Paper detail

1/m_Q Corrections to the Bethe-Salpeter Equation for Λ_{Q} in the Diquark Picture

Corrections of order 1/m_Q (Q=b or c) to the Bethe-Salpeter (B-S) equation for Λ_Q are analyzed on the assumption that the heavy baryon Λ_Q is composed of a heavy quark and a scalar, light diquark. It is found that in addition to the one B-S scalar function in the limit m_Q -> \infty, two more scalar functions are needed at the order 1/m_Q. These can be related to the B-S scalar function in the leading order. The six form factors for the weak transition Λ_b -> Λ_c are expressed in terms of these wave functions and the results are consistent with heavy quark effective theory to order 1/m_Q. Assuming the kernel for the B-S equation in the limit m_Q -> \infty to consist of a scalar confinement term and a one-gluon-exchange term we obtain numerical solutions for the B-S wave functions, and hence for the $Λ_b \to Λ_c$ form factors to order 1/m_Q. Predictions are given for the differential and total decay widths for Λ_b -> Λ_c l \barν, and also for the nonleptonic decay widths for Λ_b -> Λ_c plus a pseudoscalar or vector meson, with QCD corrections being also included.