Valence Quark PDFs of the Proton from Two-Current Correlations in Lattice QCD

TL;DR

This paper presents a lattice QCD approach to compute valence quark PDFs of the proton by analyzing two-current correlations in position space, adapting formalism to specific operators, and extracting PDFs from lattice data.

Contribution

It adapts the lattice cross section formalism to new operators and demonstrates extraction of valence quark PDFs from four-point function lattice calculations.

Findings

Lattice data successfully converted to MSbar scheme at 2 GeV

Valence quark PDFs extracted using a model fit to lattice data

Calculation performed on a 2+1 flavor gauge ensemble with specific lattice parameters

Abstract

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the $x$ dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term lattice cross section. In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a $n_f = 2+1$ gauge ensemble with lattice spacing $a = 0.0856~\mathrm{fm}$ and pseudoscalar masses $m_\pi = 355~\mathrm{MeV}$ and $m_K = 441~\mathrm{MeV}$. The four-point functions have been evaluated in a previous project. The lattice data is converted to the $\overline{\mathrm{MS}}$ scheme at a scale $\mu=2~\mathrm{GeV}$ and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs.