Test of special relativity and equivalence principle from K physics

Abstract

A violation of local Lorentz invariance (VLI) and hence the special theory of relativity or a violation of the equivalence principle (VEP) in the kaon system can, in principle, induce oscillations between K⁰ and K̅⁰. We construct a general formulation in which simultaneous pairwise diagonalization of mass, momentum, weak or gravitational eigenstates is not assumed. We discuss this problem in a general way and point out that, as expected, the VEP and VLI contributions are indistinguishable. We then insist on the fact that VEP or VLI can occur even when CPT is conserved. Possible CP violation of the superweak type induced by VEP or VLI is introduced and discussed. We show that the general VEP mechanism (or the VLI mechanism, but not both simultaneously), with or without conserved CPT, could be clearly tested experimentally through the energy dependence of the K_L-K_S mass difference and of η₊₋, η₀₀, δ. Constraints imposed by present experiments are calculated.