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

Parton distribution functions (PDFs) and light cone distribution amplitudes (LCDAs) are central nonperturbative 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. D73, 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 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 operator product expansion formulas for the unpolarized PDF, helicity PDF and pseudoscalar meson LCDAs. Although these Wilson coefficients for the PDFs can be inferred from existing results in the literature, those for the LCDAs are new.