Time reversal violation in $K^+ \to μ^+ νγ$ decay and three Higgs model

Transverse muon polarization in the $K^+ \rightarrow \mu^+ \nu \gamma$ decay is calculated in the model with scalar and pseudo scalar four-Fermi interactions. Combined with a similar calculation in the $K^+ \rightarrow \mu^+ \nu \pi^0$ decay, a possible constraint on parameters in the three-Higgs model is obtained assuming sensitivity of the up-coming KEK experiment. It is pointed out that the predictions for the two polarizations are strongly correlated in the three Higgs model.