  Motivated by the claimed possibility of a large contribution of the first
radial excitation of the $D^{(\ast )}$ to the $B$ semileptonic decay into
charmed mesons, also invoked to solve the "$1/2$ vs. $3/2$ semileptonic
puzzle", we discuss the transitions to heavy-light radial excitations by a
heavy $b \to c$ quark current. We first consider a HQET sum rule, which
provides a bound on the slopes of Isgur-Wise functions which we then calculate
in the Bakamjian-Thomas framework which both guaranties covariance in the heavy
quark limit and satisfies a set of HQET sum rules. We observe a remarkable
property that for a large variety of wave functions the transition to the first
radial excitation is very small while the transition matrix element to the
second radial excitation is large and dominant in saturating the HQET sum rule.
This is opposite to what is found in non-relativistic models, where the
transition to the first radial excitation dominates the sum rule. The relative
magnitude of the transition to the second excitation appears to be weakly
dependent on the dynamical scale (radius of the bound states), and the same
holds true for the slope of the elastic transition. These features could be
tested in the heavy mass limit of lattice QCD. This pattern is shown to be
related to the general structure of the Bakamjian-Thomas model, it is
independent of the spin structure of the approach and derives mainly from the
Lorentz transformation of the spatial wave function, a feature often
disregarded in quark models.
