@misc{10481/61258,
year = {2020},
month = {2},
url = {http://hdl.handle.net/10481/61258},
abstract = {In this work, we analyze how scaling properties of Yang-Mills field theory manifest as self-similarity of
truncated n-point functions by scale evolution. The presence of such structures, which actually behave as
fractals, allows for recurrent nonperturbative calculation of any vertex. Some general properties are indeed
independent of the perturbative order, what simplifies the nonperturbative calculations. We show that for
sufficiently high perturbative orders a statistical approach can be used, the nonextensive statistics is
obtained, and the Tsallis index, q, is deduced in terms of the field theory parameters. The results are applied
to QCD in the one-loop approximation, where q can be calculated, resulting in a good agreement with the
value obtained experimentally. We discuss how this approach allows us to understand some intriguing
experimental findings in high energy collisions, as the behavior of multiplicity against collision energy,
long-tail distributions, and the fractal dimension observed in intermittency analysis},
organization = {A. D. and D. P. M. are partially
supported by the Conselho Nacional de Desenvolvimento
Cientfico e Tecnolgico (CNPq-Brazil) and by Project INCTFNA
Proc. No. 464898/2014-5. A. D. is partially supported
by FAPESP under Grant No. 2016/17612-7. The work of
E. M. is supported by the Spanish MINEICO and European
FEDER funds under Grants No. FIS2014-59386-P and
No. FIS2017-85053-C2-1-P, by the Junta de Andalucía
under Grant No. FQM-225, and by the Consejería de
Conocimiento, Investigación y Universidad of the Junta
de Andalucía and European Regional Development Fund
Grant No. SOMM17/6105/UGR. The research of E. M. is
also supported by the Ramón y Cajal Program of the Spanish
MINEICO under Grant No. RYC-2016-20678.},
publisher = {American Physical Society},
title = {Fractals, nonextensive statistics, and QCD},
doi = {10.1103/PhysRevD.101.034019},
author = {Deppman, Airton and Megías Fernández, Eugenio and Menezes, Debora P.},
}