$Λ_c \to Λ\ell^+ ν_\ell$ form factors and decay rates from lattice QCD with physical quark masses

Abstract

The first lattice QCD calculation of the form factors governing $Λ_c \to Λ\ell^+ ν_\ell$ decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the $Λ_c \to Λe^+ ν_e$ and $Λ_c \to Λμ^+ ν_μ$ decay rates divided by $|V_{cs}|^2$ are $0.2007(71)(74)\:{\rm ps}^{-1}$ and $0.1945(69)(72)\:{\rm ps}^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ from a global fit and the $Λ_c$ lifetime from experiments, this translates to branching fractions of $\mathcal{B}(Λ_c\toΛe^+ν_e)=0.0380(19)_{\rm LQCD\:\:}(11)_{τ_{Λ_c}}$ and $\mathcal{B}(Λ_c\toΛμ^+ν_μ)=0.0369(19)_{\rm LQCD\:\:}(11)_{τ_{Λ_c}}$. These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives $|V_{cs}|= 0.949(24)_{\rm LQCD\:\:}(14)_{τ_{Λ_c}}(49)_{\mathcal{B}}$.

6 pages, 3 figures, form factor parameters included as ancillary files