Parity violating longitudinal muon polarization in K⁺ → π⁺ μ⁺ μ^- beyond leading logarithms

We generalize the existing analyses of the parity violating muon polarization asymmetry Δ_LR in K⁺ → π⁺ μ⁺ μ ^- beyond the leading logarithmic approximation. The inclusion of next-to-leading QCD corrections reduces the residual dependence on the renormalization scales, which is quite pronounced in the leading order. This leads to a considerably improved accuracy in the perturbative calculation of the short distance dominated quantity Δ_LR. Accordingly this will also allow to obtain better constraints on the Wolfenstein parameter ρ{variant} from future measurements of Δ_LR. For -0.25 ≤ ρ{variant} ≤ 0.25, V_cb = 0.040±0.004 and m_t = (170±20) GeV we find 3.0 · 10^-3 ≤ |Δ_LR| ≤ 9.6 · 10^·.