  Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the
heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In
particular, we obtain new sum rules involving the elastic subleading form
factors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin and
L_mag perturbations of the Lagrangian. To the sum rules contribute only the
same intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enter
in the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil.
This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of the
chi_i(w) and the shape of the elastic IW function xi(w). An important
theoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) =
chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvature
attain their lowest values rho^2->3/4, sigma^2->15/16. These constraints should
be taken into account in the exclusive determination of |V_(cb)|.
