Relativistic Heavy Quark Effective Action

TL;DR

This paper develops an improved lattice QCD fermion action for heavy quarks, enabling accurate low-energy physics simulations even when quark masses are comparable to or larger than the inverse lattice spacing.

Contribution

It introduces a refined heavy quark effective action with three mass-dependent coefficients, allowing precise spectrum calculations for heavy quark systems on the lattice.

Findings

Spectrum accuracy through first order in momentum expansion

Effective action with three tunable coefficients

Applicability for arbitrary heavy quark masses

Abstract

We study the fermion action needed to accurately describe the low energy physics of systems including heavy quarks in lattice QCD even when the heavy fermion mass $m$ is on the order of, or larger than, the inverse lattice spacing: $m \ge 1/a$. We carry out an expansion through first order in $|\vec p| a$ (where $\vec p$ is the heavy quark momentum) and all orders in $ma$, refining the analysis of the Fermilab and Tsukuba groups. We demonstrate that the spectrum of heavy quark bound states can be determined accurately through $|\vec p| a$ and $(ma)^n$ for arbitrary exponent $n$ by using a lattice action containing only three unknown coefficients: $m_0$, $\zeta$ and $c_P$ (a generalization of $c_{SW}$), which are functions of $ma$. In a companion paper, we show how these three coefficients can be precisely determined using non-perturbative techniques.