Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices

TL;DR

This paper formulates massive domain wall fermions on anisotropic lattices, analyzing their dispersion relations, self-energy, and stability, providing guidance for future lattice QCD simulations.

Contribution

It introduces a formulation for massive domain wall fermions on anisotropic lattices and calculates key renormalization constants at one-loop, aiding parameter tuning.

Findings

Dispersion relation matches the usual form at low momentum with proper parameter tuning.

Quark self-energy and field renormalization constants are computed at one-loop.

Chiral modes remain stable against quantum fluctuations on anisotropic lattices.

Abstract

We formulate the massive domain wall fermions on anisotropic lattices. For the massive domain wall fermion, we find that the dispersion relation assumes the usual form in the low momentum region when the bare parameters are properly tuned. The quark self-energy and the quark field renormalization constants are calculated to one-loop in bare lattice perturbation theory. For light domain wall fermions, we verified that the chiral mode is stable against quantum fluctuations on anisotropic lattices. This calculation serves as a guidance for the tuning of the parameters in the quark action in future numerical simulations.