Cosmic Ray Bounds on Violation of Lorentz Invariance

Recently Coleman and Glashow [Coleman and Glashow 1997] have developed a model which allows the introduction of a small violation of Lorentz invariance. Observational signatures arise because this interaction also violates flavor conservation and allows the radiative decay of the muon, ! e + , whose branching ratio increases as b 4 where is the Lorentz factor of the muon with respect to the reference frame in which the dipole anisotropy of the universal microwave radiation vanishes. In this paper we place a bound on the Lorentz invariance violating parameter,b, of b 10,25 based on observations of horizontal air showers with ne 5 x 106 . Similar considerations of cosmic ray neutrinos in the atmosphere improve these bounds by twenty orders of magnitude.