Abstract :
New double ratios of exponential moments of different two-point functions, which are less sensitive to the heavy quark mass and to the continuum effects than the commonly used ratio of moments, are presented for a more refined analysis of the mass-splittings between the different heavy quarkonia states. Using the present value of the QCD coupling αs, we deduce the value: 〈αsG2〉 = (7.5 ± 2.5) × 10−2 GeV4 of the gluon condensate from Mψ − Mηc and Mχb − Mυ, which combined with the recent estimate from τ-like decay sum rule in e+e− → I = 1 hadrons data, leads to the update average value 〈αsG2〉 = (7.1 ± 0.9) × 10−2 GeV4 from the light and heavy quark systems. We also find that Mχc(P11) − Mχc(P13) is governed by the radiative corrections and gives αs(1.3 GeV) ≈- 0.64−0.18+0.36 ± 0.02 for 4 flavours, leading to αs(MZ) ≈- 0.127 ± 0.011, which is compatible with the one from LEP and τ-decay data. Our predictions for the splittings of different heavy quarkonia states are summarized in Table 2, where, in particular, we find Mυ − Mηb ≈ 63+51−29 MeV implying the possible observation of the ηb in the ϒ radiative decay. The validity of the 1m-expansion, including finite mass corrections is tested, while a connection of our mass and width formulae, with the potential model ones is done.
