Tests of the infinite mass effective theory and properties of the charming and beautiful mesons

Abstract

Using an operator product expansion (OPE) in the inverse of the heavy quark massM _Q and a dispersive approach, we rederive theB andB ^* couplings and the Isgur-Wise function predicted by the infinite mass effective theory (IMET). We find that, at the subtraction pointM _Q and using VDM for the spectral function, these observables are governed by the universal$\left\langle {\bar qq} \right\rangle$ light quark condensate. We also find that the corrections induced by finite values ofM _c andM _b are large and are due to the splitting Δ_b between the ground state and its radial excitation. We review the determinations of the different decay constants, couplings and masses from QCD spectral sum rules (QSSR). Forf _B andf _D , we conclude the optimum average:f _B =(1.59±0.09±0.27)f _π andf _D =(1.31±0.12)f _π, where the main error is due to the quark mass, while the first one inf _B is due to the non-perturbative terms and to the choice of the continuum thresholdt _c from the onset of sum rule variable stability until thet _c -stability regions. We also find that the vector coupling γ_V satisfies approximately the IMETM ^3/2_Q mass dependence scaling law, whilef _P obeys in units of GeV:f P/f_π≅(4.6±0.4)M ^−1/2_Q (1–1.56/M _Q +0.88/M ²_Q ), forM _Q ≥M _c . We also predict the flavour independence:M _P -M _Q ≅0.6-0.7 GeV andM _V -M _Q ≅0.7-0.8 GeV of the mass differences between the mesons and the corresponding quark. Finally we find that theB→Dev _e form factorf ₊(0)≅(0.55±0.10) deviates from the naive expectation (f ₊(0)=1).