  We consider the non-forward amplitude within the Heavy Quark Effective
theory. We show that one can obtain new information on the subleading
corrections in 1/m_Q. We illustrate the method by deriving new simple relations
between the functions Xsi_3(w) and Lambdabar Xsi(w) and the sums Sum_n
DeltaE^(n)_j tau^(n)_j(1) tau^(n)_j(w) (j=1/2,3/2), that involve leading
quantities, namely the Isgur-Wise functions tau^(n)_j(w) and the level spacings
DeltaE^(n)_j. The simplicity of our results follows from the fact that, for the
non-forward amplitude B(v_i)->D^(n)(v')->B(v_f), there are three variables
(w_i,w_f,w_if)=(v_i.v',v_f.v',v_i.v_f) independent in a certain domain, and we
consider the zero recoil frontier (w,1,w) where only a finite number of j^P
states contribute (1/2^+,3/2^+). These sum rules reduce to known results at
w=1, for Lambdabar obtainted by Voloshin, and for Xsi_3(1) obtained by Le
Yaouanc et al. and by Uraltsev, and generalizes them to all values of w. We
discuss phenomenological applications of these results, in particular the check
of Bakamjian-Thomas quark models and the comparison with the QCD Sum Rules
approach.
