One interesting new sum rule extending Bjorkenʹs to order 1/mQ

We explicitly check quark-hadron duality to order (mb−mc)Λ/mb2 for b→clν decays in the limit mb−mc≪mb including ground state and orbitally excited hadrons. Duality occurs thanks to a new sum rule which expresses the subleading HQET form factor ξ3 or, in other notations, a+(1) in terms of the infinite mass limit form factors and some level splittings. We also demonstrate the sum rule, which is not restricted to the condition mb−mc≪mb, applying OPE to the longitudinal axial component of the hadronic tensor without neglecting the 1/mb subleading contributions to the form factors. We argue that this method should produce a new class of sum rules, depending on the current, beyond Bjorken, Voloshin and the known tower of higher moments. Applying OPE to the vector currents we find another derivation of the Voloshin sum rule. From independent results on ξ3 we derive a sum rule which involves only the τ1/2(n) and τ3/2(n) form factors and the corresponding level splittings. The latter strongly supports a theoretical evidence that the B semileptonic decay into narrow orbitally-excited resonances dominates over the decay into the broad ones, in apparent contradiction with some recent experiments. We discuss this issue.