$K^{+}\to {\pi }^{+}\nu \bar{\nu }$ Beyond Leading Logs and $V_{td}$

Abstract

The calculation of QCD corrections beyond the leading logarithmic approximation for the short-distance dominated rare decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ is summarized. This analysis requires the complete $\mathcal{O}({\alpha }_s)$ corrections to the top contribution to all orders in the top-quark mass and a two-loop renormalization group (RG) calculation for the charm contribution. The inclusion of these QCD corrections reduces considerably the theoretical uncertainty in calculating $B(K^{+}\to {\pi }^{+}\nu \bar{\nu })$. Implications for the determination of $V_{td}$ from this decay are discussed.

5 pages, MPI-PhT/94-3