Restoring rotational invariance for lattice QCD propagators

TL;DR

This paper introduces a method to reduce discretization errors in lattice QCD calculations by exploiting artifacts that break rotational symmetry, improving the rotational invariance of two-point Green functions.

Contribution

The paper presents a novel technique to recover rotational invariance in lattice QCD propagators by combining position and momentum space analyses to identify and correct artifacts.

Findings

Method successfully reduces discretization errors in Klein-Gordon propagator

Application to gluon propagator in quenched lattice QCD demonstrates effectiveness

Improves rotational symmetry in lattice QCD Green functions

Abstract

This note presents a method to reduce the discretization errors appearing when solving a Quantum Field Theory in a hypercubic lattice in both position and momentum-space. The method exploits the artifacts that break rotational symmetry to recover rotationally invariant results for two-point Green functions. We show that a combination of the results obtained in position and momentum space can be useful to signal the presence of rotationally invariant artifacts making use of their approximate Fourier transforms in the continuum. The method will be introduced using a Klein-Gordon propagator, and a direct application to gluon propagator in quenched lattice QCD will be given.