Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action

TL;DR

This paper introduces a coordinate space renormalization scheme for lattice QCD that is gauge invariant, computationally efficient, and can be converted to the MSbar scheme, with results matching the RI-MOM scheme for $N_f=2$ twisted mass fermions.

Contribution

The paper develops and applies a coordinate space renormalization method for lattice QCD, demonstrating its effectiveness and agreement with existing schemes for $N_f=2$ twisted mass fermions.

Findings

The coordinate space scheme is gauge invariant and easy to implement.

Results agree with the RI-MOM scheme within uncertainties.

The method allows conversion to the MSbar scheme using 4-loop perturbative formulas.

Abstract

We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MSbar scheme via 4-loop continuum perturbative formulae. Our results for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method.