Charmonium properties from lattice QCD +QED : Hyperfine splitting, J /ψ leptonic width, charm quark mass, and a_{μ}^{c}
Abstract
We have performed the first n_{f}=2 +1 +1 lattice QCD computations of the properties (masses and decay constants) of groundstate charmonium mesons. Our calculation uses the Highly Improved Staggered Quark (HISQ) action to generate quarkline connected twopoint 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 /ψ} and including the effect of the c quark's electric charge through quenched QED. We obtain M_{J /ψ}M_{ηc}(connected)=120.3 (1.1 ) MeV and interpret the difference with experiment as the impact on M_{η c} of the η_{c} decay to gluons, missing from the lattice calculation. This allows us to determine Δ M_{η}^{c annihiln}=+7.3 (1.2 ) MeV , giving its value for the first time. Our result of f_{J /ψ}=0.4104 (17 ) GeV gives Γ (J /ψ →e^{+}e^{})=5.637 (49 ) 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 m_{¯ c}(3 GeV )=0.9841 (51 ) GeV . We have also used the time moments of the vector charmonium currentcurrent 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_{μ}^{c}=14.638 (47 )×10^{10}, which is 2.5 σ higher than the value derived using moments extracted from some sets of experimental data on R (e^{+}e^{}→hadrons). This value for a_{μ}^{c} includes our determination of the effect of QED on this quantity, δ a_{μ}^{c}=0.0313 (28 )×10^{10}.
 Publication:

Physical Review D
 Pub Date:
 September 2020
 DOI:
 10.1103/PhysRevD.102.054511
 arXiv:
 arXiv:2005.01845
 Bibcode:
 2020PhRvD.102e4511H
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 Added extra discussion on QED setup, some new results to study the effects of strong isospin breaking in the sea (including new Fig. 1) and a fit stability plot for the hyperfine splitting (new Fig. 7). Version accepted for publication in PRD