Self-Similarity, Fractality and Entropy Principle in Collisions of Hadrons and Nuclei at Tevatron, RHIC and LHC

TL;DR

This paper discusses a $z$-scaling approach based on self-similarity and fractality in hadron and nuclear collisions at high energies, revealing universal behaviors and new conservation laws.

Contribution

It introduces a $z$-scaling framework incorporating fractal dimensions and entropy principles, providing new insights into particle production and energy loss in high-energy collisions.

Findings

Scaling function $b(z)$ is energy, angular, multiplicity, and flavor independent.

Energy loss can be estimated from $z$-scaling and entropy principles.

A new conservation law involving fractal dimensions is proposed.

Abstract

$z$-Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated. The scaling for negative particle production in $Au+Au$ collisions from BES-I program at RHIC is demonstrated. The scaling variable $z$ depends on the momentum fractions of the colliding objects carried by the interacting constituents, and on the momentum fractions of the fragmenting objects in the scattered and recoil directions carried by the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final state are expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function $\psi(z)$ reveals energy, angular, multiplicity, and flavor independence. It has a power behavior at high $z$ (high $p_T$). Based on the entropy principle and $z$-scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated. New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed.