Sum rules in the heavy quark limit of QCD

In the leading order of the heavy quark expansion, we propose a method within the operator product expansion and the trace formalism that allows us to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise (IW) function xi(w) in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the nonforward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any w. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope rho(2)=-xi(')(1) and also on the curvature sigma(2)=xi(')(1) and imply, modulo a very natural assumption, the inequality sigma(2)greater than or equal to(5/4)rho(2), and therefore the absolute bound sigma(2)greater than or equal to15/16.