Comment on calculations of theKL→μμ¯decay rate in gauge theories

Abstract

We reexamine the calculations of the $K_L\to \mu \overline{\mu }$ decay rate and the $K_L-K_S$ mass difference in the Weinberg-Salam model with the Glashow-Iliopoulos-Maiani mechanism incorporated. We consider both the free-quark model and corrections due to strong interactions in an asymptotically free theory, and compare our results with those of other recent calculations. Our conclusions are basically identical to those drawn from our original free-quark calculation: The decay amplitude for $K_L\to {\mu }^{+}{\mu }^{-}$ is dominated by the conventional two-photon exchange, and the decay rate places no useful limit on the charmed-quark mass, whereas the $K_L-K_S$ mass difference constrains this mass by $m_c\lesssim$ a few GeV, as noted previously.