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 TMF, 2005, Volume 145, Number 2, Pages 221–239 (Mi tmf1898)

Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large $Q^2$

A. I. Alekseev

Institute for High Energy Physics

Abstract: Based on the analytic invariant charge obtained from the results of the standard perturbation theory up to the four-loop approximation, we construct a “synthetic” model of the invariant charge in quantum chromodynamics. In the suggested model, the perturbative discontinuity on the timelike semiaxis in the complex $Q^2$ plane is preserved, and nonperturbative contributions not only cancel nonphysical perturbation theory singularities in the infrared region but also rapidly decrease in the ultraviolet region. On one hand, the effective coupling function in this model is enhanced at zero (the dual superconductivity property of the quantum chromodynamics vacuum); on the other hand, a dynamical gluon mass appears. In our approach, fixing the parameter corresponding to the string tension parameter and normalizing (for example, at the point $M_\tau$) entirely fix the synthetic invariant-charge model. The dynamical gluon mass $m_{\mathrm{g}}$ is then fixed and is stable as the number of loops of the original perturbative approximation increases.

Keywords: analytic approach, infrared region of quantum chromodynamics, running coupling constant, nonperturbative contributions

DOI: https://doi.org/10.4213/tmf1898

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English version:
Theoretical and Mathematical Physics, 2005, 145:2, 1559–1575

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Revised: 27.04.2005

Citation: A. I. Alekseev, “Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large $Q^2$”, TMF, 145:2 (2005), 221–239; Theoret. and Math. Phys., 145:2 (2005), 1559–1575

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf1898
• https://doi.org/10.4213/tmf1898
• http://mi.mathnet.ru/eng/tmf/v145/i2/p221

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Alekseev AI, “Synthetic running coupling of QCD”, Few-Body Systems, 40:1–2 (2006), 57–70
2. Prosperi GM, Raciti M, Simolo C, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387–438
3. Cvetic G, Valenzuela C, “Various versions of analytic QCD and skeleton-motivated evaluation of observables”, Physical Review D, 74:11 (2006), 114030
4. D. V. Shirkov, I. L. Solovtsov, “Ten years of the analytic perturbation theory in QCD”, Theoret. and Math. Phys., 150:1 (2007), 132–152
5. Cvetic G, Valenzuela C, “Exponentially modified QCD coupling”, Physical Review D, 77:7 (2008), 074021
6. Deur A. Brodsky S.J. de Teramond G.F., “The QCD running coupling”, Prog. Part. Nucl. Phys., 90 (2016), 1–74
7. Ayala C., Cvetic G., Koegerler R., “Lattice-Motivated Holomorphic Nearly Perturbative QCD”, J. Phys. G-Nucl. Part. Phys., 44:7 (2017), 075001
8. Ayala C., Cvetic G., Koegerler R., Kondrashuk I., “Nearly Perturbative Lattice-Motivated QCD Coupling With Zero Ir Limit”, J. Phys. G-Nucl. Part. Phys., 45:3 (2018), 035001
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