KL−KSmass difference and rareKdecays in a phenomenological gauge model

Abstract

We discuss the $K_L-K_S$ mass difference and many rare decay modes of $K$ mesons in a phenomenological unified gauge model of strong, electromagnetic, and weak interactions. The strong interactions of the system of pseudoscalar mesons which belong to a 15-dimensional representation of SU(4) are described by a phenomenological Lagrangian which possesses approximate chiral SU(4) × SU(4) symmetry. The additional quantum number is charm. The weak and electromagnetic interactions are described by the Weinberg-Salam model. In general, the results are in qualitative agreement with those of the free-quark-model calculations. Results on the $K_L-K_S$ mass difference indicate that charmed hadrons must not be very heavy. As in the quark -model calculation, we also find a surprising cancellation of the leading terms in the $K^0\to \mu \overline{\mu }$ amplitude. The result for the $K^{+}\to {\pi }^{+}e\overline{e}$ branching ratio is in reasonably good agreement with the recent experimental result. Calculations of the branching ratios for the decays $K^{+}\to {\pi }^{+}\nu \overline{\nu }$, $K_{L,S}\to {\pi }^0\nu \overline{\nu }$, and $K_{L,S}\to {\pi }^{0}e\overline{e}$ are also performed.