Moments of Ioffe time parton distribution functions from non-local matrix elements

TL;DR

This paper investigates how moments of parton distribution functions can be extracted from non-local matrix elements in lattice QCD, demonstrating their equivalence to traditional local operator methods after continuum limit and scheme matching.

Contribution

It establishes a theoretical and numerical connection between moments derived from non-local matrix elements and those from local operators in lattice QCD, confirming their agreement in the quenched approximation.

Findings

Non-local matrix elements yield finite moments after continuum limit.

Numerical results agree with local operator computations in quenched QCD.

Supports using non-local operators for parton distribution analysis.

Abstract

We examine the relation of moments of parton distribution functions to matrix elements of non-local operators computed in lattice quantum chromodynamics. We argue that after the continuum limit is taken, these non-local matrix elements give access to moments that are finite and can be matched to those defined in the $\overline{MS}$ scheme. We demonstrate this fact with a numerical computation of moments through non-local matrix elements in the quenched approximation and we find that these moments are in excellent agreement with the moments obtained from direct computations of local twist-2 matrix elements in the quenched approximation.