Supersymmetric prediction for the muon transverse polarization in the K+->pi(0)mu(+)nu(mu) decay

The muon transverse polarization in the K+ --> 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, 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.