# Perturbative QCD in acceptable schemes with holomorphic coupling

Contreras C, Cvetic G, Kögerler R, Kroeger P, Orellana O (2015)

International Journal of Modern Physics A 30(15).

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Perturbative QCD in mass independent schemes leads in general to running coupling a(Q(2)) which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta \Q(2)\ less than or similar to 1 GeV2. Such (Landau) singularities are inconvenient in the following sense: evaluations of spacelike physical quantities D(Q(2)) with such a running coupling a(kappa Q(2)) (kappa similar to 1) give us expressions with the same kind of singularities, while the general principles of local quantum field theory require that the mentioned physical quantities have no such singularities. In a previous work, certain classes of perturbative mass independent beta functions were found such that the resulting coupling was holomorphic. However, the resulting perturbation series showed explosive increase of coefficients already at (NLO)-L-4 order, as a consequence of the requirement that the theory reproduce the correct value of the tau lepton semihadronic strangeless decay ratio r(tau). In this paper, we successfully extend the construction to specific classes of perturbative beta functions such that the perturbation series do not show explosive increase of coefficients, the perturbative coupling is holomorphic, and the correct value of r(tau) is reproduced. In addition, we extract, with Borel sum rule analysis of the V + A channel of the semihadronic strangeless decays of tau lepton, reasonable values of the corresponding D = 4 and D = 6 condensates.

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Contreras C, Cvetic G, Kögerler R, Kroeger P, Orellana O. Perturbative QCD in acceptable schemes with holomorphic coupling.

*International Journal of Modern Physics A*. 2015;30(15).Contreras, C., Cvetic, G., Kögerler, R., Kroeger, P., & Orellana, O. (2015). Perturbative QCD in acceptable schemes with holomorphic coupling.

*International Journal of Modern Physics A*,*30*(15).Contreras, C., Cvetic, G., Kögerler, R., Kroeger, P., and Orellana, O. (2015). Perturbative QCD in acceptable schemes with holomorphic coupling.

*International Journal of Modern Physics A*30.Contreras, C., et al., 2015. Perturbative QCD in acceptable schemes with holomorphic coupling.

*International Journal of Modern Physics A*, 30(15).C. Contreras, et al., “Perturbative QCD in acceptable schemes with holomorphic coupling”,

*International Journal of Modern Physics A*, vol. 30, 2015.Contreras, C., Cvetic, G., Kögerler, R., Kroeger, P., Orellana, O.: Perturbative QCD in acceptable schemes with holomorphic coupling. International Journal of Modern Physics A. 30, (2015).

Contreras, Carlos, Cvetic, Gorazd, Kögerler, Reinhart, Kroeger, Pawel, and Orellana, Oscar. “Perturbative QCD in acceptable schemes with holomorphic coupling”.

*International Journal of Modern Physics A*30.15 (2015).
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arXiv 1405.5815

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