# Lattice-motivated holomorphic nearly perturbative QCD

Ayala C, Cvetic G, Kögerler R (2017) *Journal of Physics. G, Nuclear and Particle Physics* 44(7): 075001.

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Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite non-zero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.

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Ayala C, Cvetic G, Kögerler R. Lattice-motivated holomorphic nearly perturbative QCD.

*Journal of Physics. G, Nuclear and Particle Physics*. 2017;44(7): 075001.Ayala, C., Cvetic, G., & Kögerler, R. (2017). Lattice-motivated holomorphic nearly perturbative QCD.

*Journal of Physics. G, Nuclear and Particle Physics*,*44*(7), 075001. doi:10.1088/1361-6471/aa6fdfAyala, C., Cvetic, G., and Kögerler, R. (2017). Lattice-motivated holomorphic nearly perturbative QCD.

*Journal of Physics. G, Nuclear and Particle Physics*44:075001.Ayala, C., Cvetic, G., & Kögerler, R., 2017. Lattice-motivated holomorphic nearly perturbative QCD.

*Journal of Physics. G, Nuclear and Particle Physics*, 44(7): 075001. C. Ayala, G. Cvetic, and R. Kögerler, “Lattice-motivated holomorphic nearly perturbative QCD”,

*Journal of Physics. G, Nuclear and Particle Physics*, vol. 44, 2017, : 075001. Ayala, C., Cvetic, G., Kögerler, R.: Lattice-motivated holomorphic nearly perturbative QCD. Journal of Physics. G, Nuclear and Particle Physics. 44, : 075001 (2017).

Ayala, Cesar, Cvetic, Gorazd, and Kögerler, Reinhart. “Lattice-motivated holomorphic nearly perturbative QCD”.

*Journal of Physics. G, Nuclear and Particle Physics*44.7 (2017): 075001.
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arXiv 1608.08240

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