Critical Behavior of Hadronic Fluctuations and the Effect of Final-State Randomization

TL;DR

This paper investigates the critical behavior of hadronic fluctuations near the quark-hadron phase transition using an adapted Ising model, identifying measurable signatures for detecting this transition in heavy-ion collision experiments.

Contribution

It introduces new fluctuation measures, including wavelet analysis, that exhibit power-law behavior near the critical point and assesses their robustness against final-state randomization effects.

Findings

Two measures show power-law behavior near critical temperature

Final-state randomization has weak effect on fluctuation measures

Proposes measurable signatures for quark-hadron phase transition detection

Abstract

The critical behaviors of quark-hadron phase transition are explored by use of the Ising model adapted for hadron production. Various measures involving the fluctuations of the produced hadrons in bins of various sizes are examined with the aim of quantifying the clustering properties that are universal features of all critical phenomena. Some of the measures involve wavelet analysis. Two of the measures are found to exhibit the canonical power-law behavior near the critical temperature. The effect of final-state randomization is studied by requiring the produced particles to take random walks in the transverse plane. It is demonstrated that for the measures considered the dependence on the randomization process is weak. Since temperature is not a directly measurable variable, the average hadronic density of a portion of each event is used as the control variable that is measurable. The event-to-event fluctuations are taken into account in the study of the dependence of the chosen measures on that control variable. Phenomenologically verifiable critical behaviors are found and are proposed for use as a signature of quark-hadron phase transition in relativistic heavy-ion collisions.