Nambu–Jona-Lasinio model with a fractal inspired coupling Megías Fernández, Eugenio Teixeira, M. J. Timóteo, V. S. Deppman, A. The work of E M is supported by the project PID2020-114767GB-I00 and by the Ramón y Cajal program under Grant RYC-2016-20678 funded by MCIN/AEI/10.13039/501100011033 and by “FSE Investing in your future”, by the FEDER/Junta de Andalucía-Consejería de Economía y Conocimiento 2014-2020 Operational Program under Grant A-FQM-178-UGR18, by Junta de Andalucía under Grant FQM-225, by the Consejería de Conocimiento, Investigación y Universidad of the Junta de Andalucía and European Regional Development Fund (ERDF) under Grant SOMM17/6105/UGR, and by the “Prórrogas de Contratos Ramón y Cajal” Program of the University of Granada. M J T is supported by São Paulo Research Foundation (FAPESP) grant 2021/12954-5. V S T is supported by FAPESP grant 2019/010889-1 and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grant 305004/2022-0. A D is partially supported by the CNPq, grant 304244/2018-0, by Project INCT-FNA Proc. No. 464 898/2014-5, and by FAPESP grant 2016/17612-7. The Nambu–Jona-Lasino model is modified by the inclusion of a running-coupling that was obtained by a fractal approach to Quantum Chromodynamics. The coupling follows a q-exponential function and, in the context of high energy collisions, explains the origin of the Tsallis non-extensive statistics distributions. The parameter q is completely determined in terms of the number of colours and the number of quark flavours. We study several aspects of the extended model and compare our results to the standard NJL model, where a constant coupling is used in combination with a sharp cutoff to regularize the gap equation. We show that the modified coupling regularizes the model in a smooth cutoff fashion and reproduces the pion mass and decay constant, providing an almost identical Gell Mann-Oakes-Renner relation as in the standard NJL model. In both models the relation is satisfied in similar cutoff scales. An important novelty of this work is the physical explanation, in terms of the fractal QCD vacuum, for a running coupling that renormalizes the quark condensate. 2025-02-17T08:48:30Z 2025-02-17T08:48:30Z 2024-12-17 journal article Published version: Megías Fernández, Eugenio et al. Nambu–Jona-Lasinio model with a fractal inspired coupling. Physics Letters B Volume 860, January 2025, 139192. https://doi.org/10.1016/j.physletb.2024.139192 https://hdl.handle.net/10481/102391 10.1016/j.physletb.2024.139192 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Elsevier