Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients

TL;DR

This paper develops a heavy-quark operator product expansion method to calculate parton distribution functions and light-cone distribution amplitudes, providing new Wilson coefficients and a framework for lattice QCD computations.

Contribution

It introduces a novel OPE approach with a fictitious heavy quark to compute PDFs and LCDAs, including new Wilson coefficients for LCDAs and a convolution framework for inversion.

Findings

Derived one-loop Wilson coefficients for unpolarized and helicity PDFs.

Provided new Wilson coefficients for light-cone distribution amplitudes.

Established a convolution method to extract parton momentum dependence.

Abstract

Parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs) are central non-perturbative objects of interest in high-energy inelastic and elastic scattering, respectively. As a result, an ab-initio determination of these objects is highly desirable. In this paper we present theoretical details for the calculation of the PDFs and LCDAs using a heavy-quark operator product expansion method. This strategy was proposed in a previous paper [Phys. Rev. D 73, 014501 (2006)] for computing higher moments of the PDFs using lattice QCD. Its central feature is the introduction of a fictitious, valence heavy quark. In the current article, we show that the operator product expansion (OPE) of the hadronic matrix element we study can also be expressed as the convolution of a perturbative matching kernel and the corresponding light-cone distribution, which in principle can be inverted to determine the parton momentum fraction dependence. Regarding the extraction of higher moments, this work also provides the one-loop Wilson coefficients in the OPE formulas for the unpolarized PDF, helicity PDF and pseudo-scalar meson LCDAs. Although these Wilson coefficients for the PDFs can be inferred from existing results in the literature, those for the LCDAs are new.