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In the heavy quark limit, the heavy baryons \omega_{Q}^{(*)} (\omega could be\Sigma, \Xi or \Omega and Q=b or c) are regarded as composed of a heavy quarkand an axial vector, light diquark with good spin and isospin quantum numbers.Based on this diquark picture we establish the Bethe-Salpeter (B-S) equationfor \omega_{Q}^{(*)} in the limit where the heavy quark has infinite mass, m_Q-> \infty. It is found that in this limit there are three components in the B-Swave function for \omega_{Q}^{(*)}. Assuming the kernel to consist of a scalarconfinement term and a one-gluon-exchange term we derive three coupled integralequations for the three B-S scalar functions in the covariant instantaneousapproximation. Numerical solutions for the three B-S scalar functions arepresented, including a discussion about their dependence on the various inputparameters. These solutions are applied to calculate the Isgur-Wise functions\xi (\omega) and \zeta (\omega) for the weak transitions \Omega_{b}^{(*)} \to\Omega_{c}^{(*)}. Using these we give predictions for the Cabibbo-allowednonleptonic decay widths and up-down asymmetries for \Omega_{b} \to\Omega_{c}^{(*)} plus a pseudoscalar or vector meson.Comment: 35 pages, 5 figures, Latex. Revised version to appear in Phys. Rev.  D. Calculations of the Isgur-Wise functions for \Omega_{b}^{(*)} \to  \Omega_{c}^{(*)} and the Cabibbo-allowed nonleptonic decay widths and up-down  asymmetries for \Omega_{b} \to \Omega_{c}^{(*)} plus a pseudoscalar or vector  meson are adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Bethe-Salpeter equation for heavy baryons<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>*</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>in the diquark picture

Bethe-Salpeter equation for heavy baryonsωQ(*)in the diquark picture