Quasi Parton Distribution Functions in Covariant Quark Models

TL;DR

This paper investigates quasi parton distribution functions (QPDFs) within covariant quark models, proving their convergence to PDFs and deriving analytical results relevant for lattice QCD studies.

Contribution

It provides general proofs of QPDF convergence and sum rules in models without gauge fields, exemplified by the Covariant Parton Model, and derives analytical small-$x_v$ behavior results.

Findings

Proved convergence and sum rules for unpolarized QPDFs in quark models

Derived analytical small-$x_v$ behavior of QPDFs and form factors

Illustrated results using the Covariant Parton Model

Abstract

Quasi parton distribution functions (QPDFs) are defined in terms of QCD fields at spacelike separations evaluated in matrix elements of hadrons moving with velocity $v$. These objects can be studied in lattice QCD. In the limit when $v$ approaches the speed of light, QPDFs converge to PDFs. It is insightful to study QPDFs and their convergence in models. In this work, we first study the QPDFs in a broad class of quark models characterized by one common feature, namely the absence of gauge degrees of freedom. We provide general proofs for the convergence and sum rules of the unpolarized quark and antiquark QPDFs for both choices $\gamma^0$ and $\gamma^3$. We choose the Covariant Parton Model (CPM) as an illustration. We derive analytical results for the small-$x_v$ behavior of QPDFs and the energy-momentum tensor form factor $\bar{c}^q(t)$ at zero momentum transfer. These results are of interest as they correspond to a Wandzura-Wilczek-type approximation.