Next-to-Leading-logarithm threshold resummation for exclusive $B$ meson decays

TL;DR

This paper advances the precision of threshold resummation in exclusive B meson decays to NLL accuracy, showing improved suppression at the endpoint and significant effects on CP asymmetries, with minimal theoretical uncertainty.

Contribution

It extends threshold resummation to NLL accuracy for exclusive B decays, improving theoretical predictions and analyzing CP asymmetries with reduced uncertainties.

Findings

NLL resummation provides stronger suppression at x~0 than LL.

NLL resummation causes 20-25% variation in CP asymmetries.

Method to avoid Landau singularity introduces little uncertainty.

Abstract

We extend the threshold resummation of the large logarithms $\ln x$ which appear in factorization formulas for exclusive $B$ meson decays, $x$ being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with $x\sim 0$ stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $B\to K\pi$ decays under the NLL resummation, and find that it induces 20-25\% variation of the direct CP asymmetries compared to those from the LL resummation. Our way to avoid the Landau singularity in the inverse Mellin transformation causes little theoretical uncertainty.