Dependence of $|V_{ub}/V_{cb}|$ on Fermi momentum $p_{_F}$ in ACCMM model

Abstract

The Gaussian width of Fermi momentum, $p_{_F}$, is the most important parameter of the ACCMM model, and its value is essential in the determination of $|V_{ub}/V_{cb}|$ because the experimental analysis is allowed only at the end-point region of inclusive semileptonic $B$-decay spectrum. We extract the value of $|V_{ub}/V_{cb}|$ as a function of $p_{_F}$. We also calculate the parameter $p_{_F}$ in the relativistic quark model using the variational method, and obtain $p_{_F} = 0.54$ GeV which is much larger than the commonly used value, $\sim 0.3$ GeV, in experimental analyses. When we use $p_{_F} = 0.5$ GeV instead of 0.3 GeV, the value of $|V_{ub}/V_{cb}|$ from ACCMM model is increased by a factor 1.81, and can give a good agreement with Isgur {\it et al.} model.

1. Section 2 has been revised by considering the fact that in the real experimental situation the only measured quantity is the number of events in the high $E_l$ region compared to the total semi- leptonic event number. 2. The article by C. Greub and D. Wyler (Phys. Lett. B295 (1992) 293) has been included in references, which reports a similar conclusion for the value of $p_{_F}$ ($p_{_F}$=566 MeV), even though they used the different approach. 3. This article will be published in Z. Phys. C (1995)