Calculation of $1/{m}_{b}^{2}$ corrections to $⟨{\ensuremath{\Lambda}}_{b}(v,s)|\overline{b}{\ensuremath{\gamma}}^{\ensuremath{\lambda}}{\ensuremath{\gamma}}_{5}b|{\ensuremath{\Lambda}}_{b}(v,s)⟩$ for polarized ${\ensuremath{\Lambda}}_{b}$ in the Bethe-Salpeter equation approach

Calculation of $1 / m_{b}^{2}$ corrections to $⟨ Λ_{b} (v, s) | \bar{b} γ^{λ} γ_{5} b | Λ_{b} (v, s) ⟩$ for polarized $Λ_{b}$ in the Bethe-Salpeter equation approach

L. Zhang and X.-H. Guo

Phys. Rev. D 87, 076013 – Published 26 April 2013

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 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 Bethe-Salpeter equation numerically. The value of the spin-dependant form factor for the matrix element $⟨ Λ_{b} (v, s) | \bar{b} γ^{λ} γ_{5} b | Λ_{b} (v, s) ⟩$ , $ϵ_{b}$ , which is nonzero at order $1 / m_{b}^{2}$ , is obtained numerically from our model.