OPE for B-meson distribution amplitude and dimension-5 HQET operators

TL;DR

This paper develops an operator product expansion approach to analyze the B-meson light-cone distribution amplitude within HQET, incorporating dimension-5 operators and providing a systematic way to include higher-order corrections.

Contribution

It introduces a gauge-invariant OPE framework for the bilocal HQET operator, including dimension-5 operators, and performs NLO matching in the MS scheme, advancing the theoretical understanding of B-meson LCDAs.

Findings

Derived Wilson coefficients with Sudakov double logarithms.

Expressed B-meson LCDA in terms of HQET parameters including dimension-5 operators.

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

Abstract

The $B$-meson light-cone distribution amplitude (LCDA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory (HQET) and is a building block of QCD factorization formula for exclusive $B$-meson decays. When the corresponding bilocal HQET operator 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 the bilocal HQET operator based on the operator product expansion (OPE), disentangling the singularities from the IR and UV regions systematically. The matching at the next-to-leading order $\alpha_s$ is performed in the $\overline{\rm MS}$ scheme with a complete set of local operators of dimension $d \le 5$, through a manifestly gauge-invariant calculation organizing all contributions in the coordinate space. The result exhibits the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This OPE yields the $B$-meson LCDA 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.