1/mQ Corrections to the Bethe-Salpeter Equation for Q in the Diquark Picture
Abstract
Corrections of order 1/mQ (Q=b or c) to the Bethe-Salpeter (B-S) equation for Q are analyzed on the assumption that the heavy baryon 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 mQ -> ∞, two more scalar functions are needed at the order 1/mQ. These can be related to the B-S scalar function in the leading order. The six form factors for the weak transition b -> c are expressed in terms of these wave functions and the results are consistent with heavy quark effective theory to order 1/mQ. Assuming the kernel for the B-S equation in the limit mQ -> ∞ 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 b c form factors to order 1/mQ. Predictions are given for the differential and total decay widths for b -> c l , and also for the nonleptonic decay widths for b -> c plus a pseudoscalar or vector meson, with QCD corrections being also included.
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