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

Abstract

We calculate the ${\Lambda }_b\to {\Lambda }_c\ell \nu$ form factors and decay rates for all possible $b\to c\ell \bar{\nu }$ four-Fermi interactions beyond the Standard Model, including nonzero charged lepton masses and terms up to order ${\alpha }_s{\Lambda }_{\text{QCD}}/m_{c,b}$ and ${\Lambda }_{\text{QCD}}^2/m_c^2$ in the heavy quark effective theory. At this order, we obtain model independent predictions for semileptonic ${\Lambda }_b\to {\Lambda }_c$ 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 ${\Lambda }_b\to {\Lambda }_c\ell \bar{\nu }$ decays, including predictions for the ratio $R({\Lambda }_c)=\mathcal{B}({\Lambda }_b\to {\Lambda }_c\tau \bar{\nu })/\mathcal{B}({\Lambda }_b\to {\Lambda }_c\mu \bar{\nu })$ 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 ${\Lambda }_b\to {\Lambda }_c\pi$ decays, and emphasize the importance of measuring at LHCb the double differential rate $d^2\Gamma ({\Lambda }_b\to {\Lambda }_c\ell \bar{\nu })/(d{q}^{2}d\cos \theta )$, in addition to the $q^2$ spectrum.

arXiv comment30 pages, 7 figures, 1 table

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