Precise determination of decay rates for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>γ</mml:mi><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> from lattice QCD

Abstract

We calculate the decay rates for ${\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c}$ and $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}{e}^{+}{e}^{\ensuremath{-}}$ 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 ${\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decays. We use gluon field configurations generated by the MILC collaboration that include ${n}_{f}=2+1+1$ flavors of highly improved staggered 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 highly improved staggered quark action. We find $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})=6.788(45{)}_{\mathrm{fit}}(41{)}_{\mathrm{syst}}\text{ }\text{ }\mathrm{keV}$, in good agreement with experimental results using $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}K\overline{K}\ensuremath{\pi}$ but in $4\ensuremath{\sigma}$ tension with the Particle Data Group global fit result [R. L. Workman (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022)]; we suggest this fit is revisited. We also calculate $\mathrm{\ensuremath{\Gamma}}(J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c})=2.219(17{)}_{\mathrm{fit}}(18{)}_{\mathrm{syst}}(24{)}_{\mathrm{expt}}(4{)}_{\mathrm{QED}}\text{ }\text{ }\mathrm{keV}$, in good agreement with results from CLEO, and predict the Dalitz decay rate $\mathrm{\ensuremath{\Gamma}}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}{e}^{+}{e}^{\ensuremath{-}})=0.01349(15{)}_{\mathrm{latt}}(15{)}_{\mathrm{expt}}(13{)}_{\mathrm{QED}}\text{ }\text{ }\mathrm{keV}$. We use our results to calibrate other theoretical approaches and to test simple relationships between the form factors and $J/\ensuremath{\psi}$ decay constant expected in the nonrelativistic limit.

Topics & Concepts