Precision bottomonium properties and b quark mass from lattice QCD

Abstract

As tests of QCD in the bottomonium system, we give the most accurate results to date for the ground-state hyperfine splitting and the $\hat{I}\yen$ leptonic width from full lattice QCD. These quantities are both accurately known from experiment, so can provide a good test of $b$ physics, but previous lattice results have been rather imprecise. We also test the impact on these quantities of the $b$ quark's electric charge. Our results are: $M_{\hat{I}}\yen -M_{\hat{I}{\cdot }_b}=$ 57.5(2.3)(1.0) MeV (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{\hat{I}{\cdot }_b}=$ 724(12) MeV and $f_{\hat{I}}\yen =$ 677.2(9.7) MeV, giving $\hat{I}“(\hat{I}\yen \to e^{+}{e}^{-})=$ 1.292(37)(3) keV. We also give a new determination of the ratio of the masses for $b$ and $c$ quarks that is completely nonperturbative in lattice QCD and includes the calculation of QED effects for the first time. This gives a result for the $b$ quark mass of ${\overline{m}}_b({\overline{m}}_b,n_f=5)=$ 4.202(21) GeV.

6 pages, The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology