Non-perturbative renormalization of moments of parton distribution functions

TL;DR

This paper presents a non-perturbative method to compute the evolution of twist-2 operators related to quark momentum distributions in nucleons, using Schrödinger Functional techniques in quenched QCD.

Contribution

It introduces a finite-size Schrödinger Functional approach with optimized boundary conditions for non-perturbative renormalization of parton distribution moments.

Findings

Successful non-perturbative computation of operator evolution.

Demonstrated importance of boundary condition choice.

Applied renormalization constants to nucleon matrix element data.

Abstract

We compute non-perturbatively the evolution of the twist-2 operators corresponding to the average momentum of non-singlet quark densities. The calculation is based on a finite-size technique, using the Schr\"odinger Functional, in quenched QCD. We find that a careful choice of the boundary conditions, is essential, for such operators, to render possible the computation. As a by-product we apply the non-perturbatively computed renormalization constants to available data of bare matrix elements between nucleon states.