Supersymmetric prediction for the muon transverse polarization in theK+→π0μ+νμdecay

The muon transverse polarization in the $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }$ decay will be measured at the ${10}^{-4}$ level in forthcoming experiments. We compare the phenomenological perspectives with the theoretical predictions in supersymmetric extensions of the standard model. In the minimal extension, $\mathrm{CP}$-violating phases lead to a nonzero transverse polarization, that, however, is too small to account for a positive experimental signal. The problems that one encounters when departing from minimal assumptions are discussed. An observable effect is possible if the hypothesis of $R$-parity conservation is relaxed, but only at the price of assuming a very special pattern for the $R$-parity-breaking couplings.