Relativistic Heavy Quarks on the Lattice

TL;DR

This paper explores relativistic lattice QCD methods for heavy quark physics, proposing a new approach on isotropic lattices to improve accuracy and reduce uncertainties compared to traditional nonrelativistic methods.

Contribution

It introduces a novel relativistic approach on isotropic lattices that mitigates power corrections and enhances the precision of heavy quark calculations in lattice QCD.

Findings

Anisotropic lattices do not offer advantages for heavy quark control.

The proposed approach reduces uncertainties to order (aΛ_QCD)^2.

Power corrections of m_Q a can be effectively avoided.

Abstract

Lattice QCD should allow quantitative predictions for the heavy quark physics from first principles. Up to now, however, most approaches have based on the nonrelativistic effective theory, with which the continuum limit can not be taken in principle. In this paper we investigate feasibility of relativistic approaches to the heavy quark physics in lattice QCD. We first examine validity of the idea that the use of the anisotropic lattice could be advantageous to control the $m_Q a$ corrections. Our perturbative calculation, however, reveals that this is not true. We instead propose a new relativistic approach to handle heavy quarks on the isotropic lattice. We explain how power corrections of $m_Q a$ can be avoided and remaining uncertainties are reduced to be of order $(a\Lambda_{QCD})^2$.