  Two new sum rules were recently discovered by Le Yaouanc et al. by applying
the operator product expansion to the nonforward matrix element of a
time-ordered product of $b \to c$ currents in the heavy-quark limit of QCD.
They lead to the constraints $\sigma^2 > 5\rho^2/4$ and $\sigma^2 >
3(\rho^2)^2/5 + 4\rho^2/5$ on the curvature of the $\bar{B} \to D^{(*)}$
Isgur-Wise function, both of which imply the absolute lower bound $\sigma^2 >
15/16$ when combined with the Uraltsev bound $\rho^2 > 3/4$ on the slope. This
paper calculates order $\alpha_s$ corrections to these bounds, increasing the
accuracy of the resultant constraints on the physical form factors. The latter
may have implications for the determination of $|V_{cb}|$ from exclusive
semileptonic $B$ meson decays.
