Fermi motion parameter $p_{_F}$ of $B$ meson from relativistic quark model

Abstract

The Fermi motion parameter $p_{_F}$ is the most important parameter of ACCMM model, and the value $p_{_F} \sim 0.3$ GeV has been used without clear theoretical or experimental evidence. So, we attempted to calculate the value for $p_{_F}$ theoretically in the relativistic quark model using quantum mechanical variational method. We obtained $p_{_F} \sim 0.5$ GeV, which is somewhat larger than 0.3 GeV, and we also derived the eigenvalue of $E_B \simeq 5.5$ GeV, which is in reasonable agreement with $m_B=5.28$ GeV. We also recalculated $|V_{ub}/V_{cb}|$ as a function of $p_{_F}$.