  In the heavy quark limit of QCD, using the Operator Product Expansion, the
formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude,
as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise
function $\xi_{\Lambda} (w)$ of the baryon transition $\Lambda_b \to \Lambda_c
\ell \overline{\nu}_{\ell}$, where the light cloud has $j^P=0^+$ for both
initial and final baryons. We recover the lower bound for the slope
$\rho_\Lambda^2 = - \xi '_\Lambda (1) \geq 0$ obtained by Isgur et al., and we
generalize it by demonstrating that the IW function $\xi_{\Lambda} (w)$ is an
alternate series in powers of $(w-1)$, i.e. $(-1)^n \xi_{\Lambda}^{(n)} (1)
\geq 0$. Moreover, exploiting systematically the sum rules, we get an improved
lower bound for the curvature in terms of the slope, $\sigma_\Lambda^2 = \xi
"_\Lambda (1) \geq {3 \over 5} [\rho_\Lambda^2 + (\rho_\Lambda^2)^2]$. This
bound constrains the shape of the Isgur-Wise function and it will be compelling
in the analysis of future precise data on the differential rate of the baryon
semileptonic decay $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, that
has a large measured branching ratio, of about 5%.
