Two-loop corrections to the Isgur-Wise function in QCD sum rules

Abstract

We complete the QCD sum rule analysis of the Isgur Wise form factor $\xi (v\cdot v^{\prime })$ at next-to-leading order in renormalization-group improved perturbation theory. To this end, the exact result for the two-loop corrections to the perturbative contribution is derived using the heavy quark effective theory. Several techniques for the evaluation of two-loop integrals involving two different types of heavy quark propagators are discussed in detail, among them the methods of integration by parts and differential equations. The order-${\alpha }_s$ corrections to the Isgur-Wise function turn out to be small and well under control. At large recoil, they tend to decrease the form factor by $5-10\%$.

Comments: 24 pages (REVTEX), 2 figures available upon request, SLAC-PUB-5992