Isgur-Wise Function and $V_{cb}$ from Bethe-Salpeter Equations

Abstract

We calculate the Isgur-Wise function from the solutions of the Bethe-Salpeter equations. The shape of the Isgur-Wise function thus calculated is a prediction of the Bethe-Salpeter equations and does not depend on undetermined parameters. We develop an analytical approximation to our Isgur-Wise function in the form $ξ( ω) = η[ 1 - \frac{ρ^2}η (ω- 1) + a (ω- 1)^{3/2}]$ where $ρ^2 = 1.279$, $a = .91$, $η= .9942$ and $ω$ is the recoil velocity. The Isgur-Wise function is then used to obtain $V_{cb}$ from the recent experimental data of ${\bar B} \to D^* \ell \barν$ decay. Our best estimate of $V_{cb}$ is $(34.7 \pm 2.5) \times 10^{-3}$, which is comparable to some of the latest estimates in the literature.