$|V_{cb}|$ from OPE Sum Rules for Heavy Flavor Transitions

Abstract

We derive a model-independent upper bound for the axial-vector form factor of the $B\text{ra}{D}^{\ast }$ transition at zero recoil, $F_{B\text{ra}{D}^{\ast }}$. The form factor turns out to be noticeably less than unity. The deviation of $F_{B\text{ra}{D}^{\ast }}$ from unity is larger than previously anticipated. Using our estimate we extract $|V_{cb}|$ from the measured exclusive rate of $B\text{ra}{D}^{\ast }l\nu$ extrapolated to the point of zero recoil. The central `` exclusive" value of $|V_{cb}|$ is in agreement with the value obtained from the inclusive semileptonic width $\Gamma (B\text{ra}{X}_{c}l\nu )$. We argue that the theoretical uncertainty in determining $|V_{cb}|$ from the total inclusive width is significantly reduced if a constraint on the quark mass difference $m_b-m_c$ stemming from the heavy quark expansion is taken into account.

Comments: 14 pages + uuencoded ps file with 1 figure, Latex, TPI-MINN-94/13-T, NSF-ITP-94-39