Non-perturbative renormalisation with interpolating momentum schemes

TL;DR

This paper explores non-perturbative renormalisation schemes with interpolating momentum in lattice QCD, analyzing scheme dependence, and providing numerical results for renormalisation factors, anomalous dimensions, and matching coefficients.

Contribution

It introduces and tests non-exceptional interpolating momentum schemes within the Rome-Southampton method for lattice renormalisation, extending previous symmetric schemes.

Findings

Computed renormalisation factors for quark mass and wave function.

Analyzed scheme dependence of discretisation effects and convergence.

Provided NNLO anomalous dimensions and matching coefficients.

Abstract

Hadronic matrix elements evaluated on the lattice can be converted to a continuum scheme such as $\MSbar$ using intermediate non-perturbative renormalisation schemes. Discretisation effects on the lattice and convergence of the continuum perturbation theory are both scheme dependent and we explore this dependence in the framework of the Rome-Southampton method for generalised kinematics. In particular, we implement several non-exceptional {\em interpolating} momentum schemes, where the momentum transfer is {\em not} restricted to the symmetric point defined in RI/SMOM. Using flavour non-singlet quark bilinears, we compute the renormalisation factors of the quark mass and wave function for $N_f=3$ flavours of dynamical quarks. We investigate the perturbative and non-perturbative scale-dependencies. Our numerical results are obtained from lattice simulations performed with Domain-Wall fermions, based on ensembles generated by RBC-UKQCD collaborations; we use two different lattice spacings $1/a \sim 1.79 $ and $2.38$ GeV. We also give the numerical values for the relevant anomalous dimensions and matching coefficients at next-to-next-to-leading order.