Calculation of 1/m^{2}_{b} corrections to {\Lambda}_b\rightarrow{\Lambda}_c decay widths in the Bethe-Salpeter equation approach

TL;DR

This paper calculates 1/m_b^2 corrections to the decay widths of Lambda_b to Lambda_c using the Bethe-Salpeter approach, incorporating QCD corrections and providing numerical results for semileptonic and nonleptonic decays.

Contribution

It introduces a second-order 1/m_Q expansion of form factors within the Bethe-Salpeter framework, including scalar confinement, one-gluon exchange, and QCD corrections.

Findings

Calculated decay widths for Lambda_b to Lambda_c semileptonic decays.

Provided numerical estimates for nonleptonic decay widths.

Quantified the impact of 1/m_Q corrections and QCD effects.

Abstract

The matrix element of the weak transition {\Lambda}_b\rightarrow{\Lambda}_c can be expressed in terms of six form factors. {\Lambda}_Q(Q = b;c) can be regarded as composed of a heavy quark Q(Q = b;c) and a diquark which is made up of the remaining two light quarks. In this picture, we express these six form factors in terms of Bethe-Salpeter wave functions to second order in the 1/m_Q expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we calculate the form factors and the decay widths of the semileptonic decay {\Lambda}_b\rightarrow{\Lambda}_clv as well as nonleptonic decays {\Lambda}_b\rightarrow{\Lambda}_cP(V) numerically. We also add QCD corrections since they are comparable with 1/m_Q corrections.