Large Self-affine fractality in $\p^+$p and K$^+$p collisions at 250 GeV/$c$

TL;DR

This study analyzes multiparticle production in high-energy collisions, revealing that fractality is self-affine rather than self-similar, with better power-law scaling observed in three-dimensional phase space.

Contribution

It demonstrates that multiparticle production exhibits self-affine fractality, contrasting with previous assumptions of self-similarity, and highlights the importance of phase space anisotropy.

Findings

Hurst exponents indicate no anisotropy in transverse plane

Significant anisotropy exists longitudinally, with Hurst exponents about half the value

Self-affine analysis provides better power-law scaling in 3D phase space

Abstract

Taking into account the anisotropy of phase space in multiparticle production, a self-affine analysis of factorial moments was carried out on the NA22 data for $\p^+\Pp$ and $\PK^+\Pp$ collisions at 250 GeV/$c$. Within the transverse plane, the Hurst exponents measuring the anisotropy are consistent with unit value (i.e. no anisotropy). They are, however, only half that value when the longitudinal direction is compared to the transverse ones. Fractality, indeed, turns out to be self-affine rather than self-similar in multiparticle production. In three-dimensional phase space, power-law scaling is observed to be better realized in self-affine than in self-similar analysis.