G. Buchalla — Page 3

arXiv1994

Parity Violating Longitudinal Muon Polarization in $K^+\toπ^+μ^+μ^-$ Beyond Leading Logarithms

We generalize the existing analyses of the parity violating muon polarization asymmetry $Δ_{LR}$ in $K^+\toπ^+μ^+μ^-$ 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 $\varrho$ from future measurements of $Δ_{LR}$. For $-0.25\leq \varrho \leq 0.25$, $V_{cb}=0.040\pm 0.004$ and $m_t=(170\pm 20)GeV$ we find $3.0\cdot 10^{-3}\leq |Δ_{LR}|\leq 9.6\cdot 10^{-3}$.

hep-ph↗

arXiv1993

The Rare Decays $K^+\toπ^+ν\barν$\ and $K_L\toμ^+μ^-$\ Beyond Leading Logarithms

We analyze the branching ratio for the FCNC mode $K^+\toπ^+ν\barν$\ in the standard model with QCD effects taken into account consistently to next-to-leading order. This involves a two-loop renormalization group analysis for the charm contribution, presented in this paper, and the calculation of $O(α_s)$ corrections to all orders in $m_t/M_W$ for the top-quark case that we have described elsewhere. The inclusion of next-to-leading corrections reduces considerably the theoretical uncertainty due to the choice of the renormalization scales, inherent in any calculation to finite order in perturbation theory. For $K^+\toπ^+ν\barν$\ this point has not been discussed previously. In particular, the related uncertainty in the determination of $|V_{td}|$ from $B(K^+\toπ^+ν\barν)$ is reduced from $\sim 30\%$ to $\sim 7\%$ for typical values of the parameters. Simultaneously also the dependence of $B(K^+\toπ^+ν\barν)$ on the choice of $m_c$ is considerably reduced. We also give the next-to-leading order expression for the short-distance part of $K_L\toμ^+μ^-$. Impacts of our calculations on the determination of the unitarity triangle are presented.

hep-ph↗