Modern status of heavy quark sum rules in QCD

Abstract

We briefly report the modern status of heavy quark sum rules (HQSR) based on stability criteria by emphasizing the recent progresses for determining the QCD parameters (αs, mc,b and gluon condensates) where their correlations have been taken into account. The results: αs(MZ) = 0.1181(16)(3), m‾c(m‾c)=1286(16)MeV, m‾b(m‾b)=4202(7)MeV, 〈αsG2〉 = (6.49±0.35)×10−2 GeV4, 〈g3G3〉 = (8.2±1.0)×GeV2〈αsG2〉 and the ones from recent light quark sum rules are summarized in Table 2. One can notice that the SVZ value of 〈αsG2〉 has been underestimated by a factor 1.6, 〈g3G3〉 which is much bigger than the instanton liquid model estimate, while the four-quark condensate which mixes under renormalization is incompatible with the vacuum saturation by a factor (2 ∼ 4). The uses of HQSR for molecules and tetraquarks states are commented.