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 $\xi (\omega )=\eta [1-\frac{{\rho }^2}{\eta }(\omega -1)+a(\omega -1{)}^{3/2}]$ where ${\rho }^2=1.279$, $a=.91$, $\eta =.9942$ and $\omega$ is the recoil velocity. The Isgur-Wise function is then used to obtain $V_{cb}$ from the recent experimental data of $\bar{B}\to D^{\ast }\ell \bar{\nu }$ 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.

Comments: 12 Pages, 6 Postscript figures (appended at the end with instructions, available also from gupta@iastate.edu)