A bound on violations of Lorentz invariance

Recently Coleman and Glashow [Phys. Lett. B 405 (1997) 249; Harvard University Theoretical Physics Preprint 98/AO76 (pvt. comm)] 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, μ → e + γ, whose branching ratio increases as bγ⁴ where γ 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 n_e ≥ 5 × 10⁶. With such small values of b the proposed radiative decay of the muon will not affect the functioning of the muon collider.