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Bethe-Salpeter Equation for Heavy Baryons ω_{Q}^{(*)} in the Diquark Picture

In the heavy quark limit, the heavy baryons ω_{Q}^{(*)} (ωcould be Σ, Ξor Ωand Q=b or c) are regarded as composed of a heavy quark and an axial vector, light diquark with good spin and isospin quantum numbers. Based on this diquark picture we establish the Bethe-Salpeter (B-S) equation for ω_{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-S wave function for ω_{Q}^{(*)}. Assuming the kernel to consist of a scalar confinement term and a one-gluon-exchange term we derive three coupled integral equations for the three B-S scalar functions in the covariant instantaneous approximation. Numerical solutions for the three B-S scalar functions are presented, including a discussion about their dependence on the various input parameters. These solutions are applied to calculate the Isgur-Wise functions ξ(ω) and ζ(ω) for the weak transitions Ω_{b}^{(*)} \to Ω_{c}^{(*)}. Using these we give predictions for the Cabibbo-allowed nonleptonic decay widths and up-down asymmetries for Ω_{b} \to Ω_{c}^{(*)} plus a pseudoscalar or vector meson.