Step Scaling with off-shell renormalisation

TL;DR

This paper introduces a refined off-shell renormalisation method using twisted boundary conditions, enabling precise vertex function definition at fixed physical momenta, reducing artefacts, and facilitating step-scaling in the RI/SMOM scheme.

Contribution

It develops a practical step-scaling scheme for off-shell renormalisation with improved precision and flexibility, incorporating twisted boundary conditions and non-exceptional momenta.

Findings

Enhanced statistical precision with volume plane-wave sources

Reduced dependence on mass and p^2 using non-exceptional momenta

Continuous step size allows arbitrarily small scaling steps

Abstract

We make use of twisted boundary conditions for off-shell Rome-Southampton renormalisation. This allows to define the vertex function precisely, at a fixed physical momentum that need not be one of the Fourier modes of a simulation. This definition includes choosing the orientation with respect to lattice axes, and so lattice artefacts including ${\cal O}(4)$ breaking then have a valid Symanzik expansion. Excellent statistical precision is afforded by volume plane-wave sources, enabling both a theoretically and statistically clean continuum limit to be taken. Thereafter all $p^2$ dependence can be unambiguously identified as continuum anomolous running. The use of non-exceptional momenta has been found to greatly reduce the dependence of non-perturbative vertex functions on both mass and $p^2$. We illustrate how this can be developed into a practical scheme for step-scaling the RI/SMOM approach with initial results. The size of the possible steps is continuous, rather than discrete allowing one to take arbitrarily small steps, and the scheme inherits from RI/MOM the property that it is easy to implement for general operators.