T-Violation in $K^+ \to μ^+ νγ$ Decay And Supersymmetry

Measurement of the transverse muon polarization $P^{\bot}_μ$ in the $K^+ \rightarrow μ^+νγ$ 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 $P^{\bot}_μ$ is sensitive to the physical $CP$-violating phases in new physics induced four-Fermi interactions, and then we calculate the dominant contributions to $P^{\bot}_μ$ from squark family mixings in generic supersymmetric models. Estimates of the upper bounds on $P^{\bot}_μ$ are also given. It is found that a supersymmetry-induced right-handed quark current from $W$ boson exchange gives an upper limit on $P^{\bot}_μ$ as large as a few per cent, whereas with charged-Higgs-exchange induced pseudoscalar interaction, $P^{\bot}_μ$ is no larger than a few tenths of a per cent. Possible correlations between the muon polarization measurements in $K^+ \rightarrow μ^+νγ$ and $K^+ \rightarrow π^0μ^+ν$ decays are discussed, and distinctive patterns of this correlation from squark family-mixings and from the three-Higgs-doublet model are noted.

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