Testing the CKM parameters with parity violating longitudinal muon polarization in K+→π+μ+π-

We point out that the parity violating longitudinal muon polarization PL in the decay K+→π+μ+μ- is closely related to the short-distance part of the decay amplitude in KL→μ+μ-. Measuring such polarization would provide not only a rather clean test on the CKM parameter ρ, but also a check on the short-distance contribution to KL→μ+μ-. The possible ranges of PL in the standard and two-Higgs doublets models are presented. We find that PL is not sensitive to extensions of the Higgs sector when taking into account all the experimental data. (orig.)