T-Violation in $K^{+}\to {\mu }^{+}\nu \gamma$ Decay And Supersymmetry

Abstract

Measurement of the transverse muon polarization $P_{\mu }^{\perp }$ in the $K^{+}\to {\mu }^{+}\nu \gamma$ decay will be attempted for the first time at the ongoing KEK E246 experiment and also at a proposed BNL experiment. We provide a general analysis of how $P_{\mu }^{\perp }$ is sensitive to the physical $CP$-violating phases in new physics induced four-Fermi interactions, and then we calculate the dominant contributions to $P_{\mu }^{\perp }$ from squark family mixings in generic supersymmetric models. Estimates of the upper bounds on $P_{\mu }^{\perp }$ are also given. It is found that a supersymmetry-induced right-handed quark current from $W$ boson exchange gives an upper limit on $P_{\mu }^{\perp }$ as large as a few per cent, whereas with charged-Higgs-exchange induced pseudoscalar interaction, $P_{\mu }^{\perp }$ is no larger than a few tenths of a per cent. Possible correlations between the muon polarization measurements in $K^{+}\to {\mu }^{+}\nu \gamma$ and $K^{+}\to {\pi }^0{\mu }^{+}\nu$ decays are discussed, and distinctive patterns of this correlation from squark family-mixings and from the three-Higgs-doublet model are noted.

Comments: Revtex, 29 pages including 4 epsf figures