Dispersion relation and unphysical poles of M\"obius domain-wall fermions in free field theory at finite $L_s$

TL;DR

This paper analyzes the dispersion relation of M"obius domain-wall fermions in free field theory at finite $L_s$, revealing extra unphysical poles that impact heavy quark simulations and discussing parameter choices to mitigate their effects.

Contribution

It identifies and characterizes unphysical poles in M"obius domain-wall fermions at finite $L_s$, providing guidance for optimal parameter selection to reduce their impact.

Findings

$L_s-1$ extra poles exist beyond the physical mode.

Unphysical poles can significantly affect heavy quark physics.

Optimal M"obius parameters can minimize unphysical contributions.

Abstract

We investigate the dispersion relation of M\"obius domain-wall fermions in free field theory at finite $L_s$. We find that there are $L_s-1$ extra poles of M\"obius domain-wall fermions in addition to the pole which realizes the physical mode in the continuum limit. The unphysical contribution of these extra poles could be significant when we introduce heavy quarks. We show in this report the fundamental properties of these unphysical poles and discuss the optimal choice of M\"obius parameters to minimize their contribution to four-dimensional physics.