Tuning Fermilab Heavy Quarks in 2+1 Flavor Lattice QCD with Application to Hyperfine Splittings

TL;DR

This paper non-perturbatively tunes heavy-quark parameters in 2+1 flavor lattice QCD using Fermilab action and validates the approach through hyperfine splitting calculations of Ds and Bs mesons, showing good agreement with experimental data.

Contribution

It introduces a method for non-perturbative tuning of heavy-quark parameters in lattice QCD with Fermilab action and applies it to compute hyperfine splittings.

Findings

Hyperfine splitting for Ds: 145 +/- 15 MeV

Hyperfine splitting for Bs: 40 +/- 9 MeV

Results agree with Particle Data Group averages

Abstract

We report the non-perturbative tuning of parameters--- kappa_c, kappa_b, and kappa_crit ---that determine the heavy-quark mass in the Fermilab action. This requires the computation of the masses of Ds^(*) and Bs^(*) mesons comprised of a Fermilab heavy quark and a staggered light quark. Additionally, we report the hyperfine splittings for Ds and Bs mesons as a cross-check of our simulation and analysis methods. We find a splitting of 145 +/- 15 MeV for the Ds system and 40 +/- 9 MeV for the Bs system. These are in good agreement with the Particle Data Group average values of 143.9 +/- 0.4 MeV and 46.1 +/- 1.5 MeV, respectively. The calculations are carried out with the MILC 2+1 flavor gauge configurations at three lattice spacings $a$ approximately 0.15, 0.12, and 0.09 fm.