Perturbative corrections to curvature sum rules

Abstract

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.