Precise predictions for ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ semileptonic decays

We calculate the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\mathrm{\ell }\nu$ form factors and decay rates for all possible $b\to c\mathrm{\ell }\bar{\nu }$ four-Fermi interactions beyond the Standard Model, including nonzero charged lepton masses and terms up to order ${\alpha }_s{\mathrm{\Lambda }}_{\text{QCD}}\mathrm{/}{m}_{c,b}$ and ${\mathrm{\Lambda }}_{\text{QCD}}^2\mathrm{/}{m}_c^2$ in the heavy quark effective theory. At this order, we obtain model independent predictions for semileptonic ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ decays in terms of only two unknown sub-subleading Isgur-Wise functions, which can be determined from fitting LHCb and lattice QCD data. We thus obtain model independent results for ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\mathrm{\ell }\bar{\nu }$ decays, including predictions for the ratio $R(\Lambda_c) = {\cal B}(\Lambda_b\to \Lambda_c \tau\bar\nu) / {\cal B}(\Lambda_b\to \Lambda_c \mu\bar\nu)$ in the presence of new physics, that are more precise than prior results in the literature, and systematically improvable with better data on the decays with $\mu$ (or $e$) in the final state. We also explore tests of factorization in ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\pi$ decays, and emphasize the importance of measuring at LHCb the double differential rate $d^2\Gamma(\Lambda_b\to\Lambda_c\ell\bar\nu) / (d q^2, d\cos\theta)$,inadditiontothe$q^2$ spectrum.