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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. 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Colquhoun, C. T. H. Davies, G. P. Lepage, K. Hornbostel, R. J. Dowdall","submitted_at":"2014-08-25T14:16:23Z","abstract_excerpt":"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. 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