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

Abstract

We perform the first lattice calculation on the semileptonic decay of $J/\psi$ 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 $\operatorname{Br}(J/\psi\rightarrow D_s e\nu_e)=1.90(6)(5)_{V_{cs}}\times 10^{-10}$ and $\operatorname{Br}(J/\psi\rightarrow D e\nu_e)=1.21(6)(9)_{V_{cd}}\times 10^{-11}$, 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 $R_{J/\psi}(D_s)=0.97002(8)$ and $R_{J/\psi}(D)=0.97423(15)$ 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.