Study of the $D_s\to \varphi \ell {\nu }_{\ell }$ semileptonic decay with (2+1)-flavor lattice QCD

Abstract

We present a systematic lattice calculation of the $D_s\to \varphi \ell {\nu }_{\ell }$ semileptonic decay using (2+1)-flavor Wilson-clover fermion configurations generated by the CLQCD collaboration. Seven gauge ensembles with different lattice spacings, from $0.052\text{fm}$ to $0.105\text{fm}$, and different pion masses, from about $210\text{MeV}$ to $320\text{MeV}$ are utilized, enabling us to take both the continuum limit and physical pion mass extrapolation. The ratios of form factors are obtained to be $r_V=1.614(19)$ and $r_2=0.741(31)$, with the precision improved by up to an order of magnitude compared to previous lattice studies. The branching fractions are given as $\mathcal{B}(D_s\to \varphi e{\nu }_e)=2.493(66{)}_{\text{stat}}(31{)}_{|V_{cs}|}\times 10^{-2}$ and $\mathcal{B}(D_s\to \varphi \mu {\nu }_{\mu })=2.351(60{)}_{\text{stat}}(29{)}_{|V_{cs}|}\times 10^{-2}$. The corresponding ratio of the branching fractions between the lepton $\mu$ and $e$ is given by ${\mathcal{R}}_{\mu /e}=0.9432(13)$, which provides essential theoretical support for future high-precision experimental tests of the lepton flavor universality. The CKM matrix element $|V_{cs}|$ is also extracted to be $0.952(12{)}_{\text{stat}}(23{)}_{\text{PDG}}$ and $0.945(12{)}_{\text{stat}}(24{)}_{\text{PDG}}$ for the $\mu$ and $e$ channels, respectively.

Comments: 43 pages, 23 figures