Heavy quark expansion for heavy-light light-cone operators

TL;DR

This paper extends the heavy quark expansion to nonlocal operators on the light-cone, establishing a connection between QCD and HQET operators and deriving matching formulas for light-cone distribution amplitudes.

Contribution

It introduces a generalized framework for heavy quark expansion applicable to nonlocal operators and provides a perturbative calculation of the matching coefficients at one-loop level.

Findings

Confirmed collinear singularities are common in QCD and HQET operators.

Derived a factorization formula linking QCD and HQET operators.

Determined the matching coefficient at one-loop level.

Abstract

We generalize the celebrated heavy quark expansion to nonlocal QCD operators. By taking nonlocal heavy-light current on the light-cone as an example, we confirm that the collinear singularities are common between QCD operator and the corresponding operator in heavy quark effective theory (HQET), at the leading power of $1/M$ expansion. Based on a perturbative calculation in operator form at one-loop level, a factorization formula linking QCD and HQET operators is investigated and the matching coefficient is determined. The matching between QCD and HQET light-cone distribution amplitudes (LCDAs) as well as other momentum distributions of hadron can be derived as a consequence.