System size dependence of the log-periodic oscillations of transverse momentum spectra

TL;DR

This paper explores how log-periodic oscillations in transverse momentum spectra depend on system size in heavy-ion collisions, proposing a complex power index modification of the Tsallis distribution to describe experimental data.

Contribution

It introduces a novel approach using complex power indices in the Tsallis distribution to model log-periodic oscillations in $p_T$ spectra across different collision centralities.

Findings

The complex power index model fits $Pb+Pb$ data well.

Comparison with a two-component Tsallis model highlights differences at higher $p_T$.

System size influences the log-periodic oscillation patterns in the spectra.

Abstract

Recently the inclusive transverse momentum distributions of primary charged particles were measured for different centralities in $Pb+Pb$ collisions. A strong suppression of the nuclear modification factor in central collisions around $p_T \sim 6-7$ GeV/c was seen. As a possible explanation, the hydrodynamic description of the collision process was tentatively proposed. However, such effect, (albeit much weaker) also exists in the ratio of data/fits, both in nuclear $Pb+Pb$ collisions, and in the elementary $p+p$ data in the same range of transverse momenta for which such an explanation is doubtful. As shown recently, in this case, assuming that this effect is genuine, it can be attributed to a specific modification of a quasi-power like formula usually used to describe such $p_T$ data, namely the Tsallis distribution. Following examples from other branches of physics, one simply has to allow for the power index becoming a complex number. This results in specific log-periodic oscillations dressing the usual power-like distribution, which can fit the $p+p$ data. In this presentation we demonstrate that this method can also describe $Pb+Pb$ data for different centralities. We compare it also with a two component statistical model with two Tsallis distributions recently proposed showing that data at still larger $p_T$ will be sufficient to discriminate between these two approaches.