$\Xi_c\to \Xi$ Form Factors and $\Xi_c\to \Xi \ell^+\nu_{\ell}$ Decay Rates From Lattice QCD

We perform the first lattice QCD calculation of the form factors governing the $\Xi_{c}\to \Xi \ell^+\nu_{\ell}$ using the 2+1 clover fermion ensembles with two lattice spacings, $a=(0.108{\rm fm},0.080{\rm fm})$. After the continuum extrapolation, partial decay widths are calculated. Using the $|V_{cs}|$ from global fit and the $\Xi_{c}$ lifetimes, we predict branching fractions as ${\cal B}(\Xi_{c}^0\to \Xi^- e^+ \nu_{e})=2.38(0.30)(0.33)\% $, ${\cal B}(\Xi_{c}^0\to \Xi^- \mu^+ \nu_{\mu})=2.29(0.29)(0.31)\% $, ${\cal B}(\Xi_{c}^+\to \Xi^0 e^+ \nu_{e})= 7.18(0.90)(0.98)\%$, and ${\cal B}(\Xi_{c}^+\to \Xi^0 \mu^+ \nu_{\mu})= 6.91(0.87)(0.93)\%$, with the two kinds of uncertainties coming from statistical fluctuations in form factors and $\Xi_c$ lifetimes, and systematic ones from continuum extrapolation and renormalization, respectively. Combing the experimental measurement by Belle, we determine the CKM matrix element as $|V_{cs}|=0.834(0.074)(0.127)$, where the two uncertainties come from theory and data.