Moments of singlet parton densities on the lattice in the Schroedinger Functional scheme

TL;DR

This paper presents a non-perturbative lattice calculation of the second moment of singlet parton densities within the Schrödinger Functional scheme, establishing a connection to the $ar{MS}$ scheme for experimental comparison.

Contribution

It introduces a gauge-invariant gluon source operator in the Schrödinger Functional scheme and computes the one-loop renormalization constants for twist-2 operators.

Findings

Computed renormalization constants for twist-2 operators.

Established link between lattice SF scheme and $ar{MS}$ scheme.

Enabled non-perturbative evaluation of singlet parton densities.

Abstract

A non perturbative computation of the evolution of singlet parton densities without gauge--fixing requires a gauge invariant gluon source operator. Within the Schr\"odinger Functional scheme (SF), such a source can be defined in terms of path ordered products of gauge links, connected to the time boundaries. In this paper we adopt this definition and perform a one loop lattice computation of the renormalization constants of the twist--2 operators that correspond to the second moment of singlet parton densities. This calculation fixes the connection between the lattice SF scheme where a non perturbative evaluation of the absolute normalization of singlet parton densities can be made at low energy and the $\bar{MS}$ scheme where one can extract the experimental values.