Sum rules of Bjorken-Uraltsev type in the Bakamjian-Thomas relativistic quark model

TL;DR

This paper demonstrates that the Bakamjian-Thomas relativistic quark model satisfies the tower of lowest moment sum rules in the heavy quark limit, providing explicit examples and discussing its limitations at finite mass.

Contribution

It shows that the Bakamjian-Thomas model satisfies Bjorken-Uraltsev sum rules in the heavy quark limit and introduces a new sum rule involving light cloud states.

Findings

The model satisfies the heavy quark limit sum rules.

A new sum rule constrains derivatives of radially excited Isgur-Wise functions.

Limitations of the model at finite mass are discussed.

Abstract

The Bakamjian-Thomas relativistic quark model, describing hadrons with a fixed number of constituents, yields in the heavy quark limit of QCD covariant Isgur-Wise functions and satisfies the whole tower of lowest moment sum rules (Bjorken-Uraltsev type sum rules). We first recall, as well as earlier results, the new formalism presented in our recent papers on Lorentz representations, which provide an elegant framework for the analysis of this model in the heavy quark limit and stress the results which have been already obtained in this direction. Then, we give some very explicit demonstrations of the fact that the Bakamjian-Thomas framework satifies the sum rules by considering simple cases of Isgur-Wise functions. In addition to the specific Bjorken and Uraltsev sum rules, an important sum rule that involves only heavy mesons with light cloud $j^P = {1 \over 2}^-$ and their radial excitations is demonstrated. This latter sum rule is phenomenologically interesting because it constrains the derivatives of the radially excited Isgur-Wise functions at zero recoil. On the other hand, we recall the limitations of the Bakamjian-Thomas scheme. At finite mass, current matrix elements with the current coupled to the heavy quark are no longer covariant, and higher moment sum rules that hold in the heavy quark limit of QCD are not satisfied.