A Numerical Study of Improved Quark Actions on Anisotropic Lattices

TL;DR

This paper numerically investigates improved Wilson quark actions on anisotropic lattices, focusing on optimizing parameters for accurate meson dispersion relations across different quark masses and gauge couplings.

Contribution

It introduces a method to determine the optimal bare speed of light parameter for improved quark actions on anisotropic lattices across various quark masses and couplings.

Findings

Optimal $ u$ values at strange and charm quark masses are provided for different gauge couplings.

Dispersion relations for pseudo-scalar mesons are measured for multiple momentum modes.

The results facilitate more accurate lattice QCD simulations involving light and heavy quarks.

Abstract

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudo-scalar meson dispersion relations are measured for 8 lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling $\beta$ and 3 different values of the bare speed of light parameter $\nu$. These results can be utilized to extrapolate or interpolate to obtain the optimal value for the bare speed of light parameter $\nu_{opt}(m)$ at a given gauge coupling for all bare quark mass values $m$. In particular, the optimal values of $\nu$ at the physical strange and charm quark mass are given for various gauge couplings. The lattice action with these optimized parameters can then be used to study physical properties of hadrons involving either light or heavy quarks.