T-Violation in \(K^+ \to \mu^+ \nu \gamma\) Decay And Supersymmetry

Abstract

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