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arXiv · 1408.5768

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

B. Colquhoun·R. J. Dowdall·C. T. H. Davies·K. Hornbostel·G. P. Lepage
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Abstract

We determine the decay rate to leptons of the ground-state $\Upsilon$ 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 $\Gamma(\Upsilon \rightarrow e^+e^-)$ = 1.19(11) keV and $\Gamma(\Upsilon^{\prime} \rightarrow e^+e^-)$ = 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 $\sigma(e^+e^- \rightarrow \mathrm{hadrons})$ 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.

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B. Colquhoun, R. J. Dowdall, C. T. H. Davies, K. Hornbostel, G. P. Lepage. 2014-08-25. The $\Upsilon$ and $\Upsilon^{\prime}$ Leptonic Widths, $a_{\mu}^b$ and $m_b$ from full lattice QCD. https://doi.org/10.1103/physrevd.91.074514

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