A Consistent Calculation of Heavy Meson Decay Constants and Transition Wave Functions in the Complete HQEFT

Abstract

Within the complete heavy quark effective field theory (HQEFT), the QCD sum rule approach is used to evaluate the decay constants including 1/m_Q corrections and the Isgur-Wise function and other additional important wave functions concerned at 1/m_Q for the heavy-light mesons. The 1/m_Q corrections to the scaling law f_M \sim F/\sqrt{m_M} are found to be small in HQEFT, which demonstrates again the validity of 1/m_Q expansion in HQEFT. It is also shown that the residual momentum v.k of heavy quark within hadrons does be around the binding energy \bar{\Lambda} of the heavy hadrons. The calculations presented in this paper provide a consistent check on the HQEFT and shows that the HQEFT is more reliable than the usual HQET for describing a slightly off-mass shell heavy quark within hadron as the usual HQET seems to lead to the breakdown of 1/m_Q expansion in evaluating the meson decay constants. It is emphasized that the introduction of the `dressed heavy quark' mass is useful for the heavy-light mesons (Qq) with m_Q >> \bar{\Lambda} >> m_q, while for heavy-heavy bound states (\psi_1\psi_2) with masses m_1, m_2 >> \bar{\Lambda}, like bottom-charm hadrons or similarly for muonium in QED, one needs to treat both particles as heavy effective particles via 1/m_1 and 1/m_2 expansions and redefine the effective bound states and modified `dressed heavy quark' masses within the HQEFT.