The Subleading Isgur-Wise Form Factor $\ddot{I}{‡}_3(v\cdot v^{\prime })$ to Order $\hat{I}{\pm }_s$ in QCD Sum Rules

Abstract

We calculate the contributions arising at order $\hat{I}{\pm }_s$ in the QCD sum rule for the spin-symmetry violating universal function $\ddot{I}{‡}_3(v\cdot v^{\prime })$, which appears at order $1/m_Q$ in the heavy quark expansion of meson form factors. In particular, we derive the two-loop perturbative contribution to the sum rule. Over the kinematic range accessible in $B\to D^{(\ast )}\ell \hat{I}½$ decays, we find that $\ddot{I}{‡}_3(v\cdot v^{\prime })$ does not exceed the level of $\sim 1\%$, indicating that power corrections induced by the chromo-magnetic operator in the heavy quark expansion are small.

12 pages ReVTeX, 3 figures available upon request, SLAC-PUB-6017, WIS-92/99/Dec-PH