Uraltsev sum rule in Bakamjian–Thomas quark models

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 rationale for the lower bound of the slope of the elastic IW function ρ2⩾3/4 obtained within the BT formalism some years ago. Uraltsev sum rule suggests an inequality |τ3/2(1)|>|τ1/2(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→D∗0,1(broad)ℓν, independently of any model calculation.