C. A. Dominguez

Determination of the gluon condensate and the four quark condensate via FESR

The dimension four gluon condensate and the dimension six four-quark condensate are estimated with the help of FESR by analyzing the ρ-meson channel. We find that the first is a factor 2–5 and the second is (in absolute value) a factor 5–8 larger than the corresponding “standard values”. We have checked our results by the “heat evolution test” of Gauss transforms. They turn out to be consistent whereas the “standard values” are not.

Mass singularities in light quark correlators: The strange quark case

The correlators of light-quark currents contain mass-singularities of the form log(m^2/Q^2). It has been known for quite some time that these mass- logarithms can be absorbed into the vacuum expectation values of other operators of appropriate dimension, provided that schemes without normal- ordering are used. We discuss in detail this procedure for the case of the mass logarithms m^4 log(m^2/Q^2), including also the mixing with the other dimension-4 operators to two-loop order. As an application we present an improved QCD sum rule determination of the strange-quark mass. We obtain m_s(1 GeV)=171 \pm 15 MeV.

Deconfinement and chiral-symmetry restoration at finite temperature☆

Abstract A QCD analysis of the two-point function involving axial-vector currents at T ≠0 provides evidence for a colour deconfinement phase transition. The critical temperature is somewhat lower that the one for chiral-symmetry restoration. Additional supporting evidence is provided by the first Weinberg sum rule at finite temperature.

Chiral condensates from tau decay: a critical reappraisal

The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d = 6 and d = 8 vacuum condensates in the Operator Product Expansion, with the results: 6(2.6 GeV2) = −(0.00226±0.00055) GeV6 , and 8(2.6 GeV2) = −(0.0054±0.0033) GeV8 from pinched FESR, and compatible values from the minimizing polynomial FESR. Some higher dimensional condensates are also determined, although we argue against extending the analysis beyond dimension d = 8. The value of the finite remainder of the (V-A) correlator at zero momentum is also redetermined: (0) = −4 10 = 0.02579±0.00023. The stability and precision of the predictions are significantly improved compared to earlier calculations using the old ALEPH data. Finally, the role and limits of applicability of the Operator Product Expansion in this channel are clarified.

QCD vacuum condensates from tau-lepton decay data

The QCD vacuum condensates in the Operator Product Expansion are extracted from the final ALEPH data on vector and axial-vector spectral functions from ?-decay. Weighted Finite Energy Sum Rules are employed in the framework of both Fixed Order and Contour Improved Perturbation Theory. An overall consistent picture satisfying chirality constraints can be achieved only for values of the QCD scale below some critical value ? 350?MeV. For larger values of ?, perturbation theory overwhelms the power corrections. A strong correlation is then found between ? and the resulting values of the condensates. Reasonable accuracy is obtained up to dimension d = 8, beyond which no meaningful extraction is possible.

CHIRAL SUM RULES AND DUALITY IN QCD

Abstract The ALEPH data on the vector and axial-vector spectral functions, extracted from tau-lepton decays, is used in order to test local and global duality, as well as a set of four QCD chiral sum rules. These are the Das-Mathur-Okubo sum rule, the first and second Weinberg sum rules, and a relation for the electromagnetic pion mass difference. We find these sum rules to be poorly saturated, even when the upper limit in the dispersion integrals is as high as 3 GeV 2 . Since perturbative QCD, plus condensates, is expected to be valid for |q 2 |≥ O (1 GeV 2 ) in the whole complex energy plane, except in the vicinity of the right hand cut, we propose a modified set of sum rules with weight factors that vanish at the end of the integration range on the real axis. These sum rules are found to be precociously saturated by the data to a remarkable extent. As a byproduct, we extract for the low energy renormalization constant L 10 the value −4 L 10 =2.43×10 −2 , to be compared with the standard value −4 L 10 =(2.73±0.12)×10 −2 . This in turn leads to a pion polarizability α E =3.7×10 −4 fm 3 .

New determination of the beauty quark mass

Abstract Ratios of Laplace transform QCD sum rules, in the non-relativistic limit, are used in order to determine the on-shell beauty-quark mass. Next to leading quark mass corrections are found to be important, as they are of the same size as the leading non-perturbative contribution. After confronting with the experimental data in the upsilon system we obtain mb=4.72±0.05 GeV. The error is due to uncertainties in the values of Λ and the gluon condensate.

Bottom-quark mass from finite energy QCD sum rules

Finite energy QCD sum rules involving both inverse and positive moment integration kernels are employed to determine the bottom quark mass. The result obtained in the

QCD sum rule determination of the charm-quark mass

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Pions at finite temperature from QCD sum rules

scheme at a reference scale of