An exploratory study of heavy domain wall fermions on the lattice

TL;DR

This study explores the use of domain wall fermions for heavy quarks in lattice QCD, identifying optimal parameters and demonstrating mild discretization effects, supporting their application in realistic simulations.

Contribution

It provides the first detailed analysis of heavy domain wall fermions, including parameter tuning, locality, and scaling behavior, for quenched lattice QCD.

Findings

Effective 4D overlap operator is exponentially local, independent of quark mass.

Maximum heavy quark mass for chiral symmetry preservation is approximately 0.4 in lattice units.

Observed very mild $a^2$ scaling towards the continuum limit.

Abstract

We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4$d$ overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of $am_h\approx 0.4$, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range $2.0-5.7\,\mathrm{GeV}$. We observe very mild $a^2$ scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.