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 $R(\Lambda_c) = {\cal B}(\Lambda_b\to \Lambda_c \tau\bar\nu) / {\cal B}(\Lambda_b\to \Lambda_c \mu\bar\nu)$ 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 $\Lambda_b \to \Lambda_c\pi$ 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.
Highlights
In a recent paper [1], it was shown that LHCb data for the semileptonic Λb → Λcμν decays [2], combined with lattice QCD calculations [3], provide sensitivity for the first time to sub-subleading OðΛ2QCD=m2cÞ terms in the heavy quark effective theory (HQET) expansion [4,5] of the Λb → Λc semileptonic decay form factors, independent of jVcbj
The kinetic energy operator in the OðΛQCD=mc;bÞ HQET Lagrangian gives rise to a heavy quark spin symmetry conserving subleading term, parametrized by ζkeðwÞ, which can be absorbed into the leading order Isgur-Wise function by redefining ζ via ζðwÞ þ ðεc þ εbÞζkeðwÞ → ζðwÞ; ð10Þ
The correspondence between the four form factors used in this paper for the tensor current, fh1; h2; h3; h4g, defined in Eq (5), and those used in the lattice QCD (LQCD) calculation [51], fhþ; h⊥; hþ; h ⊥g, are given in Appendix A
Summary
In a recent paper [1], it was shown that LHCb data for the semileptonic Λb → Λcμν decays [2], combined with lattice QCD calculations [3], provide sensitivity for the first time to sub-subleading OðΛ2QCD=m2cÞ terms in the heavy quark effective theory (HQET) expansion [4,5] of the Λb → Λc semileptonic decay form factors, independent of jVcbj. The Λb → Λcμνdecays involve the same underlying b → cτν new physics (NP) operators as B → DðÃÞτν, but the HQET expansion for the ground-state baryon form factors is simpler than for mesons. We compute the relevant form factors including OðΛ2QCD=m2cÞ terms, and we compare the fit results of Ref. We further emphasize the importance of measuring at LHCb the double differential rate d2ΓðΛb → ΛclνÞ=ðdq2d cos θÞ in addition to the q2 spectrum, and we explore tests of factorization in Λb → Λcπ decay
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have