The Subleading Isgur-Wise Form Factor ${\chi }_3(v\cdot v^{\prime })$ to Order ${\alpha }_s$ in QCD Sum Rules

Abstract

We calculate the contributions arising at order ${\alpha }_s$ in the QCD sum rule for the spin-symmetry violating universal function ${\chi }_3(v\cdot v^{\prime })$, 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 $B\to D^{(\ast )}\ell \nu$ decays, we find that ${\chi }_3(v\cdot v^{\prime })$ 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.

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