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

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.

arXiv comment34 pages, 8 figures, 26 tables; some sections rearranged for clarity; conclusions unchanged; version accepted by Phys. Rev.D

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• $B_{(s)}^0$-mixing matrix elements from lattice QCD for the Standard Model and beyond
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• The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea
• D Pi scattering and D meson resonances from lattice QCD
• Update of $|V_{cb}|$ from the $\bar{B}\to D^{\ast }\ell \bar{\nu }$ form factor at zero recoil with three-flavor lattice QCD
• $B\to K{l}^{+}{l}^{-}$ decay form factors from three-flavor lattice QCD
• Predicting positive parity $B_s$ mesons from lattice QCD
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
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• Studying the $\rho$ resonance parameters with staggered fermions
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• Lattice QCD study on $K^{\ast }(892)$ meson decay width
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• Chiral Perturbation Theory for All-Staggered Heavy-Light Mesons
• Preliminary lattice study of $\sigma$ meson decay width
• The preliminary lattice QCD calculation of $\kappa$ meson decay width
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• A fully non-perturbative charm-quark tuning using machine learning
• Studying $\kappa$ meson with a MILC fine lattice
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