Determination of ${\overline{m}}_b/{\overline{m}}_c$ and ${\overline{m}}_b$ from $n_f=4$ lattice QCD$+$QED

Abstract

We extend HPQCD's earlier $n_f=4$ lattice-QCD analysis of the ratio of $\overline{\mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that ${\overline{m}}_b(\mu )/{\overline{m}}_c(\mu )=4.586(12)$ at renormalization scale $\mu =3$\,GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD$+$QED determination of ${\overline{m}}_c(3\mathrm{GeV})$ gives a new value for the $b$-quark mass: ${\overline{m}}_b(3\mathrm{GeV})=4.513(26)$GeV. The $b$-mass corresponds to ${\overline{m}}_b({\overline{m}}_b,n_f=5)=4.202(21)$GeV. These results are the first based on simulations that include QED.

8 pages, 4 figures

References in corpus (13)

• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• High-precision scale setting in lattice QCD
• The five-loop beta function of Yang-Mills theory with fermions
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Five-loop renormalisation of QCD in covariant gauges
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling
• The mass of the b-quark from lattice NRQCD and lattice perturbation theory
• Bottomonium precision tests from full lattice QCD: hyperfine splitting, ${\rm Y}$ leptonic width and $b$ quark contribution to $e^{+}{e}^{-}\to$ hadrons

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• Form factors for the processes $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$ and $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}(\nu \overline{\nu })$ from lattice QCD
• Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
• Determination of the Strong Coupling Constant ${\alpha }_s$ from Inclusive Semi-leptonic $B$ Meson Decays