Quantum chromodynamics Lagrangian density and SU(3) gauge symmetry: A fractional approach

Quantum ChromoDrynamics (QCD) is a quantum field theory, which describes the strong interaction. It explains how quarks and gluons combine to form hadrons. QCD is part of the standard model of particle physics, along with ElectroWeak (EW) theory. The aim of this study is to explore fractional orders in the QCD Lagrangian density using the Atangana–Baleanu fractional derivative. Starting from the fractional Euler–Lagrange equation, we were able to derive the equation of motion of the quark and gluon fields. Then, based on fractional QCD Lagrangian density, the fractional Hamilton equations were obtained. We demonstrate that the principle of local gauge invariance, a fundamental symmetry in QCD, is preserved under a fractional extension of the theory. Our findings indicate that the fractional equations of QCD encompass the classical equations as a specific case, offering a broader perspective on quark-gluon dynamics. The fractional QCD Lagrangian density provides new insights that are not accessible through classical derivatives, potentially enhancing our understanding of quark-gluon plasmas and contributing to advancements in collider phenomenology and precision measurements. This study opens new avenues for exploring the fundamental nature of the strong interaction and its implications for particle physics beyond the Standard Model.