Simple operator formulation of the Bakamjian-Thomas approach to heavy quark current , with generalisation to HQET, and with applications to transitions of Lambda-b

TL;DR

This paper presents a simplified operator-based formulation of the Bakamjian-Thomas approach to heavy quark currents, generalizes it to Heavy Quark Effective Theory (HQET), and applies it to Lambda_b transitions, providing a unified and intuitive framework.

Contribution

It introduces a simple differential operator formulation within the Bakamjian-Thomas approach, extending it to HQET and enabling a unified treatment of heavy quark transitions.

Findings

Operator O describes light quark motion in the heavy quark limit.

The formulation provides an intuitive, relativistic generalization of the dipole operator.

Application to Lambda_b transitions demonstrates the approach's effectiveness.

Abstract

Starting from the general formulation of current matrix elements in the Bakamjian-Thomas (BT) approach to quark models, certain aspects of their heavy quark limit are exhibited in an intuitive form, allowing a common treatment for any number of quarks and angular momenta j,j'. We use the general Falk interpretation of Isgur-Wise functions as overlaps of light parton states in motion. Then, in BT, for small collinear velocities, the motion of these states is described by a very simple dimensionless differential operator O acting on the internal wave functions of the light quarks, which is a relativistic generalisation of the dipole operator times the quark mass : it appears as the generator of Lorentz transformations for N free light particles.