Test of special relativity from K physics

Abstract

A breakdown of the Local Lorentz Invariance and hence the special theory of relativity in the Kaon system can, in principle, induce oscillations between the K⁰ and K̅⁰ states. We construct a general formulation in which simultaneous pairwise diagonalization of mass, momentum and weak eigenstates is not assumed and the maximum attainable speeds of the momentum eigenstates are different. This mechanism permits Local Lorentz Invariance violation in a manner that may or may not violate CPT. In the CPT-conserving case, we show that violation of special relativity could be clearly tested experimentally via the energy dependence of the K_L-K_S mass difference and we discuss constraints imposed by present experiments. In the CPT-violating case the K⁰-K̅0 system also allows the possiblity of testing different Lorentz properties of matter and antimatter.