B → D∗∗ semileptonic decay in covariant quark models à la Bakamjian-Thomas

Once chosen the dynamics in one frame, for example the rest frame, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the heavy quark limit, fully covariant current form factors as matrix elements of the quark current operator. They also verify the Isgur-Wise scaling and give a slope parameter p3 > 34 for all the possible choices of the dynamics. In this paper we study the L = 1 excited states and derive the general formula, valid for any dynamics, for the scaling invariant form factors τ12(n)(w) and τ32(n)(w). We also check the Bjorken-Isgur-Wise sum rule already demonstrated elsewhere in this class of models.