The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD

Abstract

We determine the decay rate to leptons of the ground-state ${\rm Y}$ meson and its first radial excitation in lattice QCD for the first time. We use radiatively-improved NRQCD for the $b$ quarks and include $u$, $d$, $s$ and $c$ quarks in the sea with $u/d$ masses down to their physical values. We find $\Gamma ({\rm Y}\to e^{+}{e}^{-})$ = 1.19(11) keV and $\Gamma ({{\rm Y}}^{\prime }\to e^{+}{e}^{-})$ = 0.69(9) keV, both in good agreement with experiment. The decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD given in the Conclusions. We also test time-moments of the vector current-current correlator against values determined from the $b$ quark contribution to $\sigma (e^{+}{e}^{-}\to \mathrm{hadrons})$ and calculate the $b$-quark piece of the hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $a_{\mu }^b=0.271(37)\times 10^{-10}$. Finally we determine the $b$-quark mass, obtaining in the $\overline{MS}$ scheme, ${\overline{m}}_b({\overline{m}}_b,n_f=5)$ = 4.196(23) GeV, the most accurate result from lattice QCD to date.

21 pages, 15 figures

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