Analytical determination of the QCD quark masses

Abstract

The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.

Finite Temperature QCD Sum Rules: A Review

“…where m u,d are the running quark masses in the M S-scheme at a scale µ = 2 GeV [17], [25]- [28], [89] and u(x), d(x), the corresponding quark fields. As usual, the relation between the QCD and the hadronic representation of current correlators is obtained by invoking Cauchy's theorem in the complex square-energy plane, Fig.2, which leads to the FESR…”

“…(60) allows to determine the quark masses entering the contour integral. Current precision determinations of quark masses [17], [25]- [28] require the introduction of integration kernels on both sides of Eq.(60). These kernels are used to enhance or quench hadronic contributions, depending on the integration region, and on the quality of the hadronic information available.…”

Hadronic vacuum polarization using gradient flow

“…The role of the perturbative and the non-perturbative regime of VPFs can be made most explicit through the OPE (see, e.g., ref. [24]):…”

Reanalysis of the X(3915) , X(4500) and X(4700) with QCD sum rules

“…The Borel parameter T 2 has no physical significance other than being a mathematical artifact, leads to rather narrow stability window for the hidden charm or hidden bottom tetraquark states. On the other hand, the continuum threshold s 0 , which has a clear physical interpretation, is often exponentially suppressed exp − s0 T 2 , or at best reduced in importance [29]. While in the finite energy QCD sum rules or Hilbert moment QCD sum rules, the threshold s 0 shows a power-like welcome feature, it is interesting to study the hidden charm or hidden bottom tetraquark states with the finite energy QCD sum rules or Hilbert moment QCD sum rules, this may be our next work.…”