# Invariance Principles and Conservation Laws

## Parity of particle and anti-particle

The parity of an anti-fermion is opposite the parity of the fermion, while the parity of an anti-boson is the same as the parity of the boson. Thus the parity of e+e- or p-pbar is -1, not including the orbital angular momentum factor. The parity of π+π- is +1, not including the orbital angular momentum factor.

As an example, the ρ meson of mass 770 MeV and J=1 (spin 1) decays (strongly) to π+π-. The spin 0 pions must be in an L=1 orbital state in order that angular momentum is conserved. Therefore, the parity of the ρ is (-1)L = -1. We write that the ρ is a state with JP = 1-.

## Charge Conjugation

The operation of charge conjugation in the classical sense is to change every positive charge with a negative charge, and vice versa. The directions of electric fields reverse under charge conjugation. The directions of magnetic fields also reverse since magnetic fields are created by moving charges -- the directions of the charges don't change, but the signs do, resulting in an overall change of sign. These changes leave Maxwell's equations unchanged since they are linear in the electric and magnetic fields.

In quantum field theory the operation of charge conjugation exchanges particle and anti-particle. For charged particles, this is the same thing as changing the sign. The difference occurs only for neutral particles which are not their own anti-particle, and examples abound: K0, D0, B0, neutrinos, Σ0, and Ξ0 are a few.

The charge conjugation or C-pairty eigenstates must be neutral, since C|π+> --> |π-> Beyond that, the C-parity operation is like parity.

#### C-parity of the photon

Both E and B fields change sign under C-parity. Therefore, photons have negative C-parity, C=-1.

#### C-parity of the π0

The π0 decays electromagnetically to two photons π0 --> γγ and therefore has even C-parity.

The decay of a π0 to one photon is ruled out by energy and momentum conservation. The decay of a π0 to three photons violates C-parity. Of course, C-parity is not a truly fundamental symmetry, and even seems to be violated since the world around us is matter dominated, and certainly not symmetric in particles and anti-particles. Therefore we'd like to know how well C-parity works. An indication of this is from limits to forbidden processes such as the 3γ decay of the pion. The limit, expressed as a fraction of the 2γ branching ratio is: < 3×10-8

## CPT Invariance

An important result from field theory is that all interactions are invariant under the simultaneous operations of C (charge conjugation), P (parity), and T (time reversal). A consequence is that particles and anti-particles must have the same mass and lifetime, and equal but opposite electric charges and magnetic moments. Up to now, the consequences of the CPT theorem have agreed with experimental tests.

## CP violation and T violation

While the combination CPT is thought to be absolutely invariant, no other combination seems to have that property. C and P are violated in the weak interaction.

Discuss C and P violation in the weak interaction using neutrinos as an example.

The combination CP was believed to be conserved by the weak interaction, until:

• it was observed to be violated in KL decays, and
• Sakharov pointed out that CP violation was required in order to explain the evolution of the universe from an initial state with equal amounts o matter and anti-matter, to our present matter-dominated universe.