Semileptonic decays of $\Lambda_b$ baryons in the relativistic quark model

TL;DR

This paper investigates semileptonic $ ext{Lambda}_b$ decays using a relativistic quark model, providing detailed form factors and decay rates that align with experimental data and extracting CKM matrix element ratios.

Contribution

It offers a relativistic, non-approximated calculation of decay form factors across the entire kinematic range, improving accuracy over previous models.

Findings

Decay form factors are explicitly calculated without nonrelativistic approximations.

Branching fractions for $ ext{Lambda}_b$ decays agree with experimental data.

The ratio $|V_{ub}|/|V_{cb}|$ is extracted and consistent with inclusive B decay results.

Abstract

Semileptonic $\Lambda_b$ decays are investigated in the framework of the relativistic quark model based on the quasipotential approach and the quark-diquark picture of baryons. The decay form factors are expressed through the overlap integrals of the initial and final baryon wave functions. All calculations are done without employing nonrelativistic and heavy quark expansions. The momentum transfer dependence of the decay form factors is explicitly determined in the whole accessible kinematical range without any extrapolations or model assumptions. Both the heavy-to-heavy $\Lambda_b\to\Lambda_c\ell\nu_\ell$ and heavy-to-light $\Lambda_b\to p\ell\nu_\ell$ decay branching fractions are calculated. The results agree within error bars with the experimental value of the branching fraction of the $\Lambda_b\to\Lambda_c^+l^-\bar\nu_l$ decay. From the recent LHCb data on the ratio of the branching fractions of the heavy-to-light and heavy-to-heavy semileptonic $\Lambda_b$ decays the ratio of the Cabbibo-Kobayashi-Maskawa matrix elements $|V_{ub}|/|V_{cb}|$ is obtained. It is consistent with the corresponding ratio determined from the inclusive $B$ meson decays.