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

TL;DR

This paper uses advanced lattice QCD techniques to precisely calculate bottomonium properties, including hyperfine splitting and leptonic widths, and compares these results with experimental data to test QCD accuracy.

Contribution

It provides the most accurate lattice QCD calculations to date for bottomonium hyperfine splitting and leptonic widths, including detailed heavy quark mass dependence analysis.

Findings

Hyperfine splitting: 57.5(2.3)(1.0) MeV

Leptonic width: 1.292(37)(3) keV

b quark contribution to muon g-2: 0.300(15)×10^{-10}

Abstract

We calculate the mass difference between the $\Upsilon$ and $\eta_b$ and the $\Upsilon$ 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: $M_{\Upsilon} -M_{\eta_b} = 57.5(2.3)(1.0) \,\mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{\eta_b}=724(12)$ MeV and $f_{\Upsilon} =677.2(9.7)$ MeV, giving $\Gamma(\Upsilon \rightarrow e^+e^-) = 1.292(37)(3) \,\mathrm{keV}$. 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 $\sigma(e^+e^- \rightarrow \mathrm{hadrons})$ 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.