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