On P-wave meson decay constants in the heavy quark limit of QCD

Abstract In previous work it has been shown that, either from a sum rule for the subleading Isgur–Wise function ξ 3 (1) or from a combination of Uraltsev and Bjorken SR, one infers for P -wave states | τ 1/2 (1)|⪡| τ 3/2 (1)|. This implies, in the heavy quark limit of QCD, a hierarchy for the production rates of P -states Γ( B d →D(1/2)lν)⪡Γ( B d →D(3/2)lν) that seems at present to be contradicted by experiment. It was also shown that the decay constants of j =3/2 P -states vanish in the heavy quark limit of QCD, f 3/2 ( n ) =0. Assuming the model of factorization in the decays B d → D s ∗∗ D , one expects the opposite hierarchy for the emission rates Γ( B d → D s (3/2)D)⪡Γ( B d → D s (1/2)D) , since j =1/2 P -states are coupled to vacuum. Moreover, using Bjorken SR and previously discovered SR involving heavy–light meson decay constants and IW functions, one can prove that the sums ∑ n f (n) /f (0) 2 , ∑ n f 1/2 (n) /f (0) 2 (where f ( n ) and f 1/2 ( n ) are the decay constants of S -states and j =1/2 P -states) are divergent. This situation seems to be realized in the relativistic quark models a la Bakamjian and Thomas, that satisfy HQET and predict decays constants f ( n ) and f 1/2 ( n ) that do not decrease with the radial quantum number n .