Subatomic Physics

276 P , C, CP, andT
(a) C, P ,andT are conserved in all interactions.
(b) C and P are violated but CP is conserved in the weak interaction.
(c) C, P ,andCP are violated, as discussed in Section 9.8.
9.32. Show that CPT invariance guarantees that a particle and its antiparticle have
equal mass.
9.33. Show that the decay of the K 0
(a) to π 0 π 0 is forbidden if the spin of the K 0 is odd,
(b) to π 0 γ is allowed if the spin of the K 0 is not zero.
9.34. How can one determine the parity of the photon? Describe a possible experiment.
9.35. (a) For the cross section, determine the order of magnitude of the ratio
of the interference term of the amplitudes of the parity-violating weak
interaction to that of the electromagnetic interaction in elastic electron
scattering on hydrogen at an energy of 20 GeV and a momentum transfer
of 1 GeV/c. Compare to experiment.
(b) Repeat part (a) for the total cross section of proton–proton scattering
at a laboratory energy of about 50 MeV.
9.36. Show that the rate of the parity-forbidden alpha decay of the 2 − level in 20 Ne
or 16 O is proportional to the square of the weak interaction, i.e., to |F| 2 ,
and does not depend on an interference term between the weak and strong
amplitudes.
9.37. The decay of the η is useful for testing C-invariance. Which of the following
decays are allowed and which are forbidden by C-invariance?
η −→ γγ
η −→ π 0 γ
η −→ π 0 π 0 π 0
η −→ 3γ
η −→ π + π − π 0
9.38. Show that the neutron or any other non-degenerate system cannot have an
electric dipole moment unless both P and T conservation are violated.