Universal geometrical scaling for hadronic interactions

TL;DR

This paper demonstrates a universal geometrical scaling in hadronic interactions, showing that transverse momentum distributions depend only on a scaled variable involving saturation momentum, across different collision types and energies.

Contribution

It introduces a universal scaling variable based on saturation momentum that collapses diverse hadronic collision data onto a single curve.

Findings

$p_T$ distributions depend only on $ au=p_T^2/Q_s^2$ for $p_T<Q_s$

Small differences in $ au$-lines for different projectiles and centralities

Hard multiplicity fraction varies from 9% in pp to 2% in Pb-Pb collisions

Abstract

It is shown that defining a suitable saturation momentum $Q_s$, the $p_T$ distributions of pp and AA collisions for any centrality and energy depend only on $\tau=p^2_T/Q_s^2$ for $p_T<Q_s$. For different projectiles, targets and centralities, the corresponding $\tau$-lines present small differences for $\tau<1$. For $\tau>1$, the higher the energy or the larger the size of the participant nuclei, the larger suppression present the respective spectra. The integrated spectrum gives a fraction of the hard multiplicity in the range from 9% for pp at 0.9 TeV to 2% for Pb-Pb central collisions at 2.76 TeV.