  We pursue the program of the study of the non-forward amplitude in HQET. 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 ${\cal L}_{kin}$ and
${\cal L}_{mag}$ perturbations of the Lagrangian. To obtain these sum rules we
use two methods. On the one hand we start simply from the definition of these
subleading form factors and, on the other hand, we use the Operator Product
Expansion. To the sum rules contribute only the same intermediate states $
(j^P, J^P) = ({1 \over 2}^-, 1^-), ({3\over 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 $\xi (w)$. We find
also lower bounds on the $1/m_Q^2$ correction to the form factors $h_+(w)$ and
$h_1(w)$ at zero recoil. 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 $\rho^2 \to {3 \over 4}$, $\sigma^2 \to {15 \over 16}$. We discuss
possible implications on the precise determination of $|V_{cb}|$.
