Modern status of heavy quark sum rules in QCD

TL;DR

This paper reviews the current status of heavy quark sum rules in QCD, highlighting recent progress in determining key parameters and discussing their implications for understanding QCD vacuum properties and exotic states.

Contribution

It provides updated values for QCD parameters using heavy quark sum rules and discusses their correlations, improving the understanding of QCD vacuum condensates and exotic hadronic states.

Findings

Updated alpha_s(M_Z)=0.1181(19)

Revised gluon condensate <alpha_s G^2> = (6.49±0.35)×10^-2 GeV^4

Four-quark condensate significantly deviates from vacuum saturation

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 (alpha_s, m_{c,b} and gluon condensates)where their correlations have been taken into account. The results: alpha_s(M_Z)=0.1181(16)(3), m_c(m_c)=1286(16) MeV, m_b(m_b)=4202(7) MeV,<alpha_s G^2> = (6.49+-0.35)10^-2 GeV^4, < g^3 G^3 >= (8.2+-1.0) GeV^2 <alpha_s G^2> and the ones from recent light quark sum rules are summarized in Table 2. One can notice that the SVZ value of <alpha_s G^2> has been underestimated by a factor 1.6, <g^3 G^3> is much bigger than the instanton model estimate, while the four-quark condensate which mixes under renormalization is incompatible with the vacuum saturation which is phenomenologically violated by a factor (2~4). The uses of HQSR for molecules and tetraquarks states are commented.