Nuclear modification factor within a dynamical approach to the complex entropic index

This work introduces a novel approach to the nuclear deformation factor $R_{\text{AA}}$, grounded in the dynamical effects of the Quark-Gluon Plasma on parton momentum. The approach uses the Blast-Wave method combined with Tsallis Statistics, within the Cooper-Frye freeze-out framework and, by profiting from appropriate simplifications, it gives analytical expressions that describe the observed $R_{\text{AA}}$ for two sets of independent measurements at $\sqrt{s}=2.76$ TeV and $\sqrt{s}=5.02$ TeV. A nonlinear dynamical equation describes the dynamics and leads to log-periodic oscillations. With the analytical solutions for that equation, it is possible to link the dynamical approach with the complex-$q$ formalism, which was proposed to describe the log-oscillations observed in experimental data.