In previous work it has been shown that, either from a sum rule for the sub
leading 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/ta
u (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 t
he 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-lig
ht meson decay constants and IW functions, one can prove that the sums Sigm
a (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 mo
dels A la Bakamjian and Thomas, that satisfy HQET and predict decays consta
nts f((n)) and f(1/2)((n)) that do not decrease with the radial quantum num
ber n. (C) 2001 Published by Elsevier Science B.V.