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

In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function xi (3)(1) or from a combination of Uraltsev and Bjorken SR, one infers for P-wave states \ tau (1/2)(1)\ much less than/tau (3/2)(1)\. This implies, in the heavy quark limit of QCD, a hierarchy for the production rates of P-states Gamma((B) over bar (d) --> D(1/2)lv much less than Gamma((B) over bar (d) --> D(3/2)lv) 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 f(3/2)((n))=0 Assuming the model of factorization in the decays (B) over bar (d) --> (D) over bar (s)**D, one expects the opposite hierarchy for the emission rates Gamma((B) over bar (d) --> (D) over bar (s)(3/2)D) much less than Gamma((B) over bar (d) (D) over bar (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 Sigma (n)(f((n))/f((o)))(2), Sigma (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. (C) 2001 Published by Elsevier Science B.V.