Charmonium properties from lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>QCD</mml:mi><mml:mo>+</mml:mo><mml:mtext>QED</mml:mtext></mml:mrow></mml:math>: Hyperfine splitting, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:math> leptonic width, charm quark mass, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>a</mml:mi><mml:mi>μ</mml:mi><mml:mi>c</mml:mi></mml:msubsup></mml:math>
D. Hatton, C. T. H. Davies, B. Galloway, J. Koponen, G. Peter Lepage, Andrew Lytle
Abstract
We have performed the first ${n}_{f}=2+1+1$ lattice QCD computations of the properties (masses and decay constants) of ground-state charmonium mesons. Our calculation uses the Highly Improved Staggered Quark (HISQ) action to generate quark-line connected two-point correlation functions on MILC gluon field configurations that include $u/d$ quark masses going down to the physical point, tuning the $c$-quark mass from ${M}_{J/\ensuremath{\psi}}$ and including the effect of the $c$ quark's electric charge through quenched QED. We obtain ${M}_{J/\ensuremath{\psi}}\ensuremath{-}{M}_{{\ensuremath{\eta}}_{c}}$ $(\text{connected})=120.3(1.1)\text{ }\text{ }\mathrm{MeV}$ and interpret the difference with experiment as the impact on ${M}_{{\ensuremath{\eta}}_{c}}$ of the ${\ensuremath{\eta}}_{c}$ decay to gluons, missing from the lattice calculation. This allows us to determine $\mathrm{\ensuremath{\Delta}}{M}_{{\ensuremath{\eta}}_{c}}^{\text{annihiln}}=+7.3(1.2)\text{ }\text{ }\mathrm{MeV}$, giving its value for the first time. Our result of ${f}_{J/\ensuremath{\psi}}=0.4104(17)\text{ }\text{ }\mathrm{GeV}$ gives $\mathrm{\ensuremath{\Gamma}}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})=5.637(49)\text{ }\text{ }\mathrm{keV}$, in agreement with, but now more accurate than, experiment. At the same time we have improved the determination of the $c$-quark mass, including the impact of quenched QED to give ${\overline{m}}_{c}(3\text{ }\text{ }\mathrm{GeV})=0.9841(51)\text{ }\text{ }\mathrm{GeV}$. We have also used the time moments of the vector charmonium current-current correlators to improve the lattice QCD result for the $c$ quark hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. We obtain ${a}_{\ensuremath{\mu}}^{c}=14.638(47)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is $2.5\ensuremath{\sigma}$ higher than the value derived using moments extracted from some sets of experimental data on $R({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons})$. This value for ${a}_{\ensuremath{\mu}}^{c}$ includes our determination of the effect of QED on this quantity, $\ensuremath{\delta}{a}_{\ensuremath{\mu}}^{c}=0.0313(28)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$.