Exploration of Lorentz violation in neutral-kaon decay

The KLOE collaboration recently reported bounds on the directional dependence of the lifetime of the short-lived neutral kaon $K^0_S$ with respect to the dipole anisotropy of the cosmic microwave background. We interpret their results in an effective field theory framework developed to probe the violation of Lorentz invariance in the weak interaction and previously applied to semileptonic processes, in particular $\beta$ decay. In this approach a general Lorentz-violating tensor $\chi^{\mu\nu}$ is added to the standard propagator of the $W$ boson. We perform an exploratory study of the prospects to search for Lorentz violation in nonleptonic decays. For the kaon, we find that the sensitivity to Lorentz violation is limited by the velocity of the kaons and by the extent to which hadronic effects can be calculated. In a simple model we derive the $K^0_S$ decay rate and calculate the asymmetry for the lifetime. Using the KLOE data, limits on the values of $\chi^{\mu\nu}$ are determined.