Pion/Kaon Decay in Very Special Relativity
P. Jain, A.C. Nayak
We consider the charged pion decay process within the framework of Very Special Relativity (VSR) using an effective Lagrangian approach. We construct an effective Lagrangian for this process which is invariant under VSR but violates Lorentz symmetry. We find that in the rest frame of pion, the final state muon distribution is not isotropic due to VSR contributions. In the laboratory frame, the decay products show azimuthal angle dependence relative to the pion beam momentum. Furthermore the differential cross section picks up a periodic time dependence with a period of 1 sidereal day. Although such effects are expected in Lorentz violating (LV) theories, this is the first illustration that they also arise within the framework of VSR. This is interesting since VSR effects are most likely to observed at low energies in contrast with all other models of LV which are expected to be significant only at very high energies. We argue that VSR leads to such effects in many high energy processes and not just the pion decay.