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

TL;DR

This paper develops a Bethe-Salpeter equation approach to calculate second-order 1/m_b corrections for the axial vector matrix element of polarized Lambda_b baryons, incorporating scalar confinement and one-gluon exchange.

Contribution

It introduces a second-order 1/m_Q expansion in the Bethe-Salpeter framework for heavy baryons, providing numerical solutions for spin-dependent form factors.

Findings

Numerical value for the 1/m_b^2 correction to the axial matrix element.

Demonstration of the Bethe-Salpeter equation's applicability to heavy baryon corrections.

Quantitative insights into spin-dependent form factors for polarized Lambda_b.

Abstract

The heavy baryon \Lambda_{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 \Lambda_{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 <\Lambda_{b}{(v,s)}|\bar{b}\gamma^{\lambda}\gamma_{5}b|\Lambda_{b}(v,s)>, \epsilon_{b}, which is non-zero at order 1/m^{2}_{b}, is obtained numerically from our model.