$\Upsilon\overline{B}B$ couplings, slope of the Isgur-Wise function and improved estimate of $V_{cb}$

We estimate the sum of the \Upsilon \bar BB couplings using QCD Spectral Sum Rules (QSSR). Our result implies the phenomenological bound \xi'(vv'=1) \geq -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'(vv'=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 \vert V_{cb} \vert \simeq \ga 1.48 \mbox{ps}/\tau_B \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.