Wilson mass dependence of the overlap topological charge density

TL;DR

This study investigates how the Wilson-mass parameter affects the overlap topological charge density, revealing a dependence that can be calibrated with smearing techniques and demonstrating the filtering effects of the overlap operator.

Contribution

It demonstrates the Wilson-mass dependence of the overlap topological charge density and shows how to calibrate it against smearing, highlighting the parameter's role as a filter.

Findings

Wilson-mass parameter influences topological charge density

Calibration possible via smearing sweeps

Overlap operator provides additional gauge field filtering

Abstract

The dependence of the overlap Dirac operator on the Wilson-mass regulator parameter is studied through calculations of the overlap topological charge densities at a variety of Wilson-mass values. In this formulation, the Wilson-mass is used in the negative mass region and acts as a regulator governing the scale at which the Dirac operator is sensitive to topological aspects of the gauge field. We observe a clear dependence on the value of the Wilson-mass and demonstrate how these values can be calibrated against a finite number of stout-link smearing sweeps. The overlap topological charge density is also computed using a pre-smeared gauge field for the input kernel. We show how applying the overlap operator leads to further filtering of the gauge field. The results suggest that the freedom typically associated with smearing algorithms, through the variable number of sweeps, also exists in the overlap operator, through the variable Wilson-mass parameter.