Precision tests of the J / ψ from full lattice QCD: Mass, leptonic width, and radiative decay rate to η c

By G. Donald, C. Davies, R. Dowdall, E. Follana, K. Hornbostel, J. Koponen, G. Peter Lepage, Craig McNeile. 2012

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We calculate the $J/\ensuremath{\psi}$ mass, leptonic width and radiative decay rate to $\ensuremath{\gamma}{\ensuremath{\eta}}_{c}$ from lattice QCD including $u$, $d$ and $s$ quarks in the sea for the first time. We use the highly improved staggered quark formalism and nonperturbatively normalized vector currents for the leptonic and radiative decay rates. Our results are: ${M}_{J/\ensuremath{\psi}}\ensuremath{-}{M}_{{\ensuremath{\eta}}_{c}}=116.5(3.2)\text{ }\text{ }\mathrm{MeV}$; $\ensuremath{\Gamma}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})=5.48(16)\text{ }\text{ }\mathrm{keV}$; $\ensuremath{\Gamma}(J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c})=2.49(19)\text{ }\text{ }\mathrm{keV}$. The first two are in good agreement with experiment, with $\ensuremath{\Gamma}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})$ providing a test of a decay matrix element in QCD, independent of Cabibbo-Kobayashi-Maskawa uncertainties, to 2%. At the same time results for the time moments of the correlation function can be compared to values from the charm contribution to $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\text{hadrons}})$, giving a 1.5% test of QCD. Our results show that an improved experimental error would enable a similarly strong test from $\ensuremath{\Gamma}(J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c})$.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7c774b3c95b9b3b83911cfdd62fee574a317b026