Uraltsev Sum Rule in Bakamjian-Thomas Quark Models

Abstract

We show that the sum rule recently proved by Uraltsev in the heavy quark limit of QCD holds in relativistic quark models à la Bakamjian and Thomas, that were already shown to satisfy Isgur-Wise scaling and Bjorken sum rule. This new sum rule provides a {\it rationale} for the lower bound of the slope of the elastic IW function ${\rho }^2\ge \frac{3}{4}$ obtained within the BT formalism some years ago. Uraltsev sum rule suggests an inequality $|{\tau }_{3/2}(1)|>|{\tau }_{1/2}(1)|$. This difference is interpreted in the BT formalism as due to the Wigner rotation of the light quark spin, independently of a possible LS force. In BT models, the sum rule convergence is very fast, the $n=0$ state giving the essential contribution in most of the phenomenological potential models. We underline that there is a serious problem, in the heavy quark limit of QCD, between theory and experiment for the decays $B\to D_{0,1}^{\ast }(broad)\ell \nu$, independently of any model calculation.

Comments: 16 pages, Latex