Fractal Structures of Yang–Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics

The research of A.D. and D.P.M. were funded by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq-Brazil) and by Project INCT-FNA Proc. No. 464898/2014-5, and by FAPESP under grant 2016/17612-7 (A.D.). The work of E.M. is funded by the Spanish MINEICO under Grant FIS2017-85053-C2-1-P, by the FEDER Andalucia 2014-2020 Operational Programme under Grant A-FQM-178-UGR18, by Junta de Andalucia under Grant FQM-225, by the Consejeria de Conocimiento, Investigacion y Universidad of the Junta de Andalucia and European Regional Development Fund (ERDF) under Grant SOMM17/6105/UGR, and by the Spanish Consolider Ingenio 2010 Programme CPAN under Grant CSD2007-00042. The research of E.M. is also supported by the Ramon y Cajal Program of the Spanish MINEICO under Grant RYC-2016-20678.
We would like to thank Constantino Tsallis for suggesting us to write this review
In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics, and neutron stars. We review some recent investigations on the power-law distributions arising in high energy physics experiments focusing on a thermodynamic description of the system formed, which could explain the power-law behavior. The possible connections with a fractal structure of hadrons is also discussed. The main objective of the present work is to delineate the state-of-the-art of those studies and show some open issues that deserve more careful investigation. We propose several possibilities to test the theory through analyses of experimental data.
Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ)
Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) 2016/17612-7
Spanish MINEICO FIS2017-85053-C2-1-P
FEDER Andalucia 2014-2020 Operational Programme A-FQM-178-UGR18
Junta de Andalucia FQM-225
Junta de Andalucia
European Commission SOMM17/6105/UGR
Spanish Government CSD2007-00042
German Research Foundation (DFG) RYC-2016-20678
Project INCT-FNA 464898/2014-5