# Quarks, Gluons, and the Big Bang

### Maurice Barnhill

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 Last revised 1999/04/14

## Class Notes IX: Discrete Symmetries

### Outline

1. Reference: Text Chapter 5
2. Discrete symmetries
1. Definitions

Symmetry Action
Parity [P] x -> -x
y -> -y
z -> -z
Charge Conjugation [C] Particle -> Antiparticle
Time Reversal [T] t -> -t
CP Particle->Antiparticle
x -> -x
y -> -y
z -> -z
CPT Particle->Antiparticle
x -> -x
y -> -y
z -> -z
t -> -t

2. Effect on position and velocity

Symmetry Action on
Position Time Velocity, Momentum Spin
Parity [P] Reversed Unchanged Reversed Unchanged
Charge Conjugation [C] Unchanged Unchanged Unchanged Unchanged
Time Reversal [T] Unchanged Reversed Reversed Reversed
CP Reversed Unchanged Reversed Unchanged
CPT Reversed Reversed Unchanged Reversed

3. Forces and discrete symmetries

Symmetry Obeyed by
Strong forces Electromagnetic forces Weak forces Gravitational forces
Parity [P] yes yes No yes
Charge Conjugation [C] yes yes No yes
Time Reversal [T] yes yes Almost yes
CP yes yes Almost yes
CPT yes yes yes yes

4. CP, CPT, and antiparticles
3. Matter vs antimatter
1. Initial conditions (esthetics): equal numbers of particles and antiparticles
2. Matter excess by CP breaking:

 X -> anti-u + anti-d and X -> u + e- B 1/3 -1/3 -1/3 1/3 1/3 0 L 1 0 0 1 0 1 B-L -2/3 -1/3 -1/3 -2/3 1/3 -1

 anti-X -> u + d and anti-X -> anti-u + e+ B -1/3 1/3 1/3 -1/3 -1/3 0 L -1 0 0 -1 0 -1 B-L 2/3 1/3 1/3 2/3 -1/3 1

3. Final number of baryons could be unequal to final number of antibaryons given the right adjustments of the decay rates

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