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 $\vert V_{cb} \vert \simeq \ga 1.48 \mbox{ps}/τ_B \dr ^{1/2}(37.3 \pm 1.2 \pm 1.4)\times 10^{-3}$ where the first error comes from the data analysis and the second one from the different model parametrizations of the Isgur-Wise function.

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

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• Lattice Study of Semi-Leptonic $B$ Decays: I. $\bar{B}\to D\ell \bar{\nu }$ Decays
• Measurement of the Lambda_b^0 Decay Form Factor
• Calculation of the Isgur-Wise function from a light-front constituent quark model
• Slope of the Isgur-Wise Function from a QSSR Constraint on the ${\rm Y}B\bar{B}$ Couplings
• Isgur--Wise function in a relativistic model of constituent quarks
• Heavy Quark Solitons in the Nambu--Jona-Lasinio Model
• Exclusive Decays of Beauty Hadrons
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