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The Isgur-Wise Function to $O(α_s)$ from Sum Rules in the Heavy Quark Effective Theory

Radiative corrections to both perturbative and non-perturbative contributions are added to existing calculations of the Isgur-Wise function $ξ_{IW}$. To this end, we develop a method for calculating two-loop integrals in the heavy quark effective theory involving two different scales. The inclusion of $O(α_s)$ terms causes $ξ_{IW}$ to decrease as compared to the lowest order result and shows the importance of quantum effects. The slope parameter $ρ^2$ violates the bound given by de Rafael and Taron.