Subleading Isgur-Wise form factorχ3(v·v′)to orderαsin QCD sum rules

We calculate the contributions arising at order ${\alpha }_s$ in the QCD sum rule for the spin-symmetry-violating universal function ${\chi }_3\left(v·v^{\prime }\right)$, which appears at order $\frac{1}{m_Q}$ 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 $B\to D^{\mathrm{}(*)\mathrm{}}\ell \nu$ decays, we find that ${\chi }_3\left(v·v^{\prime }\right)$ does not exceed the level of ∼ 1%, indicating that power corrections induced by the chromomagnetic operator in the heavy quark expansion are small.