${\mathrm{\Xi }}_c\to \mathrm{\Xi }$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of ${\mathrm{\Xi }}_c^0$ decay rates

We present a lattice-QCD determination of the vector and axial-vector form factors that describe the charm-baryon semileptonic decays ${\mathrm{\Xi }}_c\to \mathrm{\Xi }{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$. The calculation uses a domain-wall action for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles of gauge-field configurations generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. We present Standard-Model predictions for the decay rates and branching fractions of ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}_c^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}_c^0{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ for $\mathrm{\ell }=e,\mu$. In particular, we obtain $\mathrm{\Gamma }({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{e}^{+}{\nu }_e)\mathrm{/}\mathrm{\mid }{V}_{cs}{\mathrm{\mid }}^2=0.2515(73){\text{ ps}}^{-1}$ and $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{e}^{+}{\nu }_e)=3.58(12)\mathrm{\%}$. These values are higher than those predicted by a previous lattice calculation and substantially higher than the experimentally measured values, but consistent with expectations from approximate $SU(3)$ flavor symmetry.