Calculation of 1/m^{2}_{b} corrections to <Λ_{b}(v,s)|\bar{b}γ^λγ_{5}b|Λ_{b}(v,s)> for polarized Λ_{b} in the Bethe-Salpeter equation approach

Abstract

The heavy baryon Λ_{Q} (Q=b or c) can be regarded as composed of a heavy quark and a scalar light diquark which has good spin and isospin quantum numbers. In this picture we establish the Bethe-Salpeter (BS) equation for Λ_{Q} to second order in the 1/m_{Q} expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we solve the BS equation numerically. The value of the spin-dependant form factor for the matrix element <Λ_{b}{(v,s)}|\bar{b}γ^λγ_{5}b|Λ_{b}(v,s)>, ε_{b}, which is non-zero at order 1/m^{2}_{b}, is obtained numerically from our model.

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