KL−KSmass difference and rareKdecays in a phenomenological gauge model

Abstract

We discuss the ${K}_{L}\ensuremath{-}{K}_{S}$ 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) \ifmmode\times\else\texttimes\fi{} 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 ${K}_{L}\ensuremath{-}{K}_{S}$ 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 ${K}^{0}\ensuremath{\rightarrow}\ensuremath{\mu}\overline{\ensuremath{\mu}}$ amplitude. The result for the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}e\overline{e}$ branching ratio is in reasonably good agreement with the recent experimental result. Calculations of the branching ratios for the decays ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, ${K}_{L,S}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, and ${K}_{L,S}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}e\overline{e}$ are also performed.