Flavor-Changing Yukawa Coupling in the Standard Model and Muon Polarization inKL→μμ¯

The muon longitudinal polarization $P_L$ in $K_L\to \mu \overline{\mu }$ decay is investigated in the standard model. The induced $\overline{s}\mathrm{dH}$ vertex responsible for $P_L$ turns out to be unexpectedly "large." The measurement of $P_L$ above ∼ ${10}^{-3\mathrm{}}$ will, therefore, be a signal of the existence of a rather light Higgs boson ($M_H\lesssim 10$ GeV). It is also shown that the mechanism of guage-dependence cancellation between Higgs-boson-exchange and box diagrams works even in the standard model.