Precise determination of decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ from lattice QCD

Abstract

We calculate the decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ in lattice QCD with $u$, $d$, $s$ and $c$ quarks in the sea for the first time. We improve significantly on previous theory calculations to achieve accuracies of 1--2\%, giving lattice QCD results that are now more accurate than the experimental values. In particular our results transform the theoretical picture for ${\eta }_c\to \gamma \gamma$ decays. We use gluon field configurations generated by the MILC collaboration that include $n_f=2+1+1$ flavours of Highly Improved Staggered (HISQ) sea quarks at four lattice spacing values from 0.15 fm to 0.06 fm and with sea u/d masses down to their physical value. We also implement the valence $c$ quarks using the HISQ action. We find $\Gamma ({\eta }_c\to \gamma \gamma )=6.788(45{)}_{\text{fit}}(41{)}_{\text{syst}}\mathrm{keV}$, in good agreement with experimental results using $\gamma \gamma \to {\eta }_c\to K\overline{K}\pi$ but in 4$\sigma$ tension with the Particle Data Group global fit result; we suggest this fit is revisited. We also calculate $\Gamma (J/\psi \to \gamma {\eta }_c)=2.219(17{)}_{\text{fit}}(18{)}_{\text{syst}}(24{)}_{\text{expt}}(4{)}_{\text{QED}}\mathrm{keV}$, in good agreement with results from CLEO, and predict the Dalitz decay rate $\Gamma (J/\psi \to {\eta }_c{e}^{+}{e}^{-})=0.01349(21{)}_{\text{latt}}(13{)}_{\text{QED}}\mathrm{keV}$. We use our results to calibrate other theoretical approaches and to test simple relationships between the form factors and $J/\psi$ decay constant expected in the nonrelativistic limit.

26 pages, 19 figures. Updated Figure 7, added 3 references and made further small changes to clarify the presentation. Further small changes to text, version accepted by Physical Review D

References in corpus (13)

• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• High-precision scale setting in lattice QCD
• Quarkonia and their transitions
• Scaling studies of QCD with the dynamical HISQ action
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Charmonium spectrum and their electromagnetic transitions with higher multipole contributions
• Two Photon Decays of Charmonia from Lattice QCD
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Measurement of the gamma gamma* --> eta_c transition form factor
• Matching lattice and continuum axial-vector and vector currents with NRQCD and HISQ quarks
• Next-to-next-to-leading-order QCD corrections to hadronic width of pseudoscalar quarkonium
• Bottomonium precision tests from full lattice QCD: hyperfine splitting, ${\rm Y}$ leptonic width and $b$ quark contribution to $e^{+}{e}^{-}\to$ hadrons
• New puzzle in charmonium decays

Cited by in corpus (11)

• Improved evaluation of the electroweak contribution to muon $g-2$
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Exclusive photon-fusion production of even-spin resonances and exotic QED atoms in high-energy hadron collisions
• Observation of the charmonium decay ${\eta }_c\to \gamma \gamma$ in $J/\psi \to \gamma {\eta }_c$
• Lattice study of $J/\psi \to \gamma {\eta }_c$ using a method without momentum extrapolation
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Constraints on axion-like particles using lattice QCD calculations of the rate for $J/\psi \to \gamma a$
• Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory
• Study of the Magnetic Dipole Transition of $J/\psi \to \gamma {\eta }_c$ via ${\eta }_c\to p\bar{p}$
• Radiative Decays of Vector Mesons with Light-Cone Sum Rules
• Line shape of the $J\psi \to \gamma {\eta }_c$ decay