A bound on violations of Lorentz invariance

Recently Coleman and Glashow [Phys. Lett. B 405 (1997) 249; Harvard Univers ity Theoretical Physics Preprint 98/AO76 (pvt. comm)] have developed a mode l which allows the introduction of a small violation of Lorentz invariance. Observational signatures arise because this interaction also violates flav or conservation and allows the radiative decay of the muon, mu --> e + gamm a, whose branching ratio increases as b gamma(4) where gamma is the Lorentz factor of the muon with respect to the reference frame in which the: dipol e anisotropy of the universal microwave radiation vanishes. In this paper w e place a bound on the Lorentz invariance violating parameter, b, of b < 10 (-25) based on observations of horizontal air showers with n(e) greater tha n or equal to 5 x 10(6). With such small values of b the proposed radiative decay of the muon will not affect the functioning of the muon collider. (C ) 1999 Elsevier Science B.V. All rights reserved.