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

Abstract

In the heavy quark limit, the heavy baryons ωQ(*) (ω stands for Σ, Ξ or Ω and 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 (BS) equation for ωQ(*) in the limit where the heavy quark has infinite mass, mQ→∞. It is found that in this limit there are three components in the BS wave function for ωQ(*). 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 BS scalar functions in the covariant instantaneous approximation. Numerical solutions for the three BS scalar functions are presented, including a discussion of 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 Ωb(*)→Ωc(*). Using these we give predictions for the Cabibbo-allowed nonleptonic decay widths and up-down asymmetries for Ωb→Ωc(*) plus a pseudoscalar or vector meson.