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

TL;DR

This work proposes a dynamical framework that combines a Blast-Wave description of QGP expansion with the Plastino–Plastino Equation to model parton momentum evolution and compute the nuclear modification factor $R_{AA}$ in heavy-ion collisions. By treating the drag-dominated, nonextensive dynamics in the fluid rest frame and translating to the lab frame, the authors reproduce the observed log-periodic oscillations in $R_{AA}$ without requiring a true complex entropic index, while establishing a concrete link between dynamical effects and the complex-$q$ formalism. The approach yields analytic expressions for $R_{AA}$ across centralities at $ sqrt{s}=2.76$ and 5.02 TeV and identifies centrality-dependent trends in model parameters; diffusion is found negligible relative to drag, though several simplifications (e.g., ultra-relativistic flow, cylindrical freeze-out shell) limit quantitative accuracy and motivate future extensions to fully relativistic PPE. The results support a dynamical origin for the oscillations and offer a pathway to richer interpretations of nonextensive statistics in the QGP, with potential improvements via numerical, relativistic treatments of the PPE and drag.

Abstract

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.

Figures (7)

• Figure 1: ALICE experimental data (black circles) for the $R_{AA}$ of charged particle production in PbPb collisions at $\sqrt{S_{NN}}=2.76$ TeV abelev2013centrality, compared with theoretical results (full line). The plots are for centrality bins $0-5\%$,$5-10\%$, $10-20\%$, $20-30\%$, $30-40\%$, $40-50\%$, $50-60\%$ and $70-80\%$ respectively.
• Figure 2: CMS experimental data (black circles) for $R_{AA}$ of charged particle production in PbPb collisions at $\sqrt{S_{NN}}=5.02$ TeV khachatryan2017charged compared with theoretical results (full line). The plots are for centrality bins $0-5\%$,$5-10\%$, $10-30\%$, $30-50\%$, $50-70\%$ and $70-90\%$ respectively.
• Figure 3: Left panel: The drag coefficient as a function of the transverse momentum. Middle panel: The oscillation of the initial momentum $p_T^o$ of the parton as a function of the observed momentum $p_T$. Right panel: The $AA$ momentum distribution after dynamical effects, $f^{AA}$, as a function of the observed transverse momentum (solid line), compared to the $pp$ transverse momentum distribution for $pp$ collision, $f$.
• Figure 4: Fitted parameters as a function of centrality for $\sqrt{s_{NN}}=2.76$ TeV (blue) and $\sqrt{s_{NN}}=5.02$ TeV (red).
• Figure 5: Fittings of the transverse momentum spectra for $pp$ data for $2.76$ GeV (left) and $5.02$ GeV (right) collsion energies. $C$ is a fitting constant, $m_T$ the transverse mass and $f(p_T$) the momentum distribution function.