Muon transverse polarization in the K-l2 gamma decay in the standard model

The muon transverse polarization in the $K^+ \to \mu^+ \nu \gamma$ process induced by the electromagnetic final state interaction is calculated in the framework of Standard Model. It is shown that one loop contributions lead to a nonvanihing muon transverse polarization. The value of the muon transverse polarization averaged over the kinematical region of $E_\gamma \geq 20$ MeV is equal to $5.63 \times 10^{-4}$.