# Study on Fractal Characteristics in the e$^+$e$^-$ Collisions at $\sqrt{s_{NN}}=250$GeV

## TL;DR

This study investigates the fractal properties of multi-particle final states in electron-positron collisions at 250 GeV using MC simulations, revealing self-affine fractality and a double-Hurst-exponent phenomenon.

## Contribution

First analysis of fractal characteristics in e+e- collisions at this energy, identifying self-affine fractality and double-Hurst-exponent behavior through simulations.

## Key findings

- Multi-particle final states are self-affine fractals.
- Existence of a double-Hurst-exponent phenomenon.
- Predicted fractal indices and fluctuation strength.

## Abstract

The fractal characteristics of multi-particle final state are first studied in the $e^+e^-$ collision of $\sqrt{s_{NN}}=250$GeV, with the MC simulation generator Jetset7.4 and Herwig5.9. The result is shown that this multi-particle final state is self-affine fractal, and exists a double-Hurst-exponent phenomenon. Their fractal indices and the effective fluctuation strength are also predicted.