The Subleading Isgur-Wise Form Factor $χ_3(v\cdot v')$ to Order $α_s$ in QCD Sum Rules

Abstract

We calculate the contributions arising at order $α_s$ in the QCD sum rule for the spin-symmetry violating universal function $χ_3(v\cdot v')$, 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 $B\to D^{(*)}\ell\,ν$ decays, we find that $χ_3(v\cdot v')$ 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.