Constraining P and CP violation in the main decay of the neutral Sigma hyperon

On general grounds based on quantum field theory the decay amplitude for $\Sigma^0 \to \Lambda \gamma$ consists of a parity conserving magnetic and a parity violating electric dipole transition moment. Because of the subsequent self-analyzing weak decay of the $\Lambda$ hyperon the interference between magnetic and electric dipole transition moment leads to an asymmetry in the angular distribution. Comparing the decay distributions for the $\Sigma^0$ hyperon and its antiparticle gives access to possible C and CP violation. Based on flavor SU(3) symmetry the present upper limit on the neutron electric dipole moment can be translated to an upper limit for the angular asymmetry. It turns out to be far below any experimental resolution that one can expect in the foreseeable future. Thus any true observation of a CP violating angular asymmetry would constitute physics beyond the standard model, even if extended by a CP violating QCD theta-vacuum-angle term.