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/mQcorrections and the Isgur–Wise function and other additional important wave functions concerned at 1/mQfor the heavy–light mesons. The number of unknown wave functions or form factors in HQEFT is shown to be much less than the one in the usual heavy quark effective theory (HQET). The values of wave functions at zero recoil are found to be consistent with the ones extracted from the interesting relations (which are resulted from the HQEFT) between the hadron masses and wave functions at zero recoil. The results for the decay constants are consistent with the ones from full QCD sum rule and Lattice calculations. The 1/mQcorrections to the scaling law [Formula: see text] are found to be small in HQEFT, which demonstrates again the validity of 1/mQexpansion in HQEFT. It is also shown that the residual momentum v·k of heavy quark within heavy–light hadrons is indeed around the binding energy [Formula: see text] of the heavy hadrons, which turns out to be in agreement with the expected one in the HQEFT. Therefore such a calculation provides 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 large 1/mQcorrections 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 [Formula: see text], while for heavy–heavy bound states (ψ1ψ2) with masses m1, [Formula: see text], like bottom-charm hadrons or similarly for muonium in QED, one needs to treat both particles as heavy effective particles via 1/m1and 1/m2expansions and redefine the effective bound states and modified "dressed heavy quark" masses within the HQEFT.