Upsilon \bar BB Couplings, Slope of the Isgur-Wise Function and Improved Estimate of \boldmath{V_{cb}$}}

Abstract

We estimate the sum of the ${\rm Y}\bar{B}B$ couplings using QCD Spectral Sum Rules (QSSR). Our result implies the phenomenological bound ${\xi }^{\prime }(v{v}^{\prime }=1)\ge -1.04$ for the slope of the Isgur-Wise function. An analytic estimate of the (physical) slope to two loops within QSSR leads to the accurate value ${\xi }^{\prime }(v{v}^{\prime }=1)\simeq -(1.00\pm 0.02)$ due to the (almost) complete cancellations between the perturbative and non-perturbative corrections at the stability points. Then, we deduce, from the present data, the improved estimate $|V_{cb}|\simeq \text{ga}1.48\text{mbox}ps/{\tau }_B{\text{dr}}^{1/2}(37.3\pm 1.2\pm 1.4)\times 10^{-3}$ where the first error comes from the data analysis and the second one from the different model parametrizations of the Isgur-Wise function.

Comments: {{\bf $\bf 10 pages, Latex, (1 Figure on request), CERN-TH-7103/93 (Phys. Lett. B in press)