Lattice hadron matrix elements with the Schroedinger functional: the case of the first moment of non-singlet quark density

TL;DR

This paper non-perturbatively computes the pion matrix element of a twist-2 operator related to quark momentum distribution using the Schroedinger functional scheme, comparing Wilson and clover actions.

Contribution

It provides the first non-perturbative determination of this matrix element within the Schroedinger functional scheme, validating continuum extrapolation methods.

Findings

Wilson and clover actions yield compatible continuum results

The ratio of results extrapolates correctly to perturbative expectations

Non-perturbative approach confirms theoretical correction factors

Abstract

We present the results of a non-perturbative determination of the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. The calculation is made within the Schroedinger functional scheme. We report the results of simulations done with the standard Wilson action and with the non-perturbatively improved clover action and we show that their ratio correctly extrapolates, in the continuum limit, to a value compatible with the residual correction factor expected from perturbation theory.