University of Delaware

PHYS146

Quarks, Gluons, and the Big Bang

Maurice Barnhill
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Last revised 1999/04/14


Class Notes IX: Discrete Symmetries

Parity, Charge Conjugation, and Time Reversal

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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