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.
Highlights
Six of the fundamental parameters of the standard model are quark masses, but because of confinement they can be determined only indirectly via their influence on hadrons
We use this function to analyze lattice-QCD data and extract quark masses and some matrix elements defined in heavy-quark effective theory
As we show in a companion paper [1], the theoretical developments in this paper provide a new way to determine the quark masses as well as heavy-quark effective theory (HQET) matrix elements such as Λand μ2π
Summary
Six of the fundamental parameters of the standard model are quark masses, but because of confinement they can be determined only indirectly via their influence on hadrons. In the language of HMχPT, λ1, λ01, and λ2 are low-energy constants; λ1 and λ01 are independent of the heavy-quark mass, while λ2 has a logarithmic dependence on mQ via αsðmQÞ [4], as elaborated below These quantities can be determined by matching HMχPT to the underlying theories, namely, HQET and QCD. V, we summarize the results and offer some outlook, both to the removal of higher renormalons and to applications in quarkonium
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