Anomalous C-violating Three Photon Decay of the Neutral Pion in Noncommutative Quantum Electrodynamics

We show that a simple and reasonable generalization of the anomalous interaction between the neutral pion and two photons can induce the C-violating three photon decay of the neutral pion in noncommutative quantum electrodynamics. We find that it is mandatory for consistency reasons to include simultaneously the normal neutral pion and photon interaction in which the neutral pion transforms under U(1) in a similar way as in the adjoint representation of a non-Abelian gauge theory. We demonstrate that the decay has a characteristic distribution although its rate still seems too small to be experimentally reachable in the near future. We also describe how to manipulate phase space integration correctly when Lorentz invariance is lost.