QCD at Low Energies

TL;DR

This paper reviews low energy QCD parameters, determines light quark mass ratios with high precision, and extracts fundamental condensates and coupling constants using tau-decay data and sum rules, confirming consistency across multiple methods.

Contribution

It provides a comprehensive analysis of vacuum condensates, quark masses, and the strong coupling constant using experimental data and sum rules, improving precision and consistency in low energy QCD parameters.

Findings

Quark mass ratios determined with 10-15% accuracy.

Gluon condensate value confirmed as 0.005  0.004 GeV^4.

Valence quark distributions in proton match deep inelastic scattering results.

Abstract

The modern status of basic low energy QCD parameters is reviewed. It is demonstrated, that the recent data allows one to determine the light quark mass ratios with an accuracy 10-15%. The general analysis of vacuum condensates in QCD is presented, including those induced by external fields. The QCD coupling constant alpha_s is found from the tau-lepton hadronic decay rate. V-A spectral functions of tau-decay are used for construction of the V-A polarization operator Pi_{V-A}(s) in the complex s-plane. The operator product expansion (OPE) is used up to dimension D=10 and the sum rules along the rays in the complex s-plane are constructed. The best values of quark condensate and alpha_s<0|qq|0>^2 are found. The value of quark condensate is confirmed by considering the sum rules for baryon masses. Gluon condensate is found in four ways: by considering of V+A polarization operator based on the tau-decay data, by studying the sum rules for polarization operators momenta in charmonia in vector, pseudoscalar and axial channels. All of these determinations are in agreement and result in <(alpha_s/pi)G^2 > =0.005 \pm 0.004 GeV^4. Valence quark distributions in proton are calculated in QCD using the OPE in proton current virtuality. The quark distributions agree with those found from the deep inelastic scattering data. The same value of gluon condensate is favoured.