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

Abstract

We perform the first lattice calculation on the semileptonic decay of $J/ψ$ 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, $m_π\sim$ 300 MeV, are utilized. After a naive continuum extrapolation using three lattice spacings, we obtain $\operatorname{Br}(J/ψ\rightarrow D_s eν_e)=1.90(6)(5)_{V_{cs}}\times 10^{-10}$ and $\operatorname{Br}(J/ψ\rightarrow D eν_e)=1.21(6)(9)_{V_{cd}}\times 10^{-11}$, 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 $μ$ and $e$ are also calculated as $R_{J/ψ}(D_s)=0.97002(8)$ and $R_{J/ψ}(D)=0.97423(15)$ 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.