On the running coupling constant in QCD

Prosperi, G. M.; Raciti, M.; Simolo, C.

doi:10.1016/j.ppnp.2006.09.001

Cited by 162 publications

(246 citation statements)

References 222 publications

(373 reference statements)

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“…The running coupling must go to zero like the fourth power of momentum being this in agreement with lattice computations as shown by Boucaud et al [17] but as also seen from experiments as shown by Prosperi et al [18,19,20]. These latter results on the running coupling give a strong clue that Yang-Mills theory is trivial as happens for the scalar field theory.…”

supporting

confidence: 85%

Yang-Mills Propagators and QCD

Frasca¹

2009

Nuclear Physics B - Proceedings Supplements

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We present a strong coupling expansion that permits to develop analysis of quantum field theory in the infrared limit. Application to a quartic massless scalar field gives a massive spectrum and the propagator in this regime. We extend the approach to a pure Yang-Mills theory obtaining analogous results. The gluon propagator is compared satisfactorily with lattice results and similarly for the spectrum. Comparison with experimental low energy spectrum of QCD supports the view that $\sigma$ resonance is indeed a glueball. The gluon propagator we obtained is finally used to formulate a low energy Lagrangian for QCD that reduces to a Nambu-Jona-Lasinio model with all the parameters fixed by those of the full theory.Comment: 4 pages, 1 figure. Contribution to proceedings of QCD 08 Conference, (Montpellier, France, July 7-12, 2008). Modified enunciation of the mapping theore

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supporting

confidence: 85%

Yang-Mills Propagators and QCD

Frasca¹

2009

Nuclear Physics B - Proceedings Supplements

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“…[115][116][117], this prescription yields a misleading result, which differs from the proper one (10) even in the deep ultraviolet asymptotic, see also Refs. [42,118,119] as well as [31] and the references therein.…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

Electron–positron annihilation into hadrons at the higher-loop levels

Нестеренко

2017

Eur. Phys. J. C

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The strong corrections to the R-ratio of electronpositron annihilation into hadrons are studied at the higherloop levels. Specifically, the derivation of a general form of the commonly employed approximate expression for the Rratio (which constitutes its truncated re-expansion at high energies) is delineated, the appearance of the pertinent π 2 -terms is expounded, and their basic features are examined. It is demonstrated that the validity range of such approximation is strictly limited to √ s/Λ > exp(π/2) 4.81 and that it converges rather slowly when the energy scale approaches this value. The spectral function required for the proper calculation of the R-ratio is explicitly derived and its properties at the higher-loop levels are studied. The developed method of calculation of the spectral function enables one to obtain the explicit expression for the latter at an arbitrary loop level. By making use of the derived spectral function the proper expression for the R-ratio is calculated up to the five-loop level and its properties are examined. It is shown that the loop convergence of the proper expression for the R-ratio is better than that of its commonly employed approximation. The impact of the omitted higher-order π 2 -terms on the latter is also discussed.

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“…(f) Finally, it is important to note that the Laplacian sun rule (54) is based on the Borel transform for the global duality relation (52), not based on the so-called strict local duality…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The expressions for the three-loop running coupling constant α s (Q 2 ) with three massless flavors (N f = 3) at renormalization scale µ [52] …”

Section: Numerical Analysismentioning

confidence: 99%

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

Chen

Liu

2017

Phys. Rev. D

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The more-carefully defined, and more appropriate 2 ++ tensor glueball current is a SUc(3) gaugeinvariant, symmetric, traceless and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted, and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. Besides taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2 ++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width and coupling constants for the 2 ++ resonance in which the glueball fraction is dominant are obtained.

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On the running coupling constant in QCD

Cited by 162 publications

References 222 publications

Yang-Mills Propagators and QCD

Yang-Mills Propagators and QCD

Electron–positron annihilation into hadrons at the higher-loop levels

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

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