (2009a)
Transversity p h± Adolph et al. (2012b) and Alekseev et al. (2010b)
p π± , K ± prelim. Pesaro (2011)
7.4 p π , π0, K ±
±
Airapetian et al. (2005b, 2010a)
3.5 n π± Qian et al. (2011)
⊥
sin(φ − φS )U T f1T ⊗ D 18 d h , π , K±, K0
± ±
Ageev et al. (2007) and Alekseev et al. (2009a)
Sivers p h± Adolph et al. (2012c) and Alekseev et al. (2010b)
p π , K±
±
prelim. Pesaro (2011)
7.4 p π , π0, K ±
±
Airapetian et al. (2005b, 2009b)
3.5 n π± Qian et al. (2011)
⊥ ⊥
cos(2φ)U U h1 ⊗ H1 18 d h± prelim. Sbrizzai (2011)
Boer-Mulders 7.4 p π± , K ± Airapetian et al. (2012a)
3.5 n π+ Osipenko et al. (2009)
⊥ ⊥
sin(3φ − φS )U T h1T ⊗ H1 18 d h± prelim. Kotzinian (2007)
Pretzelosity 18 p h± prelim. Parsamyan (2011)
7.4 p π± , K ± prelim. Pappalardo (2010)
⊥ ⊥
sin(2φ)U L h1L ⊗ H1 18 d h± Alekseev et al. (2010a)
±
Worm-gear 1 7.4 p π , π0 Airapetian et al. (2000b, 2001)
±
d π , π0, K + Airapetian et al. (2003)
3.5 n π± , π0 Avakian et al. (2010)
⊥
cos(φ − φS )LT g1T ⊗D 18 d h± prelim. Kotzinian (2007)
Worm-gear 2 18 p h± prelim. Parsamyan (2011)
7.4 p π , π0, K ±
±
prelim. Pappalardo and Diefenthaler (2011)
3.5 n π± Huang et al. (2012)

fect from COMPASS and HERMES. The Sivers, Collins, in the nucleon, though the mapping from Sivers observ-
worm-gear and pretzelosity effects are all consistent with ables to quark (and gluon) orbital angular momentum is
zero in the deuteron target data. The Collins and Sivers (so far) model dependent with present theoretical tech-
effects observed in the proton data therefore contain a nology.
predominant isovector contribution. The Sivers distribution has the interesting property
We next focus on the Sivers, Boer-Mulders and Collins that it is odd under time reversal. Due to this fea-
effects. ture, such a correlation was believed to be forbidden
for more than a decade. Then Brodsky et al. (2002a,b)
showed that, with initial- or final-state interactions, the
1. The Sivers and Boer-Mulders TMD distributions Sivers effect could be non-zero in QCD processes. Final-
state interactions in SIDIS can generate the azimuthal
The Sivers distribution was first proposed in Sivers asymmetry before the quark fragments into hadrons.
(1990) in an attempt to explain the large transverse sin- Shortly afterwards, Collins (2002) realized that initial-
gle spin asymmetries observed in the 1970s and 1980s. It state color interactions in the case of Drell-Yan and final-
describes the correlation between the transverse momen- state interactions in the case of SIDIS would lead to
tum kt of the struck quark and the spin S and momentum a process-dependent sign difference in the Sivers dis-
p of its parent nucleon tribution. SIDIS measurements (Adolph et al., 2012c;
S · (kt × p̂) Airapetian et al., 2005b, 2009b; Alekseev et al., 2010b;
fq/p↑ (x, kt ) = f1q (x, kt2 ) − f1t
⊥q
(x, kt ) . (36) Pesaro, 2011; Qian et al., 2011), suggest sizable asymme-
M
tries at the level of about 5 − 10% for a proton and a neu-
The kt dependence means that the Sivers distribution is tron target, while Drell-Yan measurements are planned
sensitive to non-zero parton orbital angular momentum for the future.

32
 0.1 π+ HERMES plitude for π + was also recently reported by JLab Hall
π−
A (Qian et al., 2011) for measurements with a 3 He (neu-
sin(φ − φS)

0.05 tron) target. In that data a negative Sivers amplitude for

π + was found which independently supports a d-quark
A UT

0 Sivers distribution opposite in sign to the u-quark one.

10 −1 0.2 0.4 0.6 0.5 1

x z p Th (GeV) The Boer-Mulders distribution (Boer and Mulders,
1998) describes the correlation between transversely po-
FIG. 18 Sivers amplitudes for charged pions measured by larized quarks in an unpolarized nucleon and the quarks’
HERMES with a proton target; from Airapetian et al. transverse momentum, sq · (kt × p̂), where sq denotes
(2009b). The Sivers amplitudes for K + (not shown here) the spin of the quark and might hence yield unexpected
appear to be nearly twice as large as those for π + . The inner
error bar represents the statistical uncertainty; the full bar spin effects even in an unpolarized nucleon. It is similar
the quadratic sum of statistical and systematic uncertainties. to the Sivers distribution in that it is T -odd. However,
it is also chiral-odd and hence must be probed in con-
junction with a second chiral-odd function. For Drell-
Yan production, the second function is a Boer-Mulders
ApSiv

positive hadrons COMPASS 2010 proton data

negative hadrons
distribution in the second incident hadron. For SIDIS,
0.05
the Collins fragmentation function described below is in-
0 volved. Like the T -odd Sivers distribution, the Boer-
−0.05
Mulders distribution is also expected to change sign be-
tween Drell-Yan production and SIDIS. Future experi-
−0.1 mental effort is planned to test this QCD prediction.
−2 −1
10 10 x 0.5 z 1 0.5 1 phT (GeV)

FIG. 19 Sivers amplitudes for unidentified charged hadrons

Azimuthal distributions sensitive to the Boer-Mulders
measured by COMPASS with a proton target (Adolph et al., distribution were originally measured in Drell-Yan ex-
2012c). The hadron yield is dominated by pions. The bands periments (Conway et al., 1989; Falciano et al., 1986;
indicate the systematic uncertainties. Guanziroli et al., 1988; Zhu et al., 2007, 2009). The
SeaQuest fixed-target Drell-Yan experiment currently
underway at Fermilab (Reimer, 2007) expects to be sen-
sitive to the Boer-Mulders distribution at high x. In
A qualitative picture of the Sivers distribution can al- SIDIS the distinctive pattern of Boer-Mulders modula-
ready be deduced from SIDIS measurements. The non- tions for oppositely charged pions and for pions and kaons
zero amplitudes shown in Figs. 18 and 19 were ob- was recently reported by HERMES (Airapetian et al.,
tained with a proton target. For HERMES the ampli- 2012a). The amplitudes for kaons are larger in mag-
tude includes a kinematic factor depending on the ratio nitude than the amplitudes for pions. The amplitudes
of transverse-to-longitudinal photon flux, which in the for the negative pions have the opposite sign to the
COMPASS data is divided out. Since scattering off u amplitudes for negative kaons. This hints at a signif-
quarks dominates these data due to the quark charge icant contribution from sea quarks, in particular from
factor, the positive Sivers amplitudes for π + (and h+ , strange quarks. Measurements of the Boer-Mulders am-
which is dominated by the pion yield), suggest a large plitudes were also reported by COMPASS for uniden-
and negative Sivers function for up quarks. The van- tified hadrons (Sbrizzai, 2011) and by CLAS for pi-
ishing amplitudes for π − (h− ) require cancellation ef- ons (Osipenko et al., 2009). The interpretation of the
fects, e.g. from a d quark Sivers distribution opposite in SIDIS amplitudes for the Boer-Mulders distribution, is,
sign to the u quark Sivers distribution. These cancella- however, complicated by contributions from the twist-
tion effects between Sivers distributions for up and down 4 Cahn effect (Cahn, 1978, 1989) which have been
quarks are supported by the vanishing Sivers amplitudes estimated to be sizable even at COMPASS kinemat-
extracted from deuteron data by the COMPASS Collab- ics (Anselmino et al., 2007b). The Cahn effect accounts
oration (Ageev et al., 2007; Alekseev et al., 2009a). An for the parton intrinsic transverse momenta in the target
interesting facet of the HERMES data is the magnitude nucleon and the fact that produced hadrons might ac-
of the K + amplitude, which is nearly twice as large as quire transverse momenta during the fragmentation pro-
that of π + (Airapetian et al., 2009b). Again, on the ba- cess. Theoretical estimates of the Boer-Mulders effect
sis of u quark dominance, one might naively expect that are still plagued by large uncertainties, mainly related to
the π + and K + amplitudes should be similar. Their dif- the insufficient knowledge of the transverse-momentum
ference in size may thus point to a significant role of dependence of the unpolarized distribution f1 (x, kt ) and
other quark flavors, e.g. sea quarks. A sizable Sivers am- fragmentation function D(z, pt ).

33
A12
HERMES

sin(φ + φS)
0.2 < z1 < 0.3 0.3 < z1 < 0.5 π+
0.2 0.05
AUL

A UT
AUC 0
0.1
−0.05
π
−

0 10 −1 0.2 0.4 0.6 0.5 1

x z p Th (GeV)
A12

0.5 < z1 < 0.7 0.7 < z1 < 1 FIG. 21 Collins amplitudes for charged pions measured
0.2 by HERMES with a proton target; from Airapetian et al.
(2010a). The inner error bar represents the statistical un-
certainty; the full bar the quadratic sum of statistical and
0.1 systematic uncertainties.

0
for HERMES and COMPASS respectively. (Note that
0.2 0.4 0.6 0.8 0.4 0.6 0.8 COMPASS uses a definition of the Collins angle which
z2 z2 results in Collins amplitudes with opposite sign to the
“Trento convention” of Bacchetta et al. (2004) used by
FIG. 20 Collins asymmetry for the double ratios of like-sign HERMES, JLab and commonly in theoretical papers).
(L), unlike-sign (U) and any charged (C) pion pairs from
There is excellent agreement between the measurements
Belle (Seidl et al., 2008). AU L and AU C are sensitive to dif-
ferent combinations of the favored and unfavored Collins frag- in similar kinematics. One finds the striking observation
mentation functions. The bands indicate the systematic un- that the Collins amplitude for π − is of similar size to π +
certainties. production but comes with opposite sign. This hints at
an unfavored Collins function of similar size and opposite
sign than the favored one, a situation very different from
that observed with unpolarized fragmentation functions.
2. The Collins TMD fragmentation function
ApColl

positive hadrons
COMPASS 2010 proton data
The Collins TMD fragmentation function describes a negative hadrons

0.05
spin-momentum correlation in the hadronization process,
sq · (kq × pt ), with a hadron produced in fragmentation 0
having some transverse momentum pt with respect to the −0.05
momentum direction k of a transversely polarized frag-
−0.1
menting quark with spin sq (Collins, 1993; Collins et al.,
−2 −1
1994). The Collins fragmentation function has been 10 10 x 0.5 z 1 0.5 1 phT (GeV)
investigated in semi-inclusive lepton-nucleon scattering
and e+ e− annihilation. The magnitude of the effect is ap- FIG. 22 Collins amplitudes for unidentified charged hadrons
proximately 5–10%, like that found for the Sivers asym- measured by COMPASS with a proton target (Adolph et al.,
metries. 2012b). The hadron yield is dominated by pions. Note that a
different definition of the Collins angle results in amplitudes
For e+ e− annihilation the chiral-odd Collins fragmen- with the opposite sign compared to other measurements. The
tation function enters with a second Collins function in bands indicate the systematic uncertainties.
the opposing jet. The Collins function has been measured
to be non-zero for the production of charged pions in
e+ e− annihilation at Belle (Abe et al., 2005; Seidl et al.,
2008), as shown in Fig. 20, and in recent preliminary data
from BABAR (Garzia, 2012). 3. Probing transversity
In SIDIS the second chiral-odd function is the transver-
sity distribution introduced in Section II and dis- The transversity distribution introduced in Section II
cussed further below (or the Boer-Mulders distribu- describes the transverse polarization of quarks within a
tion). The HERMES (Airapetian et al., 2005b, 2010a), transversely polarized nucleon. Along with the unpolar-
COMPASS (Adolph et al., 2012b; Ageev et al., 2007; ized and helicity distributions, it survives integration over
Alekseev et al., 2009a, 2010b; Pesaro, 2011) and JLab partonic transverse momentum and is thus a collinear
Hall A (Qian et al., 2011) experiments have performed distribution.
SIDIS measurements of the Collins effect. The measure- The first moment of the transversity distribution is
ments for a proton target are shown in Figs. 21 and 22 proportional to the nucleon’s C-odd tensor charge, viz.

34
 R1
δq = 0 dxhq1 (x) with applied rigorously for the first time with separately iden-
tifiable TMD distributions and fragmentation functions.
hp, s| q̄iσµν γ5 q |p, si = (1/M )(sµ pν − sν pµ )δq. (37) Building upon this progress, the evolution of previously
unevolved models and fits has now been published for
The difference between the transversity and helicity spin
unpolarized TMD distributions and fragmentation func-
distributions reflects the relativistic character of quark
tions (Aybat and Rogers, 2011b) and the Sivers distribu-
motion in the nucleon. In Bag models this effect is mani-
tion (Aybat et al., 2012a). QCD evolution is just starting
fest as follows. The lower component of the Dirac spinor
to be applied to phenomenological studies (Aybat et al.,
enters the relativistic spin depolarization factor with the
2012b), which will be a major step forward in interpreting
opposite sign to ∆q because of the extra factor of γµ
and comparing results from different experiments. The
in the tensor charge (Jaffe and Ji, 1992). The relativis-
new definitions of TMD distributions also recently made
tic Bag depolarization factor mentioned in Section VI
possible a determination of the hard parts for SIDIS and
becomes 0.83 for transversity in contrast to 0.65 for he-
Drell-Yan at next-to-leading order (Aybat and Rogers,
licity and the nucleon’s axial-charges. In leading order
2011a), which should lead to improved phenomenology.
QCD the transversity distributions are bound by Soffer’s
inequality |hq1 (x, Q2 )| ≤ 21 [{q + q̄}(x, Q2 ) + ∆q(x, Q2 )], Much effort has been dedicated to phenomenolog-
Soffer (1995). QCD motivated fits to transversity ob- ical extractions of TMDs and parameterizations of
servables are reported in Anselmino et al. (2009b), which the Sivers distribution from SIDIS data, see e.g.
also reviews the comparison to model predictions. Anselmino et al. (2009a) and Anselmino et al. (2011),
Transversity is measured through the Collins effect and with QCD evolution now starting to be consid-
also in in dihadron production, where the chiral-odd part- ered (Anselmino et al., 2012). One parameterization of
ner of hq1 is given by the dihadron fragmentation func- the Sivers function includes both semi-inclusive deep
tion H1<)q (Bacchetta et al., 2011; Bianconi et al., 2000; inelastic and proton-proton data (Kang and Prokudin,
Collins et al., 1994). This describes how the transverse 2012), modulo issues related to factorization break-
spin of the fragmenting quark is transferred to the rel- ing (Rogers and Mulders, 2010) discussed below. Fits
ative orbital angular momentum of the hadron pair. to the Collins TMD fragmentation function have been
Consequently, this mechanism does not require trans- performed using both e+ e− and SIDIS data as in-
verse momentum of the produced hadron pair. Standard put (Anselmino et al., 2007a; Efremov et al., 2006). The
collinear factorization applies allowing one to study the Boer-Mulders distribution has been extracted based on
transversity distribution without having to worry about Drell-Yan (Lu and Schmidt, 2010; Zhang et al., 2008) as
solving convolution integrals over transverse momentum well as SIDIS data (Barone et al., 2010b).
or issues of TMD factorization and evolution. These first phenomenological fits to TMD observables
Pioneering measurements of two-pion produc- have been performed using a simple Gaussian ansatz
tion in polarized semi-inclusive DIS by HER- for the transverse momentum dependence of quarks in
MES (Airapetian et al., 2008a) and COM- the nucleon and fragmentation functions. For exam-
PASS (Adolph et al., 2012f) reveal a sizable effect ple, the Sivers function in Eq.(36) was parametrized
and have already been employed for an extraction of in the fits by the product of the unpolarized distribu-
transversity (Courtoy et al., 2012a). First measurements tion fq/p↑ (x, kt ) with an x dependent factor and an x-
of azimuthal correlations of two pion pairs in back-to- independent Gaussian ∼ M kt −kt2 /M12
e containing all the
back jets in e+ e− annihilation related to the dihadron 1
kt dependence. While the Gaussian ansatz is unstable
fragmentation function have just become available from with respect to QCD evolution with increasing Q2 , the
Belle (Vossen et al., 2011) and a first extraction of the method does provide a reasonable fit to present data with
dihadron fragmentation function from these data was values hkt2 i = 0.25 GeV2 and hp2t i = 0.20 GeV2 taken
performed in Courtoy et al. (2012b). from fits to the Cahn effect in unpolarized scattering
(Anselmino et al., 2005). A longer term goal for TMD
4. Current status and recent progress with TMD distributions experiments is to observe deviation from Gaussian behav-
ior for transverse momentum dependence. With exten-
There has been considerable progress in the under- sive unpolarized Drell-Yan and weak boson production
standing of intrinsic transverse momentum and spin- data available over scales from ∼ 4 GeV2 to MZ2 , new fits
momentum correlations in QCD over the past decade, of unpolarized TMD distributions are quite promising as
motivated by the theoretical breakthroughs regarding T - a means to test the Q2 evolution of TMD distributions as
odd TMD distributions (Brodsky et al., 2002a,b; Collins, well as to learn more about the shape of the distributions
2002) and by a vast program of theoretical and experi- in kt .
mental activity. Lattice calculations of the Sivers and Boer-Mulders
A recent monograph, Collins (2011) gives definitions distributions have been performed (Göckeler et al., 2007;
of TMD distributions which allow QCD evolution to be Hägler et al., 2009; Musch et al., 2012). There have

35
 AN
π+−
0.4
π 0.4 0.4 0.4

0.2 0.2 0.2 0.2

0 0 0 0

−0.2 −0.2 −0.2 −0.2

−0.4 ANL −0.4 BNL −0.4 Fermilab −0.4 RHIC

s=4.9 GeV s=6.6 GeV s=19.4 GeV s=62.4 GeV
−0.6 −0.6 −0.6 −0.6
0 0.2 0.4 0.6 0.8 xF 0 0.2 0.4 0.6 0.8 xF 0 0.2 0.4 0.6 0.8 xF 0 0.2 0.4 0.6 0.8 xF
FIG. 23 The transverse single spin asymmetry in forward π ± production as measured in polarized proton-proton collisions
across a range of center-of-mass energies. From left to right, the data are from Klem et al. (1976), Allgower et al. (2002),
Adams et al. (1991), and Arsene et al. (2008). Error bars are statistical errors only.

also been efforts in recent years to implement TMDs long-distance quantum entanglement effects in QCD. In
in Monte Carlo event generators (Bianconi, 2011; the longer-term future, it may be possible to develop well-
Hautmann et al., 2012). Models can provide helpful in- defined functions within the framework of pQCD which
sight into TMD distributions, and a wealth of different describe the correlations between the partons in the in-
model calculations have been explored and published. coming and/or outgoing hadrons.
We refer to Avakian et al. (2009), Bacchetta (2012), In the meantime, single spin asymmetries for forward
Lorce and Pasquini (2011), and Pasquini and Schweitzer meson production in p + p collisions have been shown
(2011) for recent discussion of models related to TMD to remain large across a very wide range of center-of-
distributions, including attempts to address the relation- mass energies (Abelev et al., 2008a; Adams et al., 1991,
ship between TMD distributions and orbital angular mo- 1996; Allgower et al., 2002; Arsene et al., 2008) and up
mentum in the nucleon. to the highest measured pT of ∼5 GeV (Koster, 2012). As
shown in Fig. 23, the transverse single spin asymmetries
in charged pion production √ as a function of Feynman-x
are remarkably similar from s =4.9 GeV all the way up
5. Proton-proton asymmetries and TMD-factorization breaking to 62.4 GeV measured by the BRAHMS experiment at
RHIC.
Despite the fact that the large transverse single spin At higher energies and in particular at pT values large
asymmetries observed in hadronic scattering originally enough to serve as a hard scale, one can try to inter-
inspired the development of TMDs, inclusive hadron pro- pret these phenomena utilizing the tools of pQCD. With
duction in p + p scattering cannot be cleanly separated no explicitly measured scale sensitive to the partonic
into Sivers, Collins, or other contributions as is possi- transverse momentum in inclusive single spin asymme-
ble in SIDIS. In recent work Rogers and Mulders (2010) tries, a more appropriate framework than TMD distri-
argue that the TMD framework is not valid in the case butions in which to interpret the asymmetries may be
of hadroproduction of hadrons, as factorization does not a collinear, twist-3 picture (Efremov and Teryaev, 1982,
hold. While the short-distance (perturbative) compo- 1985; Qiu and Sterman, 1999). A relationship between
nents are still believed to factorize from the long-distance the TMD and the collinear, twist-3 frameworks was laid
(non-perturbative) ones, the long-distance components out in Ji et al. (2006).
become entangled and no longer factorize from one an- Surprises continue to emerge from these kinds of mea-
other into independent TMD distributions and/or frag- surements, with large asymmetries for negative kaons as
mentation functions. What is particularly interesting is well as antiprotons from BRAHMS (Arsene et al., 2008)
that the factorization breaking effects are relevant in pre- suggesting that the pion asymmetries are not a valence
cisely the kinematic regime where a parton description is quark effect as previously believed, and a recent hint from
generally expected to apply. It will be exciting to see this STAR (Adamczyk et al., 2012c) that the asymmetry for
tested experimentally in the upcoming years, exploring eta mesons may be larger than that of neutral pions.

VIII. FUTURE PROJECTS briefly outline these experiments and their prime physics
objectives.
A new program of dedicated experiments is planned to
investigate key open questions in QCD spin physics. We
36
 Since May 2012 CEBAF is undergoing a major up- ticular interest to nucleon structure studies are potential
grade that will bring the maximum available energy of upgraded forward spectrometers capable of reconstruct-
the electron beam to 12 GeV. The experimental equip- ing jets, with hadronic particle identification and Drell-
ment in all three halls will be upgraded (Hall A and C) Yan measurement capabilities up to pseudorapidities of
or completely renewed (Hall B), in order to better match ∼ 4. The ability to perform full jet reconstruction in the
the increased energy and luminosity. A new experimental forward region where large transverse single spin asym-
Hall D is being built. Commissioning of the new acceler- metries are observed, and in addition to measure and
ator and of the experimental halls is expected for 2014. identify hadrons within the jet, would allow separation of
The future physics program focuses on dedicated studies effects due to distribution versus fragmentation functions
of large x phenomena, hard exclusive reactions and TMD and shed great light on the origin of these significant spin-
effects in kinematics where valence quarks dominate the momentum correlations. An integrated design process for
physics (Dudek et al., 2012). new detectors is underway such that they would be able
At CERN a proposal by the COMPASS Collaboration to take full advantage of electron-proton and electron-
(Gautheron et al., 2010) to study TMDs and GPDs in ion collisions in the longer-term future should an electron
the period 2014–2017 has been approved. The COM- beam be added to RHIC.
PASS data will provide a link between the kinematic Ideas for future polarization measurements are also dis-
domains of HERA on one hand and of HERMES and cussed and investigated in more detail at FAIR (Ger-
JLAB on the other. The program will start with the first many), J-PARC (Japan) and NICA (Russia).
ever polarized Drell–Yan experiment using a transversely A possible Electron-Ion Collider (EIC) is being dis-
polarized ammonia (proton) target and a negative pion cussed in connection with the future of RHIC and JLab.
beam. Due to the underlying annihilation of the anti up- The goal is to achieve highly polarized (greater than 70%)
quark from the pion and the target up quark, the process electron and light-nucleus beams with center-of-mass en-
is dominated by the up quark distribution in the valence ergies ranging from about 20–150 GeV at maximum col-
region. An important goal is to check the QCD prediction lision luminosities typically ∼ 1034 cm−2 s−1 . Signifi-
of a sign change in the naive T -odd TMDs with respect cant R&D is ongoing to realize the technical challenges
to the DIS case. A study of GPDs in DVCS and hard for reaching this luminosity frontier for colliders and for
exclusive meson production with a polarized muon beam achieving and maintaining polarization of light nuclei (D
will follow in 2015 using a liquid hydrogen target, a dedi- and 3 He) in a storage ring. An EIC with the above per-
cated target recoil detector and an additional large-angle formance would offer unique access to the small-x re-
electromagnetic calorimeter. An important measurement gion where gluons dominate as well as to the intermedi-
is the beam charge-and-spin asymmetry, which uses the ate and high x regions at unprecedented high Q2 . One
property of the muon beam that polarization changes could then study gluon polarization down to x values of
sign when going from positive to negative muons. A first about 10−4 (Aschenauer et al., 2012a). The high lumi-
result on the correlation of transverse size and longitudi- nosity would enable us to measure and map GPDs over
nal momentum fraction might already be expected from a broad range of the kinematic variables and study the
a 2012 pilot run. In parallel semi-inclusive DIS data will QCD evolution of the DVCS process plus TMD distribu-
be taken on the pure hydrogen target. tions in kinematics where sea/glue effects are expected
There are proposals to create a polarized fixed-target to be important. In addition to being the first ep col-
Drell-Yan program at Fermilab following the SeaQuest lider exploring the structure of polarized protons, an EIC
experiment, scheduled to complete data taking in 2014. would also be the first electron-nucleus collider allowing
R&D has begun for a suitable polarized target, and a for- precision studies of the gluon and sea quark structure
mal proposal to polarize the 120 GeV proton beam in the of nuclei. Unpolarized ion beams from deuterium to the
Main Injector has been submitted to Fermilab manage- heaviest nuclei – uranium or lead – would also be ac-
ment (Courant et al., 2011). One of the primary physics celerated. Knowledge about the spatial distribution of
motivations for such a program would be to explore in quarks and gluons in nuclei is needed for example in the
detail the QCD spin-momentum correlations described interpretation of heavy-ion collision data and the search
by TMD distributions such as the Sivers distribution, in for quark-gluon plasma. A comprehensive review of EIC
particular the role of color flow in Drell-Yan versus semi- physics opportunities is given in Boer et al. (2011).
inclusive DIS interactions.
A variety of possibilities for the medium-term future of
RHIC is currently under discussion. R&D is ongoing for IX. CONCLUSIONS AND OUTLOOK
a polarized 3 He source for RHIC (Zelenski et al., 2008),
which would allow the neutron spin structure to be stud- The challenge to understand the internal spin structure
ied in collider kinematics for the first time. There are of the nucleon has inspired a global program of enormous
also proposals to significantly extend the detector capa- experimental and theoretical work in QCD during the
bilities at RHIC; see e.g. Aidala et al. (2012). Of par- last 25 years.

37
 For longitudinal spin structure, there is a good conver- TMDs will test QCD evolution in a regime where trans-
gence of spin measurements from CERN, DESY, JLab, verse structure becomes important. The aim for precise
RHIC and SLAC taking into account the Q2 dependence information about quark (and gluon) total and orbital
of the data and kinematics of the different experiments. angular momentum in the nucleon is also a driving force
There is also good convergence of theoretical understand- for much theoretical work. Highlights include models of
ing with the data, including QCD inspired models of transverse spin phenomena, lattice calculations and de-
the nucleon and lattice calculations with disconnected velopment of QCD fitting technology to extract GPDs
diagrams included. Semi-inclusive measurements in po- and TMDs from the newly measurable observables.
larized lepton-nucleon and proton-proton collisions have
yielded much information about the size of the separate
valence, sea and gluon spin contributions to the nucleon’s ACKNOWLEDGMENTS
spin. The small value of the nucleon’s flavor-singlet axial-
charge, about 0.35, extracted from polarized deep inelas- The research of SDB is supported by the Austrian Sci-
tic scattering seems to be a valence quark effect. No ence Fund, FWF, through grants P20436 and P23753.
significant sea-quark polarization is observed in semi- We thank M. Diehl, R. Fatemi, A. Korzenev, S. Kuhn,
inclusive deep inelastic scattering experiments; the sum W. Melnitchouk, B. Pasquini, T.C. Rogers, M. Strat-
of valence spin contributions is in close agreement with mann, S. Taneja, A. W. Thomas, F. Videbaek, R. Wind-
(0)
the measured total spin contribution gA |pDIS . While molders, A. Zelenski and E. Zemlyanichkina for helpful
gluon polarization ∆g at the scale of the experiments may discussions.
be as much as 50% of the nucleon’s spin at the scale of
the experiments, the QCD anomaly correction −3 α 2π ∆g
s

(0)
is too small to resolve the difference between gA |pDIS
and the early quark models predictions, about 0.6. Prime
theory candidates to explain the small “quark spin con-
tent” include transfer of valence quark spin to quark or-
bital angular momentum through the pion cloud and a
possible topological effect whereby some fraction of the
valence quarks’ “spin” resides at Bjorken x = 0, where
it is missed by polarized deep inelastic scattering exper-
iments. The proton spin puzzle seems to be telling us
about the interplay of valence quarks with chiral dynam-
ics and the complex vacuum structure of QCD. Ongoing
and planned experimental activity will improve the pre-
cision on the size of gluon and strangeness polarization
in the nucleon.
Finite orbital angular momentum of the valence quarks
is expected, induced also by confinement which intro-
duces a transverse scale in the physics. Quark or-
bital angular momentum through spin-orbit coupling is
a prime candidate to explain the large transverse sin-
gle spin asymmetries observed in proton-proton collisions
and lepton-nucleon scattering. The desire to understand
and measure QCD orbital angular momentum effects in
the nucleon has spawned a new program to explore and
map the three-dimensional structure of the nucleon –
both in spatial co-ordinates (generalized parton distri-
butions) and transverse momentum dependence.
Studies of transverse nucleon structure will drive the
experimental program in the near future, with dedicated
running or approved programs at COMPASS, the 12 GeV
upgrade of JLab, FNAL and RHIC. These experiments
will test our understanding of initial and final state inter-
actions in QCD (through comparison of Sivers and Boer-
Mulders observables in Drell-Yan and semi-inclusive deep
inelastic scattering). Precise measurements of GPDs and

38
REFERENCES Adeva, B., et al. (SMC Collaboration) (1998b),
Phys. Rev. D58, 112001
Aaron, F. D., et al. (H1 Collaboration) (2008), Adeva, B., et al. (SMC Collaboration) (2004),
Phys. Lett. B659, 796 Phys. Rev. D70, 012002
Abbon, P., et al. (COMPASS Collaboration) (2007), Nucl. Adler, S., et al. (PHENIX Collaboration) (2006), Phys.Rev.
Instrum. Meth. A577, 455 D74, 072002
Abe, K., et al. (E154 Collaboration) (1997), Adolph, C., et al. (COMPASS Collaboration) (2012a),
Phys. Rev. Lett. 79, 26 Nucl.Phys. B865, 1
Abe, K., et al. (E143 collaboration) (1998), Adolph, C., et al. (COMPASS Collaboration) (2012b),
Phys. Rev. D58, 112003 Phys.Lett. B717, 376
Abe, K., et al. (Belle Collaboration) (2005), hep-ex/0507063 Adolph, C., et al. (COMPASS Collaboration) (2012c),
Abelev, B. I., et al. (STAR Collaboration) (2008a), Phys. Rev. Phys.Lett. B717, 383
Lett. 101, 222001 Adolph, C., et al. (COMPASS Collaboration) (2012d),
Abelev, B. I., et al. (STAR Collaboration) (2008b), arXiv:1211.6849 [hep-ex]
Phys. Rev. Lett. 100, 232003 Adolph, C., et al. (COMPASS Collaboration) (2012e),
Abelev, B. I., et al. (STAR Collaboration) (2009), arXiv:1202.4064 [hep-ex]
Phys. Rev. D80, 111108 Adolph, C., et al. (COMPASS Collaboration) (2012f), Phys.
Ackermann, K. H., et al. (STAR Collaboration) (2003), Nucl. Lett. B713, 10
Instrum. Meth. A499, 624 Ageev, E. S., et al. (COMPASS Collaboration) (2006),
Ackerstaff, K., et al. (HERMES Collaboration) (1999a), Phys. Lett. B633, 25
Phys. Rev. Lett. 82, 1164 Ageev, E. S., et al. (COMPASS Collaboration) (2007), Nucl.
Ackerstaff, K., et al. (HERMES Collaboration) (1999b), Phys. B765, 31
Phys. Lett. B464, 123 Aggarwal, M. M., et al. (STAR Collaboration) (2011),
Adamczyk, L., et al. (STAR Collaboration) (2012a), Phys. Rev. Lett. 106, 062002
Phys.Rev. D86, 032006 Aidala, C., et al. (PHENIX Collaboration) (2012),
Adamczyk, L., et al. (STAR Collaboration) (2012b), arXiv:1207.6378 [nucl-ex]
arXiv:1206.1928 [nucl-ex] Airapetian, A., et al. (HERMES Collaboration) (2000a),
Adamczyk, L., et al. (STAR Collaboration) (2012c), Phys. Rev. Lett. 84, 2584
Phys.Rev. D86, 051101 Airapetian, A., et al. (HERMES Collaboration) (2000b),
Adamczyk, M., et al. (BRAHMS Collaboration) (2003), Nucl. Phys. Rev. Lett. 84, 4047
Instrum. Meth. A499, 437 Airapetian, A., et al. (HERMES Collaboration) (2001),
Adams, D., et al. (SMC Collaboration) (2000), Phys. Rev. D64, 097101
Nucl. Instrum. Meth. A443, 1 Airapetian, A., et al. (HERMES Collaboration) (2003),
Adams, D. L., et al. (FNAL E704 Collaboration) (1991), Phys. Lett. B562, 182
Phys. Lett. B264, 462 Airapetian, A., et al. (HERMES Collaboration) (2004a),
Adams, D. L., et al. (FNAL E581/704 Collaboration) (1994), Phys. Rev. Lett. 92, 012005
Phys. Lett. B336, 269 Airapetian, A., et al. (HERMES Collaboration) (2004b),
Adams, D. L., et al. (FNAL E704 Collaboration) (1996), Eur.Phys.J. D29, 21
Phys. Rev. D53, 4747 Airapetian, A., et al. (HERMES Collaboration) (2005a),
Adare, A., et al. (PHENIX Collaboration) (2007), Phys. Rev. D71, 012003
Phys. Rev. D76, 051106 Airapetian, A., et al. (HERMES Collaboration) (2005b),
Adare, A., et al. (PHENIX Collaboration) (2009a), Phys. Rev. Lett. 94, 012002
Phys. Rev. D79, 012003 Airapetian, A., et al. (HERMES Collaboration) (2005c),
Adare, A., et al. (PHENIX Collaboration) (2009b), Nucl. Instrum. Meth. A540, 68
Phys. Rev. Lett. 103, 012003 Airapetian, A., et al. (HERMES Collaboration) (2007a),
Adare, A., et al. (PHENIX Collaboration) (2011a), Phys. Rev. D75, 012007
Phys. Rev. D83, 032001 Airapetian, A., et al. (HERMES Collaboration) (2007b),
Adare, A., et al. (PHENIX Collaboration) (2011b), Phys. Rev. D75, 011103
Phys. Rev. Lett. 106, 062001 Airapetian, A., et al. (HERMES Collaboration) (2008a),
Adare, A., et al. (PHENIX Collaboration) (2012), JHEP 0806, 017
arXiv:1202.4020 [hep-ex] Airapetian, A., et al. (HERMES Collaboration) (2008b),
Adcox, K., et al. (PHENIX Collaboration) (2003), Nucl. In- JHEP 0806, 066
strum. Meth. A499, 469 Airapetian, A., et al. (HERMES Collaboration) (2008c),
Adeva, B., et al. (SMC Collaboration) (1993), Phys. Lett. B666, 446
Phys. Lett. B302, 533 Airapetian, A., et al. (HERMES Collaboration) (2009a),
Adeva, B., et al. (Spin Muon Collaboration (SMC)) (1994a), Phys. Lett. B679, 100
Nucl.Instrum.Meth. A349, 334 Airapetian, A., et al. (HERMES Collaboration) (2009b),
Adeva, B., et al. (Spin Muon Collaboration (SMC)) (1994b), Phys. Rev. Lett. 103, 152002
Nucl.Instrum.Meth. A343, 363 Airapetian, A., et al. (HERMES Collaboration) (2009c),
Adeva, B., et al. (SMC Collaboration) (1996), JHEP 0911, 083
Phys. Lett. B369, 93 Airapetian, A., et al. (HERMES Collaboration) (2010a),
Adeva, B., et al. (SMC Collaboration) (1998a), Phys. Lett. B693, 11
Phys. Lett. B420, 180 Airapetian, A., et al. (HERMES Collaboration) (2010b),
JHEP 1006, 019

39
Airapetian, A., et al. (HERMES Collaboration) (2010c), Phys. Lett. B463, 339
JHEP 1008, 130 Anthony, P. L., et al. (E155 Collaboration) (2000),
Airapetian, A., et al. (HERMES Collaboration) (2010d), Phys. Lett. B493, 19
Nucl. Phys. B829, 1 Anthony, P. L., et al. (E155 Collaboration) (2003),
Airapetian, A., et al. (HERMES Collaboration) (2011a), Phys. Lett. B553, 18
Nucl. Phys. B842, 265 Antille, J., et al. (1980), Phys. Lett. B94, 523
Airapetian, A., et al. (HERMES Collaboration) (2011b), Apokin, V. D., et al. (1990), Phys. Lett. B243, 461
Phys. Lett. B704, 15 Arsene, I., et al. (BRAHMS Collaboration) (2008), Phys. Rev.
Airapetian, A., et al. (HERMES Collaboration) (2012a), Lett. 101, 042001
arXiv:1204.4161 [hep-ex] Artru, X., and M. Mekhfi (1990), Z. Phys. C45, 669
Airapetian, A., et al. (HERMES Collaboration) (2012b), Aschenauer, E. C., R. Sassot, and M. Stratmann (2012a),
JHEP 1207, 032 Phys.Rev. D86, 054020
Airapetian, A., et al. (HERMES Collaboration) (2012c), Aschenauer, E.-C., et al. (RHIC Spin) (2012b),
JHEP 1210, 042 “The RHIC Spin Program: Achievements and fu-
Akopov, N., E. Aschenauer, K. Bailey, S. Bernreuther, ture opportunities,” White Paper, available at
N. Bianchi, et al. (2002), Nucl.Instrum.Meth. A479, 511, http://www.bnl.gov/npp/docs/RHIC-Spin-WriteUp-
arXiv:physics/0104033 [physics] 121105.pdf
Alcorn, J., et al. (JLab Hall A Collaboration) (2004), Ashman, J., et al. (EMC Collaboration) (1988), Phys. Lett.
Nucl. Instrum. Meth. A522, 294 B206, 364
Alekseev, I., et al. (2003), Nucl. Instrum. Meth. A499, 392 Ashman, J., et al. (EMC Collaboration) (1989), Nucl. Phys.
Alekseev, M., et al. (COMPASS Collaboration) (2009a), B328, 1
Phys. Lett. B673, 127 Aubert, J. J., et al. (European Muon Collaboration) (1981),
Alekseev, M., et al. (COMPASS Collaboration) (2009b), Nucl. Instrum. Meth. 179, 445
Phys. Lett. B680, 217 Avakian, H., S. J. Brodsky, A. Deur, and F. Yuan (2007),
Alekseev, M., et al. (COMPASS Collaboration) (2009c), Phys. Rev. Lett. 99, 082001
Phys. Lett. B676, 31 Avakian, H., A. V. Efremov, P. Schweitzer, O. Teryaev,
Alekseev, M. G., et al. (COMPASS Collaboration) (2010a), F. Yuan, et al. (2009), Mod. Phys. Lett. A24, 2995
Eur.Phys.J. C70, 39, arXiv:1007.1562 [hep-ex] Avakian, H., et al. (CLAS Collaboration) (2010),
Alekseev, M. G., et al. (COMPASS Collaboration) (2010b), Phys. Rev. Lett. 105, 262002
Phys. Lett. B692, 240 Aybat, S. M., J. C. Collins, J.-W. Qiu, and T. C. Rogers
Alekseev, M. G., et al. (COMPASS Collaboration) (2010c), (2012a), Phys. Rev. D85, 034043
Phys. Lett. B693, 227 Aybat, S. M., A. Prokudin, and T. C. Rogers (2012b),
Alekseev, M. G., et al. (COMPASS Collaboration) (2010d), Phys.Rev.Lett. 108, 242003
Phys. Lett. B690, 466 Aybat, S. M., and T. C. Rogers (2011a),
Alexakhin, V. Y., et al. (COMPASS Collaboration) (2007), arXiv:1107.3973 [hep-ph]
Phys. Lett. B647, 8 Aybat, S. M., and T. C. Rogers (2011b),
Alguard, M. J., et al. (1976), Phys. Rev. Lett. 37, 1261 Phys. Rev. D83, 114042
Alguard, M. J., et al. (1978), Phys. Rev. Lett. 41, 70 Bacchetta, A. (2012), Nuovo Cim. C035N2, 19
Allgower, C. E., et al. (2002), Phys. Rev. D65, 092008 Bacchetta, A., A. Courtoy, and M. Radici (2011),
Altarelli, G., R. D. Ball, S. Forte, and G. Ridolfi (1997), Phys. Rev. Lett. 107, 012001
Nucl. Phys. B496, 337 Bacchetta, A., U. D’Alesio, M. Diehl, and C. A. Miller (2004),
Altarelli, G., R. D. Ball, S. Forte, and G. Ridolfi (1998), Acta Phys. Rev. D70, 117504
Phys. Polon. B29, 1145 Bacchetta, A., and M. Radici (2011),
Altarelli, G., and G. Parisi (1977), Nucl. Phys. B126, 298 Phys. Rev. Lett. 107, 212001
Altarelli, G., and G. G. Ross (1988), Phys. Lett. B212, 391 Bacchetta, A., et al. (2007), JHEP 02, 093
Anselmino, M., M. Boglione, U. D’Alesio, A. Kotzinian, Bakker, B. L. G., E. Leader, and T. L. Trueman (2004), Phys.
S. Melis, et al. (2009a), Eur. Phys. J. A39, 89 Rev. D70, 114001
Anselmino, M., M. Boglione, U. D’Alesio, A. Kotzinian, Bali, G. S., et al. (QCDSF Collaboration) (2012),
F. Murgia, et al. (2005), Phys. Rev. D71, 074006 Phys. Rev. Lett. 108, 222001
Anselmino, M., M. Boglione, U. D’Alesio, A. Kotzinian, Ball, J., G. Baum, P. Berglund, I. Daito, N. Doshita, et al.
F. Murgia, et al. (2007a), Phys. Rev. D75, 054032 (2003), Nucl.Instrum.Meth. A498, 101
Anselmino, M., M. Boglione, U. D’Alesio, A. Kotzinian, Ball, R. D., L. Del Debbio, S. Forte, A. Guffanti, J. I. Latorre,
F. Murgia, et al. (2009b), Nucl. Phys. Proc. Suppl. 191, 98 et al. (2010), Nucl. Phys. B838, 136
Anselmino, M., M. Boglione, U. D’Alesio, S. Melis, F. Murgia, Ball, R. D., S. Forte, and G. Ridolfi (1996),
et al. (2011), arXiv:1107.4446 [hep-ph] Phys. Lett. B378, 255
Anselmino, M., M. Boglione, and S. Melis (2012), Ball, R. D., et al. (NNPDF Collaboration) (2012),
Phys.Rev. D86, 014028 Nucl. Phys. B855, 153
Anselmino, M., M. Boglione, A. Prokudin, and C. Turk Barber, D. P., M. Boge, H. D. Bremer,
(2007b), Eur. Phys. J. A31, 373 R. Brinkmann, E. Gianfelice-Wendt, et al. (1994),
Anselmino, M., A. Efremov, and E. Leader (1995), Nucl. Instrum. Meth. A338, 166
Phys. Rept. 261, 1 Barber, D. P., H. D. Bremer, M. Boge, R. Brinkmann,
Anthony, P. L., et al. (E142 Collaboration) (1996), W. Bruckner, et al. (1993), Nucl. Instrum. Meth. A329, 79
Phys. Rev. D54, 6620 Barone, V., F. Bradamante, and A. Martin (2010a),
Anthony, P. L., et al. (E155 Collaboration) (1999), Prog. Part. Nucl. Phys. 65, 267

40
Barone, V., A. Drago, and P. G. Ratcliffe (2002), Brodsky, S. J., F. J. Llanes-Estrada, and A. P. Szczepaniak
Phys. Rept. 359, 1 (2009b), Phys.Rev. D79, 033012
Barone, V., S. Melis, and A. Prokudin (2010b), Brommel, D., et al. (QCDSF-UKQCD Collaboration) (2007),
Phys. Rev. D81, 114026 PoS LAT2007, 158
Bass, S. D. (1999a), Eur. Phys. J. A5, 17 Bunce, G., N. Saito, J. Soffer, and W. Vogelsang (2000),
Bass, S. D. (1999b), Phys. Lett. B463, 286 Ann. Rev. Nucl. Part. Sci. 50, 525
Bass, S. D. (2003), Phys. Rev. D67, 097502 Buon, J., and K. Steffen (1986),
Bass, S. D. (2005), Rev. Mod. Phys. 77, 1257 Nucl. Instrum. Meth. A245, 248
Bass, S. D. (2007a), Mod. Phys. Lett. A22, 1005 Burkardt, M. (2003), Int. J. Mod. Phys. A18, 173
Bass, S. D. (2007b), The Spin structure of the proton (World Burkardt, M., C. A. Miller, and W. D. Nowak (2010),
Scientific, Singapore) Rept. Prog. Phys. 73, 016201
Bass, S. D., A. Casey, and A. W. Thomas (2011), Burkhardt, H., and W. N. Cottingham (1970), Annals Phys.
Phys. Rev. C83, 038202 56, 453
Bass, S. D., R. J. Crewther, F. M. Steffens, and A. W. Cahn, R. N. (1978), Phys. Lett. B78, 269
Thomas (2002), Phys. Rev. D66, 031901 Cahn, R. N. (1989), Phys. Rev. D40, 3107
Bass, S. D., B. L. Ioffe, N. N. Nikolaev, and A. W. Thomas Camacho, C. M., et al. (JLab Hall A DVCS Collaboration)
(1991), J. Moscow. Phys. Soc. 1, 317 (2006), Phys. Rev. Lett. 97, 262002
Bass, S. D., and P. V. Landshoff (1994), Cao, F.-G., and A. I. Signal (2001), Eur. Phys. J. C21, 105
Phys. Lett. B336, 537 Carlitz, R. D., J. C. Collins, and A. H. Mueller (1988),
Bass, S. D., and A. W. Thomas (1993), J. Phys. G G19, 925 Phys. Lett. B214, 229
Bass, S. D., and A. W. Thomas (2010), Chekanov, S., et al. (ZEUS Collaboration) (2009),
Phys. Lett. B684, 216 JHEP 0905, 108
Baum, G., et al. (1980), Phys. Rev. Lett. 45, 2000 Chen, P., and X. Ji (2008), Phys. Lett. B660, 193
Baum, G., et al. (1983), Phys. Rev. Lett. 51, 1135 Chen, S., et al. (CLAS Collaboration) (2006),
Baumgarten, C., B. Braun, V. Carassiti, G. Ciullo, G. Court, Phys. Rev. Lett. 97, 072002
et al. (2003a), Nucl.Instrum.Meth. A496, 277 Chen, X.-S., X.-F. Lu, W.-M. Sun, F. Wang, and T. Goldman
Baumgarten, C., B. Braun, M. Contalbrigo, G. Court, (2008), Phys. Rev. Lett. 100, 232002
G. Ciullo, et al. (2003b), Nucl.Instrum.Meth. A508, 268 Cheng, H.-Y. (1996), Int. J. Mod. Phys. A11, 5109
Baumgarten, C., B. Braun, G. Court, G. Ciullo, P. Dalpiaz, Cloet, I., R. Horsley, J. Londergan, Y. Nakamura, D. Pleiter,
et al. (2003c), Nucl.Instrum.Meth. A496, 263 et al. (2012), Phys.Lett. B714, 97
Baumgarten, C., et al. (HERMES Target Group) (2002), Close, F. E. (1979), An Introduction to Quarks and Partons
Nucl.Instrum.Meth. A482, 606 (Academic, New York)
Bazilevsky, A., et al. (2003), AIP Conf. Proc. 675, 584 Close, F. E., and R. G. Milner (1991), Phys. Rev. D44, 3691
Beckmann, M., A. Borissov, S. Brauksiepe, F. Burkart, Close, F. E., and R. G. Roberts (1993),
H. Fischer, et al. (2002), Nucl. Instrum. Meth. A479, 334 Phys. Lett. B316, 165
Belitsky, A. V., X. Ji, and F. Yuan (2003), Close, F. E., and R. G. Roberts (1994),
Phys. Rev. Lett. 91, 092003 Phys. Lett. B336, 257
Belitsky, A. V., D. Mueller, and A. Kirchner (2002), Close, F. E., and A. W. Thomas (1988),
Nucl. Phys. B629, 323 Phys. Lett. B212, 227
Beringer, J., et al. (Particle Data Group) (2012), Collins, J. (2011), Foundations of perturbative QCD (Cam-
Phys. Rev. D 86, 010001 bridge University Press, Cambridge, England)
Bianconi, A. (2011), arXiv:1109.0688 [hep-ph] Collins, J. C. (1993), Nucl. Phys. B396, 161
Bianconi, A., S. Boffi, R. Jakob, and M. Radici (2000), Phys. Collins, J. C. (2002), Phys. Lett. B536, 43
Rev. D62, 034008 Collins, J. C., S. F. Heppelmann, and G. A. Ladinsky (1994),
Bjorken, J. D. (1966), Phys. Rev. 148, 1467 Nucl. Phys. B420, 565
Bjorken, J. D. (1970), Phys. Rev. D1, 1376 Conway, J. S., et al. (FNAL E615 Collaboration) (1989),
Blümlein, J., and H. Böttcher (2010), Nucl. Phys. B841, 205 Phys. Rev. D39, 92
Bodwin, G. T., and J.-W. Qiu (1990), Phys. Rev. D41, 2755 Cortes, J., B. Pire, and J. Ralston (1992), Z.Phys. C55, 409
Boer, D., and P. J. Mulders (1998), Phys. Rev. D57, 5780 Courant, E. D., et al. (SPIN-Fermilab Collaboration) (2011),
Boer, D., et al. (2011), arXiv:1108.1713 [nucl-th] arXiv:1110.3042 [physics.acc-ph]
Bourrely, C., J. Soffer, and F. Buccella (2002), Courtoy, A., A. Bacchetta, and M. Radici (2012a), PoS
Eur. Phys. J. C23, 487 QNP2012, 042
Broadhurst, D. J., J. Gunion, and R. L. Jaffe (1973), Courtoy, A., A. Bacchetta, M. Radici, and A. Bianconi
Annals Phys. 81, 88 (2012b), Phys. Rev. D85, 114023
Brodsky, S. J., M. Burkardt, and I. Schmidt (1995), Crabb, D., and W. Meyer (1997),
Nucl. Phys. B441, 197 Ann.Rev.Nucl.Part.Sci. 47, 67
Brodsky, S. J., J. R. Ellis, and M. Karliner (1988), Crewther, R. J. (1978), Acta Phys. Austriaca Suppl. 19, 47
Phys. Lett. B206, 309 Cudell, J. R., A. Donnachie, and P. V. Landshoff (1999),
Brodsky, S. J., D. S. Hwang, and I. Schmidt (2002a), Phys. Phys. Lett. B448, 281
Lett. B530, 99 Derbenev, Y. S., et al. (1978), Part. Accel. 8, 115
Brodsky, S. J., D. S. Hwang, and I. Schmidt (2002b), Nucl. Dharmawardane, K., et al. (CLAS Collaboration) (2006),
Phys. B642, 344 Phys. Lett. B641, 11
Brodsky, S. J., F. J. Llanes-Estrada, J. T. Londergan, and Diehl, M. (2002), Eur. Phys. J. C25, 223
A. P. Szczepaniak (2009a), arXiv:0906.5515 [hep-ph] Diehl, M. (2003), Phys. Rept. 388, 41

41
Diehl, M., and S. Sapeta (2005), Eur. Phys. J. C41, 515 Nucl. Phys. B44, 189
Djawotho, P. (STAR Collaboration) (2011), Huang, J., et al. (Jefferson Lab Hall A Collaboration) (2012),
arXiv:1106.5769 [nucl-ex] Phys.Rev.Lett. 108, 052001
Donnachie, A., and P. V. Landshoff (2011), Jaffe, R. (1996), Phys.Lett. B365, 359
arXiv:1112.2485 [hep-ph] Jaffe, R. L. (1990), Comments Nucl. Part. Phys. 19, 239
Dragoset, W. H., et al. (1978), Phys. Rev. D18, 3939 Jaffe, R. L. (2001), AIP Conf. Proc. 588, 54
Dudek, J., et al. (2012), arXiv:1208.1244 [hep-ex] Jaffe, R. L., and X.-D. Ji (1992), Nucl. Phys. B375, 527
Efremov, A. V., K. Goeke, and P. Schweitzer (2006), Jaffe, R. L., and A. Manohar (1990), Nucl. Phys. B337, 509
Phys. Rev. D73, 094025 Ji, X., J.-W. Qiu, W. Vogelsang, and F. Yuan (2006),
Efremov, A. V., and O. V. Teryaev (1982), Sov. J. Nucl. Phys. Rev. Lett. 97, 082002
Phys. 36, 140 Ji, X., X. Xiong, and F. Yuan (2012),
Efremov, A. V., and O. V. Teryaev (1985), Phys. Lett. B150, arXiv:1207.5221 [hep-ph]
383 Ji, X.-D. (1997a), Phys. Rev. D55, 7114
Efremov, A. V., and O. V. Teryaev (1988), JINR Report Ji, X.-D. (1997b), Phys. Rev. Lett. 78, 610
No. E2-88-287 Ji, X.-D. (1998), J. Phys. G G24, 1181
Ellis, J. R., and R. L. Jaffe (1974), Phys. Rev. D9, 1444 Ji, X.-D., J. Tang, and P. Hoodbhoy (1996),
Ellis, J. R., and M. Karliner (1995), Phys. Rev. Lett. 76, 740
arXiv:hep-ph/9601280 [hep-ph] Jones, M. K., et al. (JLab Hall A Collaboration) (2000),
Falciano, S., et al. (NA10 Collaboration) (1986), Phys. Rev. Lett. 84, 1398
Z. Phys. C31, 513 Kang, Z.-B., and A. Prokudin (2012), Phys. Rev. D85,
Filippone, B. W., and X.-D. Ji (2001), 074008
Adv. Nucl. Phys. 26, 1 Kaplan, D. B., and A. Manohar (1988),
de Florian, D., R. Sassot, and M. Stratmann (2007), Nucl. Phys. B310, 527
Phys. Rev. D75, 114010 Kazimi, R., K. Beard, J. F. Benesch, A. Freyberger,
de Florian, D., R. Sassot, M. Stratmann, and W. Vogelsang J. Grames, et al. (2004), EPAC-2004-TUPLT164, JLAB-
(2008), Phys. Rev. Lett. 101, 072001 ACO-04-251
de Florian, D., R. Sassot, M. Stratmann, and W. Vogelsang Keith, C., M. Anghinolfi, M. Battaglieri, P. E. Bosted,
(2009), Phys. Rev. D80, 034030 D. Branford, et al. (2003), Nucl.Instrum.Meth. A501, 327
Fritzsch, H. (1989), Phys. Lett. B229, 122 Kiryluk, J. (STAR Collaboration) (2005),
Garzia, I. (BaBar Collaboration) (2012), arXiv:hep-ex/0501072 [hep-ex]
Nuovo Cim. C035N2, 79 Klem, R. D., J. E. Bowers, H. W. Courant, H. Kagan, M. L.
Gautheron, F. (COMPASS Collaboration) (2007), Marshak, et al. (1976), Phys. Rev. Lett. 36, 929
AIP Conf.Proc. 915, 961 Kodaira, J. (1980), Nucl. Phys. B165, 129
Gautheron, F., et al. (COMPASS Collaboration) (2010), Koster, J. (2012), Nuovo Cim. C035N2, 187
COMPASS-II Proposal, CERN-SPSLC-2010-14, CERN- Kotzinian, A. (COMPASS Collaboration) (2007),
SPSLC-P-340 arXiv:0705.2402 [hep-ex]
Gayou, O., et al. (Jefferson Lab Hall A Collaboration) (2002), Kuhn, S. E., J.-P. Chen, and E. Leader (2009),
Phys. Rev. Lett. 88, 092301 Prog. Part. Nucl. Phys. 63, 1
Girod, F. X., et al. (CLAS Collaboration) (2008), Kulagin, S. A., and W. Melnitchouk (2008a),
Phys. Rev. Lett. 100, 162002 Phys. Rev. C77, 015210
Göckeler, M., et al. (QCDSF Collaboration, UKQCD Collab- Kulagin, S. A., and W. Melnitchouk (2008b),
oration) (2007), Phys. Rev. Lett. 98, 222001 Phys. Rev. C78, 065203
Goeke, K., M. V. Polyakov, and M. Vanderhaeghen (2001), Kumano, S., and M. Miyama (2002),
Prog. Part. Nucl. Phys. 47, 401 Phys. Rev. D65, 034012
Goldstein, G. R., J. O. Hernandez, and S. Liuti (2011), Kumericki, K., and D. Mueller (2010), Nucl. Phys. B841, 1
Phys. Rev. D84, 034007 Lampe, B., and E. Reya (2000), Phys. Rept. 332, 1
Goloskokov, S. V., and P. Kroll (2008), Eur. Phys. J. C53, Larin, S. A., T. van Ritbergen, and J. A. M. Vermaseren
367 (1997), Phys. Lett. B404, 153
Goloskokov, S. V., and P. Kroll (2009), Leader, E. (2011), Phys. Rev. D83, 096012
Eur. Phys. J. C59, 809 Leader, E., A. V. Sidorov, and D. B. Stamenov (1998),
Guanziroli, M., et al. (NA10 Collaboration) (1988), Phys. Rev. D58, 114028
Z. Phys. C37, 545 Leader, E., A. V. Sidorov, and D. B. Stamenov (2006),
Guidal, M. (2010), Phys. Lett. B693, 17 Phys. Rev. D73, 034023
Hägler, P., B. U. Musch, J. W. Negele, and A. Schäfer (2009), Leader, E., A. V. Sidorov, and D. B. Stamenov (2010),
Europhys. Lett. 88, 61001 Phys. Rev. D82, 114018
Hägler, P., et al. (LHPC Collaboration) (2008), Leemann, C., D. Douglas, and G. Krafft (2001),
Phys. Rev. D77, 094502 Ann.Rev.Nucl.Part.Sci. 51, 413
Hatta, Y. (2012), Phys.Lett. B708, 186 Lepage, G. P., and S. J. Brodsky (1980),
Hautmann, F., M. Hentschinski, and H. Jung (2012), Phys. Rev. D22, 2157
arXiv:1205.6358 [hep-ph] Lorce, C. (2012), arXiv:1205.6483 [hep-ph]
Hirai, M., and S. Kumano (AAC Collaboration) (2009), Lorce, C., and B. Pasquini (2011), Phys. Rev. D84, 034039
Nucl. Phys. B813, 106 Lu, Z., and I. Schmidt (2010), Phys. Rev. D81, 034023
’t Hooft, G. (1986), Phys. Rept. 142, 357 MacKay, W. W., et al. (2003) (IEEE) p. 1697, proc. of the
’t Hooft, G., and M. J. G. Veltman (1972), 2003 Part. Acc. Conf.

42
Manion, A. (PHENIX Collaboration) (2011), Phys. Rev. D81, 094006
J. Phys. Conf. Ser. 295, 012070 Romalis, M. V., et al. (1998),
Manohar, A. V. (1990), Phys.Rev.Lett. 65, 2511 Nucl. Instrum. Meth. A402, 260
Mattingly, A. C., and P. M. Stevenson (1994), Saroff, S., et al. (1990), Phys. Rev. Lett. 64, 995
Phys. Rev. D49, 437 Sbrizzai, G. (COMPASS Collaboration) (2011),
Mazouz, M., et al. (JLab Hall A Collaboration) (2007), J.Phys.Conf.Ser. 295, 012043
Phys. Rev. Lett. 99, 242501 Schreiber, A. W., and A. W. Thomas (1988),
Mecking, B. A., et al. (CLAS Collaboration) (2003), Phys. Lett. B215, 141
Nucl. Instrum. Meth. A503, 513 Seidl, R., et al. (Belle Collaboration) (2008),
Mertig, R., and W. L. van Neerven (1996), Z. Phys. C70, 637 Phys. Rev. D78, 032011, erratum ibid. D86, 039905
Meyer, W. (2004), Nucl.Instrum.Meth. A526, 12 Shore, G. M. (1998), arXiv:hep-ph/9812355 [hep-ph]
Mueller, D., D. Robaschik, B. Geyer, F. Dittes, and J. Horejsi Shore, G. M. (2008), Lect. Notes Phys. 737, 235
(1994), Fortsch. Phys. 42, 101 Shore, G. M., and B. E. White (2000),
Mulders, P. J., and R. D. Tangerman (1996), Nucl. Phys. Nucl. Phys. B581, 409
B461, 197, erratum-ibid.B484:538-540,1997 Sinclair, C., P. Adderley, B. Dunham, J. Hansknecht, P. Hart-
Musch, B. U., P. Hägler, M. Engelhardt, J. W. Negele, and mann, et al. (2007), Phys.Rev.ST Accel.Beams 10, 023501
A. Schäfer (2012), Phys. Rev. D85, 094510 Sivers, D. W. (1990), Phys. Rev. D41, 83
Myhrer, F., and A. W. Thomas (1988), Soffer, J. (1995), Phys. Rev. Lett. 74, 1292
Phys. Rev. D38, 1633 Sokolov, A. A., and I. M. Ternov (1964), Sov. Phys. Dokl. 8,
Myhrer, F., and A. W. Thomas (2008), 1203
Phys. Lett. B663, 302 Steffens, F. M., H. Holtmann, and A. W. Thomas (1995),
Myhrer, F., and A. W. Thomas (2010), Phys. Lett. B358, 139
J. Phys. G G37, 023101 Stepanyan, S., et al. (CLAS Collaboration) (2001),
Nakagawa, I., et al. (2008), AIP Conf. Proc. 980, 380 Phys. Rev. Lett. 87, 182002
Narison, S., G. M. Shore, and G. Veneziano (1995), Stutzman, M., P. Adderley, J. Brittian, J. Clark, J. Grames,
Nucl. Phys. B433, 209 et al. (2007), Nucl.Instrum.Meth. A574, 213
Nocera, E. R., S. Forte, G. Ridolfi, and J. Rojo (2012), Thomas, A. W. (2008), Phys. Rev. Lett. 101, 102003
arXiv:1206.0201 [hep-ph] Thomas, A. W., A. Casey, and H. H. Matevosyan (2010),
Okada, H., I. G. Alekseev, A. Bravar, G. Bunce, S. Dhawan, Int. J. Mod. Phys. A25, 4149
et al. (2006), Phys. Lett. B638, 450 Towell, R. S., et al. (FNAL E866/NuSea Collaboration)
Osipenko, M., et al. (CLAS Collaboration) (2009), Phys. Rev. (2001), Phys. Rev. D64, 052002
D80, 032004 Tsushima, K., T. Yamaguchi, Y. Kohyama, and K. Kubodera
Pagliaroli, G., C. Lujan-Peschard, M. Mitra, and F. Vissani (1988), Nucl. Phys. A489, 557
(2012), arXiv:1210.4225 [hep-ph] Vanderhaeghen, M., P. A. M. Guichon, and M. Guidal (1999),
Pappalardo, L. L. (2010), Nuovo Cim. B125N1, 51 Phys. Rev. D60, 094017
Pappalardo, L. L., and M. Diefenthaler (HERMES Collabo- Vogelsang, W. (1996), Phys. Rev. D54, 2023
ration) (2011), arXiv:1107.4227 [hep-ex] Vossen, A., et al. (Belle Collaboration) (2011),
Parsamyan, B. (2011), J.Phys.Conf.Ser. 295, 012046 Phys. Rev. Lett. 107, 072004
Pasquini, B., and P. Schweitzer (2011), Wakamatsu, M. (2003), Phys. Rev. D67, 034005
Phys. Rev. D83, 114044 Wakamatsu, M. (2007), Phys. Lett. B646, 24
Pate, S. F., D. W. McKee, and V. Papavassiliou (2008), Wakamatsu, M. (2010), Phys. Rev. D81, 114010
Phys. Rev. C78, 015207 Walker, M. (2011), arXiv:1107.0917 [hep-ex]
Peng, J.-C. (2003), Eur. Phys. J. A18, 395 Windmolders, R. (2002), arXiv:hep-ph/0211350 [hep-ph]
Pesaro, G. (COMPASS Collaboration) (2011), Zelenski, A., J. G. Alessi, A. Kponou, and D. Raparia (2008),
J. Phys. Conf. Ser. 295, 012058 Conf. Proc. C0806233, TUOBM03
Procureur, S. (COMPASS Collaboration) (2006), Zelenski, A., et al. (2002), Rev. Sci. Instrum. 73, 888
arXiv:hep-ex/0605043 [hep-ex] Zelenski, A., et al. (2005), Nucl. Instrum. Meth. A536, 248
Qian, X., et al. (JLab Hall A Collaboration) (2011), Phys. Zhang, B., Z. Lu, B.-Q. Ma, and I. Schmidt (2008),
Rev. Lett. 107, 072003 Phys. Rev. D77, 054011
Qiu, J.-W., and G. Sterman (1999), Phys. Rev. D59, 014004 Zheng, X., et al. (JLab Hall A Collaboration) (2004),
Radyushkin, A. V. (1997), Phys. Rev. D56, 5524 Phys. Rev. Lett. 92, 012004
Ralston, J. P., and D. E. Soper (1979), Zhu, L. Y., et al. (FNAL-E866/NuSea Collaboration) (2007),
Nucl. Phys. B152, 109 Phys. Rev. Lett. 99, 082301
Ratcliffe, P. G. (2004), Czech. J. Phys. 54, B11 Zhu, L. Y., et al. (FNAL E866/NuSea Collaboration) (2009),
Reimer, P. E. (2007), Eur. Phys. J. A31, 593 Phys. Rev. Lett. 102, 182001
Roberts, R. G. (1990), The Structure of the proton: Deep in- Zijlstra, E. B., and W. L. van Neerven (1994),
elastic scattering (Cambridge University Press, Cambridge, Nucl. Phys. B417, 61
England)
Rogers, T. C., and P. J. Mulders (2010),

43