Continuous external momenta in non-perturbative lattice simulations: a computation of renormalization factors

TL;DR

This paper introduces a novel lattice simulation method using continuous external momenta via special boundary conditions to compute challenging renormalization factors, exemplified by the twist-2 operator for non-singlet quark densities.

Contribution

It presents a new approach for calculating renormalization factors on the lattice using continuous external momenta, enabling computations previously deemed very difficult.

Findings

Computed the renormalization group invariant step scaling function for a twist-2 operator.

Demonstrated the feasibility of using special boundary conditions for continuous external momenta.

Provided a method to improve non-perturbative renormalization calculations.

Abstract

We discuss the usage of continuous external momenta for computing renormalization factors as needed to renormalize operator matrix elements. These kind of external momenta are encoded in special boundary conditions for the fermion fields. The method allows to compute certain renormalization factors on the lattice that would have been very difficult, if not impossible, to compute with standard methods. As a result we give the renormalization group invariant step scaling function for a twist-2 operator corresponding to the average momentum of non-singlet quark densities.