Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators

TL;DR

This paper develops an operator product expansion for the B-meson distribution amplitude in HQET, incorporating dimension-5 operators and radiative corrections, to better understand nonperturbative effects at short distances.

Contribution

It introduces a coordinate-space OPE for the B-meson distribution amplitude including dimension-5 operators and \\alpha_s corrections, addressing UV and IR singularities simultaneously.

Findings

Derived Wilson coefficients with Sudakov double logarithms.

Expressed the distribution amplitude in terms of HQET parameters \\bar{\Lambda} and dimension-5 matrix elements.

Discussed the impact of new HQET parameters on the decay-related parameter \\lambda_B.

Abstract

When the bilocal heavy-quark effective theory (HQET) operator for the B-meson distribution amplitude has a light-like distance t between the quark and antiquark fields, the scale \sim 1/t separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat these notorious UV and IR behaviors simultaneously using the operator product expansion, with the local operators of dimension $d \le 5$ and radiative corrections at order \alpha_s for the corresponding Wilson coefficients. The result is derived in the coordinate space, which manifests the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This result yields the B-meson distribution amplitude for t less than \sim 1 GeV^{-1}, in terms of $\bar{\Lambda}=m_B - m_b$ and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive B decays, \lambda_B, is also discussed.