Long- and short-distance contributions to the KL-KS mass difference

Abstract

The long-distance hadronic contributions to the KL-KS mass difference are shown to be small based on their dominant influence upon the K2π weak decays. This phenomenological fact is supported by a gauge-invariant version of the electroweakSU2×U1 quark model. However, the latter model also has gauge-invariant short-distance box graph contributions which can be consistently extracted via the Gaillard-Lee vacuum saturation procedure. Together, these gauge-invariant, minimal long-distance and maximal short-distance graphs provide a realistic and accurate determination of the KL-KS mass difference.