Relations between Heavy-light Meson and Quark Masses

TL;DR

This paper develops a scale- and ambiguity-free definition of renormalized quark masses and integrates it into heavy-light meson mass descriptions using lattice QCD, heavy-quark effective theory, and chiral perturbation theory.

Contribution

It introduces a novel renormalized quark mass definition and extends chiral perturbation theory corrections for lattice QCD with staggered fermions, enabling practical analysis of heavy-light meson masses.

Findings

Derived a practical formula for heavy-light meson masses in lattice QCD.

Extended one-loop chiral perturbation theory corrections for staggered fermions.

Facilitated extraction of quark masses from lattice QCD data.

Abstract

The study of heavy-light meson masses should provide a way to determine renormalized quark masses and other properties of heavy-light mesons. In the context of lattice QCD, for example, it is possible to calculate hadronic quantities for arbitrary values of the quark masses. In this paper, we address two aspects relating heavy-light meson masses to the quark masses. First, we introduce a definition of the renormalized quark mass that is free of both scale dependence and renormalon ambiguities, and discuss its relation to more familiar definitions of the quark mass. We then show how this definition enters a merger of the descriptions of heavy-light masses in heavy-quark effective theory and in chiral perturbation theory ($\chi$PT). For practical implementations of this merger, we extend the one-loop $\chi$PT corrections to lattice gauge theory with heavy-light mesons composed of staggered fermions for both quarks. Putting everything together, we obtain a practical formula to describe all-staggered heavy-light meson masses in terms of quark masses as well as some lattice artifacts related to staggered fermions. In a companion paper, we use this function to analyze lattice-QCD data and extract quark masses and some matrix elements defined in heavy-quark effective theory.