Heavy quarkonia mass-splittings in QCD: gluon condensate, αs and [formula omitted

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 α s , we deduce the value: 〈 α s G 2〉 = (7.5 ± 2.5) × 10 −2 GeV 4 of the gluon condensate from M ψ − M ηc and M χb − M υ , 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 〈 α s G 2〉 = (7.1 ± 0.9) × 10 −2 GeV 4 from the light and heavy quark systems. We also find that M χc ( P 1 1) − M χc ( P 1 3) is governed by the radiative corrections and gives α s (1.3 GeV) ≈- 0.64 −0.18 +0.36 ± 0.02 for 4 flavours, leading to α s ( M Z ) ≈- 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 M υ − M ηb ≈ 63 +51 −29 MeV implying the possible observation of the η b in the ϒ radiative decay. The validity of the 1 m - expansion , including finite mass corrections is tested, while a connection of our mass and width formulae, with the potential model ones is done.