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

Abstract

Corrections of order 1/m_Q (Q=b or c) to the Bethe-Salpeter (B-S) equation for \Lambda_Q are analyzed on the assumption that the heavy baryon \Lambda_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 \Lambda_b -> \Lambda_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 $\Lambda_b \to \Lambda_c$ form factors to order 1/m_Q. Predictions are given for the differential and total decay widths for \Lambda_b -> \Lambda_c l \bar{\nu}, and also for the nonleptonic decay widths for \Lambda_b -> \Lambda_c plus a pseudoscalar or vector meson, with QCD corrections being also included.