Muon transverse polarization in the $K_{l2\gamma}$ process within the SM and three Higgs doublets Weinberg model

We consider two possible sources of the $T$-violating muon transverse polarization in the process $K^+ \to \mu^+ \nu \gamma$: electromagnetic final state interaction in the SM and contribution due to charged-Higgs exchange diagrams in the framework of the Weinberg three doublets model. It is shown that at the one-loop level of the SM the muon transverse polarization, $P_T^{SM}$, varies within $(0.0 \div 1.1 \cdot 10^{-3})$ in the Dalitz plot region. Averaged value of the muon polarization, $ $, in the kinematic region of $E_\gamma \geq 20$ MeV is equal to $4.76\cdot 10^{-4}$. In the case of the model with three Higgs doublets the muon transverse polarization is calculated as a function of charged Higgs masses, imaginary part of the Yukawa coupling constants product and vacuum expectation values of the Higgs doublets. The averaged value of the transverse polarization in the Weinberg model is $ = - 6.62 \cdot 10^{-5}$. Perspectives to probe the effect caused by the charged Higgs exchange diagrams in planned kaon experiments are discussed.