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

Abstract

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 $B\to D_0\ell \bar{\nu }$, $B\to D_1^{\ast }\ell \bar{\nu }$, where $D_0$ and $D_1^{\ast }$ 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 $D_0$, $D_1^{\ast }$. Finally, we discuss the phenomenological implications of this calculation.

Comments: RevTex, 29 pages, 3 figures