Subatomic Physics

9.4. Charge Conjugation 255
The π 0 and η 0 decay electromagnetically into two photons.
π 0 −→ 2γ and η 0 −→ 2γ,
and therefore must have positive C parity if C is conserved in the decay:
ηc(π 0 )=1, ηc(η 0 )=1. (9.44)
If C parity were applicable only to the photon, π 0 and η 0 ,itwouldnotbe
very useful. However, there exist many particle–antiparticle systems that are fully
neutral. Examples are positronium (e + e − ),π + π − ,pp, nn. The C parity of these
systems depends on angular momentum and spin, and it is a useful quantity for
discussing the possible decay modes.
Use of charge parity for discussion of a decay requires ηc to be a good quantum
number. It is conserved if C commutes with the Hamiltonian H. It is easy to see
that C is not conserved in the weak interaction,
[Hw,C] �= 0. (9.45)
Fig. 7.2 shows that neutrino and antineutrino have opposite polarization (helicity).
If charge conjugation were conserved in the weak interaction, the two particles would
have to have the same helicity.
C conservation in the hadronic interactions has been tested in numerous reactions,
such as
C acting on the reaction gives
pp −→ π + π − π 0 . (9.46a)
pp −→ π − π + π 0 . (9.46b)
If the proton produces the π + forward and the p the π − backwards in the reaction
(9.46a), then the reaction (9.46b) would give rise to π − forward and π +
backward. Thus, if the hadronic Hamiltonian commutes with C, the angular distribution
and energy spectra of the positive and negative pion must be identical.
Comparison of the two distributions and similar tests in other reactions show the
expected symmetry. The result can be stated as (16)
�
�
�
�
C-nonconserving amplitude�
�
� C-conserving amplitude � � 0.01. (9.47)
To test conservation of C in the electromagnetic interaction, charge–parityforbidden
decays are looked for. Consider the decays
π 0 −→ 3γ and η 0 −→ 3γ.
16 C. Baltay, N. Barash, P. Franzini, N. Gelfand, L. Kirsch, G. Lütjens, J. C. Severiens, J.
Steinberger, D. Tycko, and D. Zanello, Phys. Rev. Lett. 15, 591 (1965).