Bottomonium precision tests from full lattice QCD: hyperfine splitting, ${\rm Y}$ leptonic width and $b$ quark contribution to $e^{+}{e}^{-}\to$ hadrons

Abstract

We calculate the mass difference between the ${\rm Y}$ and ${\eta }_b$ and the ${\rm Y}$ leptonic width from lattice QCD using the Highly Improved Staggered Quark formalism for the $b$ quark and including $u$, $d$, $s$ and $c$ quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the $b$ quark mass. Our results are: $M_{{\rm Y}}-M_{{\eta }_b}=57.5(2.3)(1.0)\mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{{\eta }_b}=724(12)$ MeV and $f_{{\rm Y}}=677.2(9.7)$ MeV, giving $\Gamma ({\rm Y}\to e^{+}{e}^{-})=1.292(37)(3)\mathrm{keV}$. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the $b$ quark contribution to $\sigma (e^{+}{e}^{-}\to \mathrm{hadrons})$ determined from experiment. Moments 4--10 provide a 2\% test of QCD and yield a $b$ quark contribution to the anomalous magnetic moment of the muon of 0.300(15)$\times 10^{-10}$. Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics.

16 pages, 9 figures Version accepted by PRD: Appendix with tables of fit parameters that allow the dependence on heavy quark mass of the hyperfine splitting and decay constants to be reconstructed added

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Cited by in corpus (10)

• Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions
• Light-quark connected intermediate-window contributions to the muon $g-2$ hadronic vacuum polarization from lattice QCD
• $B_s\to D_s^{\ast }$ Form Factors for the full $q^2$ range from Lattice QCD
• Precise determination of decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ from lattice QCD
• Indirect constraints on lepton-flavour-violating quarkonium decays
• Determination of ${\overline{m}}_b/{\overline{m}}_c$ and ${\overline{m}}_b$ from $n_f=4$ lattice QCD$+$QED
• Charm-quark mass effects in NRQCD matching coefficients and the leptonic decay of the ${\rm Y}(1S)$ meson
• Constraints on axion-like particles using lattice QCD calculations of the rate for $J/\psi \to \gamma a$
• Review of Neutral Naturalness
• Prospects for observing the ${\eta }_t$ $\to$ $W^{+}{W}^{-}$ decay at the HL-LHC