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9.6 Particle Physics

9.6.1 Classification of Elementary Particles
9.6.1.1 Leptons
Thses are simplest & elementary particle with no internal structure known. They are
affected by electromagnetic, weak & gravitational forces but not by strong interaction.
These are 3 pairs:

Electrons  e  , Muon    , Tauon   , Electron-neutrino  e  , Muon-neutrino    ,

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Tau-neutrino    .

They also have corresponding antiparticles.

9.6.1.2 Baryons
Protons and particles heavier than proton form this group. Proton  p  and neutron  n 

are called nucleons and rests are called Hyperons.

Hyperons are a special class of baryons characterized by a time decay of the order of
 1010 sec and mass value intermediate between those of the neutrons and deuteron.

Their decay time is very much greater than the time of their formation time   1023 sec  .
zi
It is because of this unsolved problem that these particles along with K-mesons are called
strange particles.
Hyperons are Lambda    , Sigma   ,0  , Xi   0 ,    , and Omega     .

9.6.1.3 Mesons
The rest mass of these particles varies between about 250me to 1000me . They are the
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agent of interaction between the particles inside the nucleus. Mesons are
Pions   ,  0 ,    , Kaons  K  , K 0  and Eta  0  .

Baryons and Mesons are together called as Hadrons.

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9.6.2 Particles and Anti-Particles

The anti particle of a particle has the same mass, spin & lifetime if unstable, but its
charge (if any) has the opposite sign. Thus the alignment between its spin and magnetic
moment is also opposite to that of the particle.
(a) Electron and Positron
Same mass and spin but opposite charge. They combine with the emission of photon
e   e   2

ks
(b) Proton and Anti-proton
Anti protons are produced by bombardment of 6 GeV Protons

p  p   energy   p  p  p  p

The K.E. of bombarding proton is converted to a p & p pair + K. E of four particles.

Antiprotons interact strongly with matter & annihilate with proton. In a typical
annihilation reaction the rest mass of the annihilation pair appears as five pions and their
K.E.
p  p           0
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(c) Neutron and Anti-neutron
The nature of anti-neutron is not well known. Both neutron and anti-neutron have zero
charge and same mass. Since neutron is supposed to have certain internal charge
distribution it is expected that antineutrons has an opposite internal charge.
Anti-neutron is quickly annihilated either by a p or n usually with the production of
fi
several pions.
If anti-neutron is not annihilated by nucleons, then it decays by the reaction
n  p  e  e

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(d) Neutrino and Anti-neutrino

1
Neutrino is elementary particle that has zero charge, spin, zero rest mass and nearly
2
zero magnetic moment. It has finite energy and momentum in flight. It travel with speed
of light c and doesn’t cause any ionization on passing through matter.
The anit-particle of neutrino is a anti-neutrino. The difference between neutrino and
anti-neutrino is only in the sense of their helicity  H  .

The spin of neutrino   is opposite in direction to the direction of its motion; viewed

ks
from behind, the neutrino spins counterclockwise. Neutrino moves in space in the manner
of a left-handed screw. Thus a neutrino possesses a “Left handed” helicity or negative
helicity.

The spin of anti-neutrino    is in the same direction as its direction of motion; viewed
from behind, the anti-neutrino spins clockwise. Neutrino moves in space in the manner of
a right-handed screw. Thus a neutrino possesses a “Right handed” helicity or positive
helicity.
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9.6.3 Elementary Particles Quantum Numbers
(a) Charge
The elementary charges are 0 and  e .
(b) Spin
The spin quantum number is either an integer or an half odd integer for the particles so
for detected
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Bosons: spin= 0,1, 2.....
Fremions: spin= 1/ 2,3 / 2,.....
(c) Baryon Number (B)
1 assigned to all Baryons, 1 assigned to all anti-Baryons, 0 for others.

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(d) Lepton Number  Le , L , L 

Le  1 (for electrons and e -neutrino)

L  1 (for muon and  -neutrino)

L  1 (for tauon and  -neutrino)

1 is assigned for their corresponding anti-particles and 0 is assigned for others.

(e) Stangeness Number  S 

ks
S  1 (for Kaons)
S  1 (for  -Hyperons)
S  1 (for  -Hyperons)
S  2 (for  -Hyperons)
S  3 (for  -Hyperons)
(f) Hypercharge  Y 

Hypercharge is equal to the sum of strangeness and Baryon number of the particles
families
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Y  BS
(g) Isospin and Isotopic quantum Number
A number of hadrons families have members having similar masses but different charges.
These families are called “multiplets” and multiplicity of these families are given
by 2 I  1 , where I is called the “Isotopic quantum number”
Ex:   ,  0 ,    ; Multiplicity  2 I  1  3  I  1 ( for pions)
fi
The components of isospin I in an abstract “Isospace” in any specified direction is
governed by a quantum number denoted by I 3 . The possible values of I 3 are restricted to

I ,  I  1 ,........., 0,..........   I  1 ,  I ( I : integral)

I ,  I  1 ,........., 1/ 2, 1/ 2,..........   I  1 ,  I ( I : half integral)

Ex:   ; I 3  1,  0 ; I 3  0,   ; I 3  1

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Class Name Symbol Spin B Le L L S Y I I3

Electron e 1 0 1 0 0
2
Muon  1 0 0 1 0
2
Tauon  1 0 0 0 1
LEPTON

2
e -neutrino e 1 0 1 0 0

ks
2
 -neutrino   1 0 0 1 0
2
 -neutrino  1 0 0 0 1
2
Pion   , 0 0 0 0 0 0 0 0 1 1, 0
MESON

Kaon K,K0 0 0 0 0 0 1 1 1 1 1
 ,
2 2 2
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 -meson 0 0 0 0 0 0 0 0 0 0

Proton p 1

1 1 0 0 0 0 1 1 2
Neutron n 2 2 1

2
 Hyperon   ,0 1 1 0 0 0 1 0 1 1, 0
BAYRON

2
fi
 Hyperon 0 ,   1 1 0 0 0 2 1 1 1 1
 ,
2 2 2 2
 Hyperon  3 1 0 0 0 3 2 0 0
2
 Hyperon 0 1 1 0 0 0 1 0 0 0
2

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9.6.4 Classification of Fundamental Forces

Four Basic interactions are summarized below:
Interaction Particles Range Relative Particle
Affected Strength Exchanged
Strong Hadrons  1015 m 1 Meson
(Spin=0)
Electromagnetic Charged   102 Photons
Particles (Spin=1)

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Weak Hadrons &  1017 m  1013 Intermediate
Leptons Bosons
(Spin=1)
Gravitational All   1040 Gravitons
(Spin=2)
Quantum numbers that are conserved in all interactions
(a) Charge
(b) Spin
zi
(c) Baryon Number (B)

(d) Lepton Number  Le , L , L 

Quantum numbers that are conserved in some interactions

Strong interactions: S  0, I  0, I 3  0

Electromagnetic interactions: S  0, I  0, I 3  0
fi
Weak interactions: S  0, I  0, I 3  0

NOTE:
1. In weak interactions leptons are affected.
2. In electromagnetic interactions photons are affected.
3. In strong interactions mesons are affected.

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Example: Identify the interactions if allowed

(a)    p  0  K 0 (b)    p   0  n

(c) p     0  p (d) 0   0  

(e)  0     (f) K 0      

(g)  0  p    (h)     0   

(i)  0  p  e  
Solution:

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(a)    p  0  K 0
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Strong interactions: since S  0, I  0, I 3  0

(b)    p   0  n
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Strong interactions: since S  0, I  0, I 3  0

(c) p     0  p
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q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Electromagnetic interactions: since S  0, I  0, I 3  0

(d) 0   0  
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Electromagnetic interactions: since S  0, I  0, I 3  0
fi
(e)  0    
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Electromagnetic interactions: since S  0, I  0, I 3  0

(f) K 0      
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Weak interactions: S  0, I  0, I 3  0

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(g)  0  p   
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Weak interactions: S  0, I  0, I 3  0

(h)     0   
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Weak interactions: S  0, I  0, I 3  0

(i)  0  p  e  

ks
q  0, s  0, B  0 and L  0 , thus interaction is allowed.
Weak interactions: S  0, I  0, I 3  0

9.6.5 Gellmann & Neeman’s classification system for Hadrons

This classification system for hadrons encompasses the many short lived resonance
particles as well as the relatively stable hadrons. This scheme collects isospin multiplets
into super multiplets whose members have the same spin but differ in Isospin  I  and a

quantity called Hypercharge  Y  .

zi
The concept of super multiplet is elaborated by showing similar spin Baryons and mesons
on a plot of hypercharge  Y  versus isotopic spin component  I z  .

1
The figure below shows the 8 member super multiplets of spin Baryons.
2
Y
n p
1
fi
 0 
1 1/ 2  0 1/ 2 1 I 3

1
 
0

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The figure below shows the 8 member super multiplets of spin 0 mesons.
Y
K0 K
1

 0 
0
1 1/ 2  1/ 2 1 I 3

1
 

ks
K K

3
The figure below shows the 10 member super multiplet of spin Baryon.
2
Y

 0   
1
zi
 0 
3 / 2 1 1/ 2 1/ 2 1 3 / 2 I3

 1 0
fi

2

Gellmann-Nishijima Relation
1
q  I3  B  S 
2

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9.6.6 Quark Model of Hadrons (Baryons and Mesons)

Murray Gell-Man and G.Zweig proposed the quark model in 1964. The theory is based
on the idea that the hadrons are built up from a limited number of “fundamental” units,
which have acquired the name quarks. The original three quarks were labeled
u (for “up”), d (for “down”) and s (for “strange”).
Quark Charge Spin B S I I3 Y

u-quark +2/3 e 1/2 1/3 0 1/2 1/2 1/3

ks
d-quark - 1/3 e 1/2 1/3 0 1/2 -1/2 1/3
s-quark -1/3 e 1/2 1/3 -1 0 0 -2/3

Each quark has a baryon number of B = 1/3. Also each quark has an anti-quark associated

with it  u , d & s  . The magnitudes of each of the quantum number for the anti-quarks

has the same magnitude as those for the quarks, but the sign is changed and Baryon is
reversed.
Anti-Quark Quantum Number:
zi
Quark Charge Spin B S I I3 Y

u -2/3 e 1/2 -1/3 0 1/2 -1/2 -1/3

d + 1/3 e 1/2 -1/3 0 1/2 +1/2 -1/3

s +1/3 e 1/2 -1/3 +1 0 0 +2/3

Composition of Baryons according to Quark Model

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A baryon is made up of 3 quarks.
e.g. The proton is made up of two u-quarks and a d-quark (uud). Hence,
Electric charge of proton = + 2/3 +2/3 -1/3 = + 1
Baryon number of proton = + 1/3 + 1/3 + 1/3 = + 1
Strangeness number of proton = 0 + 0 + 0 = 0
All are in agreement with the quantum numbers for proton.

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Quantum Number and Quark Contents

(i) Baryon: 1/2 spin

Particle Quark Content I I3 Y B S

p uud ½ ½ 1 1 0
n udd ½ -½ 1 1 0
∑+ uus 1 1 0 1 -1
sud  sdu

ks
∑0 1 0 0 1 -1
2
∑- dds 1 -1 0 1 -1
Ξo uss ½ ½ -1 1 -2
Ξ- dss ½ -½ -1 1 -2
sdu  sud
Λo 0 0 0 1 -1
2
zi
(ii) Baryon: 3/2 spin
Particle Quark Content I I3 Y B S
∆- ddd 3/2 -3/2 1 1 0
∆o ddu 3/2 -½ 1 1 0
∆+ duu 3/2 +½ 1 1 0
∆++ uuu 3/2 +3/2 1 1 0
-
Ω sss 0 0 -2 1 -3
fi

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Mesons are made up of one quark and one anti-quark.

A π+ meson is a combination of a u-quark and a d-anti-quark  ud  .

Electric charge of π+ = + 2/3 +1/3 = + 1

Baryon number of π+ = + 1/3 – 1/3 = 0
Strangeness number of π+ = 0 + 0 = 0
All these are in agreement with the quantum numbers for the meson.
Particle Quark Content I I3 Y B S

ks
π+ du 1 1 0 0 0

πo
uu  dd  1 0 0 0 0
2
π- ud 1 -1 0 0 0
+
K su ½ ½ 1 0 1
o
K sd ½ -½ 1 0 1
-
K su ½ -½ -1 0 -1
Ko sd ½ ½ -1 0 -1
zi
Charm, Bottom and Top
In 1970, the existence of a fourth quark, called “c” or charmed quark was proposed. The
charmed quark was suggested to explain the suppression of certain decay process that is
2
not observed. The charm quark has a charge of  e , strangeness 0 and a charm quantum
fi
3
number of +1. Other quarks have 0 charm.
Later on two more quarks were proposed named ‘t’ or top quark and ‘b’ or bottom quark.
2 1
‘t’ quark has electric charge  e and ‘b’ quark has electric charge  e .
3 3

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Three generation of quarks and leptons:

Both leptons and quarks appear to come in three generations of doublets with all particles
having spin 1/2. The table below shows the properties of the three generations of quarks
and leptons. The first generation contains two leptons, the electron and the electron-
neutrino, and two quarks up and down. All properties of ordinary matter can be
understood on the basis of these particles. The second generation includes the muon and
muon-neutrino and the charm and strange quarks. These particles are responsible for
most of the unstable particles and resonances created in high energy collisions. The third

ks
generation includes the tau and tau-neutrino and the top and bottom quarks.
Generation Quark Symbol Charge Strangeness Charm
Up u 2 0 0
 e
3
1
Down d 1 0 0
 e
3
Charm c 2 0 +1
 e
Quark 3
2
zi
Strange s 1 -1 0
 e
3
Top t 2 0 0
 e
3
3
Bottom b 1 0 0
 e
3
Generation Lepton Symbol Charge
fi
1 Electron e- -1
e-neutrino e 0
Lepton
2 Meson μ- -1
μ-neutrino μ 0
3 Tau τ- -1

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