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

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arxiv 1408.5768 v1 pith:QK72OMCY submitted 2014-08-25 hep-lat hep-ph

B. Colquhoun , R. J. Dowdall , C. T. H. Davies , K. Hornbostel , G. P. Lepage This is my paper · ORCID
classification hep-lathep-ph
keywords upsilonlatticedecayoverlinequarkrightarrowconstantscontribution
verification ladder T0 review T1 audit T2 compute T3 formal

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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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