Analysis of systematic errors in the calculation of renormalization constants of the topological susceptibility on the lattice

TL;DR

This paper compares two methods for calculating renormalization constants of topological susceptibility on the lattice, finding good agreement and discussing the independence of the renormalization constant from background charge.

Contribution

It introduces a Ginsparg-Wilson based calibration method and compares it with cooling, providing insights into their consistency and properties.

Findings

Methods agree within 3-4% statistical errors

Renormalization constant Z is independent of background topological charge

Provides validation for Ginsparg-Wilson based calibration

Abstract

A Ginsparg-Wilson based calibration of the topological charge is used to calculate the renormalization constants which appear in the field-theoretical determination of the topological susceptibility on the lattice. A systematic comparison is made with calculations based on cooling. The two methods agree within present statistical errors (3%-4%). We also discuss the independence of the multiplicative renormalization constant Z from the background topological charge used to determine it.