Gauge fields renormalization groups and thermofractals

TL;DR

This paper explores a fractal-based approach to quantum chromodynamics (QCD), addressing low-energy calculation challenges by linking fractal structures with renormalization group concepts, and providing analytic expressions consistent with experimental data.

Contribution

It introduces a fractal framework for QCD that connects renormalization group equations and self-energy corrections, offering new insights into the theory's structure and low-energy behavior.

Findings

Analytic expression for the running coupling consistent with experiments

Fractal structures linked to renormalization group and self-energy corrections

Conceptual clarification of fractal origins in quantum field theory

Abstract

The perturbative approach to QCD has been shown to be limited, and the difficulties to obtain accurate calculations in the low-energy region seems to be insurmountable. A recent approach uses the fractal structures of Yang-Mills Field Theory to circumvent those difficulties, allowing for the determination of an analytic expression for the running coupling. The results obtained are in agreement with several experimental findings, and explain many of the observed phenomena at high-energy collisions. In this work, we address some of the conceptual aspects of the fractal approach, which are expressed in terms of the renormalization group equation and the self-energy corrections to the parton mass. We associate these well-known concepts with the origins of the fractal structure in the quantum field theory.