Nambu--Jona-Lasinio model with a fractal inspired coupling

TL;DR

This paper introduces a fractal-inspired running coupling in the NJL model, explaining non-extensive statistics in high energy collisions and providing a smooth regularization that reproduces key mesonic properties.

Contribution

The work extends the NJL model by incorporating a fractal-based running coupling, linking fractal QCD vacuum properties to quark condensate renormalization.

Findings

The fractal coupling regularizes the model smoothly.

Reproduces pion mass and decay constant accurately.

Maintains the Gell-Mann-Oakes-Renner relation similar to standard NJL.

Abstract

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.