Lévy walk of pions in heavy-ion collisions

Abstract

The process of Lévy walk, i.e., movement patterns described by heavy-tailed random walks, plays a role in various phenomena, from chemical and microbiological systems through marine predators to climate change. Recent experiments have suggested that this phenomenon also appears in heavy-ion collisions. However, the theoretical interpretation supporting such findings is still debated. In high-energy collisions of heavy nuclei, the strongly interacting Quark Gluon Plasma is created, which, similarly to the early Universe, undergoes a rapid expansion and transition back to hadronic matter. In the subsequent expanding hadron gas, particles interact until kinetic freeze-out, when their momenta stop changing, and they freely transition toward the detectors. Measuring spatial freeze-out distributions is a crucial tool in understanding the dynamics of the created matter and the interactions among its constituents. In this paper, we introduce a three-dimensional analysis of the spatial freeze-out distribution of pions (the most abundant particles in such collisions). Utilising Monte-Carlo simulations of high-energy collisions, we show that the chain of processes ending in a final state pion has a step length distribution leading to Lévy-stable distributions. Subsequently, we show that simulated pion freeze-out distributions indeed exhibit heavy tails and can be described by a three-dimensional elliptically contoured symmetric Lévy-stable distribution.

23 pages, 7 figures

References in corpus (20)

• Power-law distributions in empirical data
• Glauber Modeling in High Energy Nuclear Collisions
• The QCD equation of state with dynamical quarks
• Core-Corona Separation in Ultra-Relativistic Heavy Ion Collisions
• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Observation of the critical end point in the phase diagram for hot and dense nuclear matter
• Correlations and Characterization of Emitting Sources
• Two-pion femtoscopic correlations in Be+Be collisions at $\sqrt{s_{\text{NN}}}=16.84$ GeV measured by the NA61/SHINE at CERN
• Femtoscopy with Lévy sources from SPS through RHIC to LHC
• Pion interferometry with Lévy-stable sources in $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at STAR
• Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Centrality dependence of Lévy-stable two-pion Bose-Einstein correlations in $\sqrt{s_{{}_{NN}}}=200$ GeV Au$+$Au collisions
• Kaon femtoscopy with Lévy-stable sources from $\sqrt{s_{{}_{\mathrm{NN}}}}=200$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC
• Charged Kaon Femtoscopy with Lévy Sources in $\sqrt{s_{\text{NN}}}$ = 200 GeV Au+Au Collisions at PHENIX
• Universal superdiffusive modes in charged two dimensional liquids
• Femtoscopy analysis in small systems at NA61/SHINE
• Centrality-dependent Lévy HBT analysis in $\sqrt{s_{{}_{\text{NN}}}}=5.02$ TeV PbPb collisions at CMS
• Femtoscopy at NA61/SHINE using symmetric Lévy sources in central ${}^{40}$Ar+${}^{45}$Sc from 40$A$ GeV/$c$ to 150$A$ GeV/$c$
• Theoretical description of proton-deuteron interactions using exact two-body dynamic of femtoscopic correlation method
• Proton-proton and proton-cluster femtoscopy at the HADES experiment

Cited by in corpus (6)

• Imaging Freeze-out Sources and Extracting Strong Interaction Parameters in Relativistic Heavy-Ion Collisions
• Three-dimensional sizes and shapes of pion emission in heavy-ion collisions
• Probing the Three-dimension Emission Source and Neutron Skin via $\pi$-$\pi$ Correlations in Heavy-Ion Collisions
• A self-consistent calculation of non-spherical Bose-Einstein correlation functions with Coulomb final-state interaction
• Geometry of particle emission in UrQMD Ar+Sc collisions at SPS energies
• Rapidity spectra in high-energy collisions and longitudinal nuclear suppression from nonadditive statistics