Hylogenesis:
A Unified Origin for Baryonic Visible Matter and Antibaryonic Dark Matter
Hooman Davoudiasl,1 David E. Morrissey,2 Kris Sigurdson,3 and Sean Tulin2
1
Department of Physics, Brookhaven National Laboratory, Upton, NY 11973, USA
2
Theory Group, TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3, Canada
3
Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
(Dated: June 2, 2018)
We present a novel mechanism for generating both the baryon and dark matter densities of the
Universe. A new Dirac fermion X carrying a conserved baryon number charge couples to the
Standard Model quarks as well as a GeV-scale hidden sector. CP-violating decays of X, produced
non-thermally in low-temperature reheating, sequester antibaryon number in the hidden sector,
arXiv:1008.2399v3 [hep-ph] 30 Aug 2010
thereby leaving a baryon excess in the visible sector. The antibaryonic hidden states are stable dark
matter. A spectacular signature of this mechanism is the baryon-destroying inelastic scattering of
dark matter that can annihilate baryons at appreciable rates relevant for nucleon decay searches.
I. Introduction: Precision cosmological measurements this mechanism in Section II.
indicate that a fraction Ωb ≃ 0.046 of the energy content A potentially spectacular signature of our model is that
of the Universe consists of baryonic matter, while Ωd ≃ rare processes can transfer baryon number from the hid-
0.23 is made up of dark matter (DM) [1]. Unfortunately, den to the visible sector. Effectively, antibaryonic dark
our present understanding of elementary particles and matter states can annihilate baryons in the visible sector
interactions, the Standard Model (SM), cannot account through inelastic scattering. These events mimic nucleon
for the abundance of either observed component of non- decay into a meson and a neutrino, but are distinguish-
relativistic particles. able from standard nucleon decay by the kinematics of
In this Letter we propose a unified mechanism, the meson. In Section III, we discuss this signature in
hylogenesis1 , to generate the baryon asymmetry and the more detail, along with its implications for direct detec-
dark matter density simultaneously. The SM is extended tion and astrophysical systems.
to include a new hidden sector of states with masses near We note that our scenario shares some elements with
a GeV and very weak couplings to the SM. Such sectors Refs. [4–11], but involves a different production mecha-
arise in many well-motivated theories of physics beyond nism and unique phenomenological consequences.
the SM, and have received much attention within the II. Genesis of Baryons and DM: In our model, the
contexts dark matter models [2], and high luminosity, hidden sector consists of two massive Dirac fermions Xa
low-energy precision measurements [3]. (a = 1, 2, with masses mX2 > mX1 & TeV), a Dirac
The main idea underlying our mechanism is that some fermion Y , and a complex scalar Φ (with masses mY ∼
of the particles in the hidden sector are charged under mΦ ∼ GeV). These fields couple through the “neutron
a generalization of the global baryon number (B) sym- portal” (XU c Dc Dc ) and a Yukawa interaction:
metry of the SM. This symmetry is not violated by any λa
of the relevant interactions in our model. Instead, equal −L ⊃ X̄a PR d ūc PR d + ζa X̄a Y c Φ∗ + h.c. (1)
M2
and opposite baryon asymmetries are created in the vis-
ible and hidden sectors, and the Universe has zero total Many variations on these operators exist, corresponding
B. These asymmetries are generated when (i) the TeV- to different combinations of quark flavors and spinor con-
scale states X1 and its antiparticle X̄1 (carrying equal tractions. With this set of interactions one can define a
and opposite B charge) are generated non-thermally in generalized global baryon number symmetry that is con-
the early Universe (e.g., during reheating), and (ii) X1 served, with charges BX = −(BY +BΦ ) = 1. The proton,
decays into visible and hidden baryonic states. The X1 Y , and Φ are stable due to their B and gauge charges if
decays violate quark baryon number and CP, and oc- their masses satisfy
cur away from equilibrium. Both the visible and hidden |mY − mΦ | < mp + me < mY + mΦ . (2)
baryons are stable due to a combination of kinematics
and symmetries. The relic density of the hidden baryons Y and Φ are the “hidden antibaryons” that comprise the
is set by their asymmetry, and they make up the dark dark matter. Furthermore, there exists a physical CP-
matter of the Universe. We compute the baryon and violating phase arg(λ∗1 λ2 ζ1 ζ2∗ ) that cannot be removed
dark matter densities within a concrete model realizing through phase redefinitions of the fields.
We also introduce a hidden U (1)′ gauge symmetry un-
der which Y and Φ have opposite charges ±e′ , while Xa is
neutral. We assume this symmetry is spontaneously bro-
1 From Greek, hyle “primordial matter” + genesis “origin.” ken at the GeV scale, and has a kinetic mixing with SM
2
u Y u states (assumed in kinetic equilibrium at temperature
X2 T with an effective number of entropy degrees of free-
X1 d X1 d
Φ dom gs (T ) ), and nB is the baryon number density in
d d the visible sector (i.e. quarks). The scale factor a(t) is
determined by the Friedmann equation H 2 ≡ (ȧ/a)2 =
FIG. 1: Tree-level and one-loop graphs for decay X1 → udd. (8πG/3) (ρϕ + ρr ), where ρr ≡ (π 2 /30)gT 4 is the total
hypercharge U (1)Y via the coupling − κ2 Bµν Zµν′
, where radiation density and g(T ) is the effective number of de-
′ ′
Bµν and Zµν are the U (1)Y and U (1) field strength ten- grees of freedom. NX is the average number of X1 states
sors. At energies well below the electroweak scale the produced per ϕ decay.
effect of this mixing is primarily to generate a vector Eq. (4a) describes the depletion of the oscillating field
coupling of the massive Z ′ gauge boson to SM particles energy due to redshifting and direct ϕ decays and has the
with strength −cW κ Qem e. The GeV-scale Z ′ masses simple solution ρϕ ∝ e−Γϕ t a−3 , while Eq. (4b) gives the
we consider here can be consistent with observations for rate of entropy production due to decays and describes
10−6 . κ . 10−2 [3]. the reheating of the Universe. We adopt the convention
Baryogenesis begins when a non-thermal, CP- that reheating occurs at temperature TRH , defined when
symmetric population of X1 and X̄1 is produced in the ρr (TRH ) = ρϕ (TRH ). This occurs near the characteristic
early Universe. These states decay through X1 → udd decay time t ≃ Γ−1
ϕ , where the total decay width Γϕ takes
or X1 → Ȳ Φ∗ (and their conjugates). An asymmetry the form [9, 13] Γϕ = m3ϕ /(4π Λ2 ). Here, Λ is a large
between the partial widths for X1 → udd and X̄1 → ūd¯d¯ energy scale corresponding to the underlying ultraviolet
arises from interference between the diagrams shown in dynamics. For example, Λ ∼ MPl = 2.43 × 1018 GeV
Fig. 1, and is characterized by for many moduli in string theory or supergravity. At
reheating, the radiation temperature is approximately [9]
1
Γ(X1 → udd) − Γ(X̄1 → ūd¯d)
¯
ǫ = (3) 1/4
2ΓX1
10 MPl mϕ 3/2
TRH ≃ 5 MeV . (5)
m5X1 Im[λ∗1 λ2 ζ1 ζ2∗ ] g Λ 100 TeV
≃ ,
256π 3 |ζ1 |2 M 4 mX2
We require TRH & 5 MeV to maintain successful nucle-
where we have assumed that the total decay rate ΓX1 osynthesis.
is dominated by X1 → Ȳ Φ∗ over the three-quark mode, Eq. (4c) determines the comoving density of visible
and that mX2 ≫ mX1 . For ǫ 6= 0, X1 decays generate baryons. The remnant of the intermediate X1 stage ap-
a baryon asymmetry in the visible sector, and by CPT pears in the right-hand-side of Eq. (4c). The factor ǫ
an equal and opposite baryon asymmetry in the hidden encodes the X1 decay asymmetry. In writing Eq. (4) we
sector. These asymmetries can be “frozen in” by the implicitly take mX1 ≫ T and ΓX1 ≫ Γϕ , H. The former
weakness of the coupling between both sectors. condition implies inverse decays and scattering reactions
We model the non-thermal production of X1 as a re- that could wash out the asymmetry, such as ūX1 → dd ,
heating process after a period where the energy content are suppressed by Boltzmann factors of e−mX1 /T , while
of the Universe was dominated by the coherent oscilla- the latter condition is satisified for |ζ1 | ≫ m2ϕ /(mX1 Λ).
tions of a scalar field ϕ. This field could be the inflaton, The hidden-visible baryon asymmetry can also be washed
or it could be a moduli field arising from an underlying out by Y Φ → 3q̄ scattering. A sufficient condition for this
theory with supersymmetry [12] or a compactification of washout process to be ineffective is
string theory [13]. As ϕ oscillates, it decays to visible −1/5
and hidden sector states reheating these two sectors. We X λa λ∗ ζ ∗ ζb TeV6
b a
suppose that a fraction of the ϕ energy density ρϕ is con- TRH . (2 GeV) . (6)
M 4 mXa mXb
verted into X1 , X̄1 states, while the remainder goes into a,b
visible and hidden sector radiation which quickly ther-
The allowed TRH increases roughly linearly with the mass
malizes due to gauge interactions.
scale (M 4 m2X1,2 )1/6 .
The dynamics of hylogenesis and reheating are gov-
The resulting baryon asymmetry today is given by
erned by the Boltzmann equations
d 3 ǫ NX TRH
a ρϕ = − Γ ϕ a 3 ρϕ , (4a) ηB ≡ nB /s = f (mϕ Γϕ ) . (7)
dt mϕ
d 3 Assuming that reheating occurs instantaneously, one can
a s = + Γϕ a3 ρϕ /T , (4b)
dt show analytically that f = 3/4. A numerical solution to
d 3 Eqs. (4) reveals f ≃ 1.2, with less than 10% variation
a nB = ǫ NX Γϕ a3 ρϕ /mϕ (4c)
dt over a wide range of (mϕ , Γϕ ). Larger values of TRH
with ϕ mass mϕ and decay rate Γϕ . s ≡ sHS + sSM = (larger mϕ for fixed Λ) allow for greater production of
(2π 2 /45)gs T 3 is the total entropy density of SM and HS baryons.
3
For the parameter values mϕ = 2000 TeV, Λ = MPl , u u +
NX = 1, we find TRH ≃ 400 MeV and ηB /ǫ ≃ 2.5×10−7. p u s̄ K
The observed value of the baryon asymmetry is obtained d
for Im[λ∗1 λ2 ζ2 /ζ1 ]m5X1 /(M 4 mX2 ) ∼ 3. Smaller values of X1,2
ǫ and mϕ are viable for Λ < MPl .
We have implicitly assumed that the Z ′ maintains ki- Y, Φ Φ∗ , Ȳ
netic equilibrium between the SM and hidden sectors.
This will occur if ΓZ ′ h1/γi > H, where γ is a relativistic
time dilation factor, which implies [14] FIG. 2: Diagram for induced nucleon decay processes pY →
K + Φ∗ and pΦ → K + Ȳ .
g 1/2 m ′ −1 T 3/2
Z
κ > 1.5 × 10−8 , (8) Y N → Φ∗ M and ΦN → Ȳ M mediated by X1,2 , where N
10 GeV GeV
is a nucleon and M is a meson (Fig. 2). We call this pro-
provided TRH > mZ ′ . After baryogenesis, the CP- cess induced nucleon decay (IND). IND mimics standard
symmetric densities of hidden states are depleted very nucleon decay N → M ν, but with different kinemat-
efficiently through annihilation Y Ȳ → Z ′ Z ′ and ΦΦ∗ → ics of the daughter meson, summarized in Table I. For
Z ′ Z ′ provided mZ ′ < mY , mΦ , with the Z ′ decaying down-scattering processes, where the mass of the initial
later to SM states by mixing with the photon. The cross- DM state is greater than the final DM state, the meson
section for Y Ȳ → Z ′ Z ′ is given by [14] momentum pM from IND can be much greater than in
nucleon decay. The quoted range of pM corresponds to
e′ 4 1 the range of allowed masses (mY , mΦ ) consistent with
q
hσvi = 1 − m2Z ′ /m2Y (9)
16π m2Y Eqs. (2, 10). For fixed masses, pM is monochromatic,
e′
4
3 GeV
2 with negligible broadening from the local DM halo ve-
≃ (1.6 × 10−25 cm3 /s) . locity. (We also note a related study considering lepton-
0.05 mY
number violating inelastic DM-nucleon scattering [18].)
Annihilation of Φ∗ Φ is given by a similar expression. To estimate the rate of IND we consider the specific op-
These cross sections are much larger than what is needed erator (λa /M 2 )(ūc d)R (X̄s)R that mediates Φp → Ȳ K + ,
to obtain the correct DM abundance by ordinary ther- illustrated in Fig. 2. Treating the Φ and Y states as
mal freeze-out, and all of the non-asymmetric DM den- spectators, the hadronic matrix element can be estimated
sity will be eliminated up to an exponentially small re- from the value computed for the p → K + ν decay through
mainder [15]. Note that the annihilation process may the corresponding three-quark operator [19]. We find
occur later than is typical for thermal freeze-out for that the sum of the IND scattering rates pΦ → K + Ȳ
TRH . mY,Φ /20, but even in this case the remaining and pY → K + Φ∗ is given by
non-asymmetric density will be negligibly small [16]. 2
The role of the hidden Z ′ in our model is to ensure −39 3
X TeV3
(σv)IN D = C (10 cm /s) (11)
the thermalization and symmetric annihilation of Y and a
ma M 2 /λ∗a ζa
Φ. A more minimal alternative is to couple Φ to the SM
Higgs boson h via the operator ξ |h|2 |Φ|2 . For ξ & 10−3 , where 0.5 < C < 1.6, depending on mΦ,Y within the al-
this interaction, together with Y XΦ and |Φ|4 , appears lowed range. We expect IND modes from other operators
to be sufficient for both thermalization and symmetric to be roughly comparable. This estimate, which relies on
annihilation. a chiral perturbation theory expansion that is expected
The residual CP-asymmetric density of Y, Φ is not to be poorly convergent for pM ∼ 1 GeV, is approximate
eliminated and makes up the DM [17]. The relic num- at best.
ber density is fixed by total baryon number conservation: An effective proton lifetime τp can be defined as the
nY = nΦ = nB . Thus the ratio between the energy den- inverse IND scattering rate per target nucleon, τp−1 =
sities of DM and visible baryons is nDM (σv)IN D . With a local DM density of 0.3 GeV/cm3 ,
(σv)IN D = 10−39 cm3 /s corresponds to a lifetime of
Ωd /Ωb = (mY + mΦ )/mp . (10) τp ≃ 1032 yr. This is similar to the current lifetime bound
Present cosmological observations imply Ωd /Ωb =
4.97 ± 0.28 [1], which corresponds to a range Decay mode pSND
M (MeV) pIND
M (MeV)
4.4 GeV . mY + mΦ . 4.9 GeV, or 1.7 GeV . N→π 460 800 - 1400
mY , mΦ . 2.9 GeV when combined with the con- N →K 340 680 - 1360
straint |mY − mΦ | < mp + me . N →η 310 650 - 1340
III. Dark Matter Signatures: A novel signature
of this mechanism is that DM can annihilate nucle-
ons through inelastic scattering processes of the form TABLE I: Daughter meson M ∈ {π, K, η} momentum pM for
standard nucleon decay (SND) and down-scattering IND.
4
on p → K + ν of 2.3 × 1033 yr [20]. However, existing nu- KS thank the Aspen Center for Physics and Perimeter In-
cleon decay bounds may not directly apply to IND due to stitute for Theoretical Physics for hospitality while this
the non-standard meson kinematics [21], and additional work was being completed. ST thanks Caltech where a
suppression can arise from the second factor in Eq. (11). portion of this work was completed. The work of HD
There is also a direct detection signal in our model due is supported in part by the United States Department
to the hidden Z ′ : Y and Φ can scatter elastically off pro- of Energy under Grant Contract DE-AC02-98CH10886.
tons. The effective scattering cross-section per nucleon The research of DM and KS is supported in part by
for either Y or Φ is spin-independent and given by NSERC of Canada Discovery Grants.
2
2Z µN 2
σ0SI = (5 × 10−39 cm2 ) (12)
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