Next-to-leading-logarithm threshold resummation for exclusive B meson decays

We extend the threshold resummation of the large logarithms $$\ln x$$ 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 $$x\sim 0$$ x ∼ 0 stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $$B\rightarrow K\pi $$ B → K π decays under the NLL resummation in the perturbative QCD approach, and find that it induces up to 20% variation of the direct CP asymmetries in various modes relative to the LL results. Our method to avoid the Landau singularity in the inverse Mellin transformation causes at most 10% theoretical uncertainty.