Study of two body hadronic decays Λb → Λ(p)P(V) in the instantaneous approximation of the Bethe-Salpeter equation approach

In this work, we study weak transitions of Lambda(b) to light baryons Lambda and p in the Bethe-Salpeter equation approach. In the heavy quark limit, based on the picture that Lambda(b) is composed of a heavy b-quark and a light diquark, the Bethe-Salpeter equation for Lambda(b) was established in previous works. Although the light baryon Lambda(p) is composed of various quark-diquark configurations based on the SU(6) spin-flavor wave functions, only the configuration s(ud)(0,0) left perpendicularu(ud)(0, 0)right perpendicular left perpendicular(ud)(0,0) is a scalar diquark composed of u and d quarksright perpendicular contributes to Lambda(b) -> Lambda(Lambda(b) -> p) transition. We establish the Bethe-Salpeter equations for the systems s(ud)(0,0) and u(ud)(0,0) and calculate their Bethe-Salpeter wave functions in the covariant instantaneous approximation with the kernel containing both scalar confinement and one-gluon-exchange terms. Then, the form factors for Lambda(b) -> Lambda and Lambda(b) -> Lambda p weak transitions are obtained with Bethe-Salpeter wave functions for Lambda(b), Lambda, and p. Consequently, we calculate the branching ratios of Lambda(b) -> Lambda P, Lambda(b) -> Lambda V, Lambda -> pP, and Lambda(b) -> pV (P and V denote pseudoscalar and vector mesons, respectively) in the factorization approach.