Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-05-15
Phys.Rev.D59:116007,1999
Physics
High Energy Physics
High Energy Physics - Phenomenology
35 pages, 5 figures, Latex. Revised version to appear in Phys. Rev. D. Calculations of the Isgur-Wise functions for \Omega_{b}
Scientific paper
10.1103/PhysRevD.59.116007
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 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 \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-S wave function for \omega_{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 \xi (\omega) and \zeta (\omega) for the weak transitions \Omega_{b}^{(*)} \to \Omega_{c}^{(*)}. Using these we give predictions for the Cabibbo-allowed nonleptonic decay widths and up-down asymmetries for \Omega_{b} \to \Omega_{c}^{(*)} plus a pseudoscalar or vector meson.
Guo Xin-Heng
Thomas Anthony W.
Williams Anthony G.
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