OPE and the NLL-resummed evolution for B-meson distribution amplitude: radiative and nonperturbative corrections to inverse moments for exclusive B decays

Abstract

The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator, associated with a long-distance component in QCD factorization formula for exclusive B decays. We treat the corresponding bilocal operator based on the operator product expansion (OPE), as the short-distance expansion for the quark-antiquark light-like distance t. The matching at the next-to-leading order α s with the local operators of dimension d 5 manifests the OPE that has the Wilson coefficients, receiving the cusp singularity, and the novel higher-dimensional operators with additional gluons. This OPE is useful for a low renormalization scale μ 1 GeV, allowing us to derive the model-independent form of the B-meson DA for t 1 μ in terms of a few nonperturbative parameters. We also discuss the evolution of the DA, which is governed by the cusp as well as the DGLAP-type anomalous dimension. These anomalous dimensions give the “quasilocal” kernel in the coordinate-space representation, and the corresponding evolution equation can be solved analytically, accomplishing the relevant Sudakov resummation. This result allows us to calculate the B-meson DA at the factorization scale mbΛQCD using our OPE-based DA as the input at μ 1 GeV. The impact of our results on the integral relevant to exclusive B decays, λB, is discussed.