First lattice QCD calculation of $J\mathrm{/}\psi$ semileptonic decay containing $D$ and $D_s$ particles

We perform the first lattice calculation on the semileptonic decay of $J\mathrm{/}\psi$ using the (2+1)-flavor Wilson-clover gauge ensembles generated by CLQCD collaboration. Three gauge ensembles with different lattice spacings, from 0.0519 fm to 0.1053 fm, and pion masses, $m_{\pi }\sim$ 300 MeV, are utilized. After a naive continuum extrapolation using three lattice spacings, we obtain $\mathrm{Br}(J\mathrm{/}\psi \to D_{s}e{\nu }_e)=1.90(6)(5{)}_{V_{cs}}\times {10}^{-10}$ and $\mathrm{Br}(J\mathrm{/}\psi \to De{\nu }_e)=1.21(6)(9{)}_{V_{cd}}\times {10}^{-11}$, where the first errors are statistical, and the second come from the uncertainties of CKM matrix element $V_{cs(d)}$. The ratios of the branching fractions between lepton $\mu$ and $e$ are also calculated as $R_{J\mathrm{/}\psi }(D_s)=0.97002(8)$ and $R_{J\mathrm{/}\psi }(D)=0.97423(15)$ after performing a continuum limit including only $a^2$ term. The ratios provide necessary theoretical support for the future experimental test of lepton flavor universality.