Energy dependence of the fundamental parameters of the K/sup 0/-K-bar/sup 0/ system. II. Theoretical formalism

We present a detailed analysis of the previously reported anomalous energy dependence of the fundamental K/sup 0/-K-bar/sup 0/ parameters ..delta..m = m/sub L/-m/sub S/, tau/sub S/, Vertical Bareta/sub +/-Vertical Bar, and tanphi/sub +/-. Such variations with energy can arise from the interaction of the kaons with an external field or medium. A phenomenological formalism is introduced to describe such energy-dependent influences on the K/sup 0/-K-bar/sup 0/ system. Using this formalism we demonstrate that effects of the type suggested by the data cannot be ascribed to an interaction of the kaons with an electromagnetic, hypercharge, or gravitational field, or to the scattering of the kaons from stray charges or cosmological neutrinos. The data are, however, compatible with an interaction which is even under charge conjugation, and models of such an interaction are discussed. We also consider the possibility that such effects may arise from a fundamental violation of Lorentz invariance. All of the mechanisms which appear capable of describing the data also suggest that similar effects could arise in neutrino oscillations, and some of the consequences of such a possibility are outlined.