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.
Highlights
This leads to the heavy quark effective theory (HQET) [1,2,3], which has proved an effective approach of studying heavy flavor hadrons, especially in B-meson physics
For many B-meson exclusive decay processes, the decay amplitude can be factorized in terms of hard scattering kernel and B-meson light-cone distribution amplitudes (LCDAs) [6,7,8,9,10,11,12], where the B-meson LCDAs are defined by the matrix elements of heavy-light operators on the light-cone in HQET [13]
A factorization theorem for LCDAs was proposed recently [21], which connects B-meson LCDAs defined in quantum chromodynamics (QCD) and HQET, based on the perturbative calculation on the LCDAs of heavy-light mesons [22]
Summary
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. The parton momentum distributions in a hadron, e.g., parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs), are defined through the matrix elements of light-cone operators. These distributions are indispensable ingredients for QCD factorization theorems. For many B-meson exclusive decay processes, the decay amplitude can be factorized in terms of hard scattering kernel and B-meson LCDAs [6,7,8,9,10,11,12], where the B-meson LCDAs are defined by the matrix elements of heavy-light operators on the light-cone in HQET [13]. We will focus on the operators instead of the momentum distributions, because factorization holds at operator level, taking matrix elements
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