Hyperfine Effects and Large $1/m_Q^2$ Corrections

Abstract

Effects associated with hyperfine mass splitting between pseudo\-scalar and vector mesons may induce surprisingly large $1/m_Q^2$ corrections in the heavy quark expansion. We demonstrate this in a relativistic quark model by calculating to all orders in $1/m_Q$, with and without hyperfine effects, and comparing to the first order results. Total corrections of 30\% or more are quite possible in the decay rates for $B\to Dl\hat{I}½$ and $B\to D^{\ast }l\hat{I}½$ near zero recoil.

12 pages, LaTeX, 2 LaTeX figures in separate file, UTPT-92-24 (revised)