Universal $τ_{1/2}(y)$ Isgur-Wise Function at the Next-to-Leading Order in QCD Sum Rules

We use QCD sum rules, in the framework of the Heavy Quark Effective Theory, to calculate the universal form factor $\tau_{1/2}(y)$ parameterizing the semileptonic transitions $B \to D_0 \ell \bar \nu$, $B \to D_1^* \ell \bar \nu$, where $D_0$ and $D^*_1$ are the members of the excited charmed doublet with $J^P=(0^+_{1/2},1^+_{1/2})$. We include two-loop corrections in the perturbative contribution to the sum rule, and present a complete next-to-leading order result. As a preliminary part of our analysis we also compute, up to order $\alpha_s$, the leptonic constant $F^+$ of the doublet $D_0$, $D_1^*$. Finally, we discuss the phenomenological implications of this calculation.