Fluctuation of gaps in hadronization at the phase transition

Abstract

Event-by-event fluctuations of hadronic patterns in heavy-ion collisions are studied in search of signatures of quark-hadron phase transition. Attention is focused on a narrow strip in the azimuthal angle with small $\ensuremath{\Delta}y.$ The fluctuations in the gaps between particles are quantified by simple measures. A scaling exponent $\ensuremath{\alpha}$ is shown to exist around ${T}_{c}.$ An index $\ensuremath{\xi}$ is shown to characterize the critical fluctuation; it is a numerical constant $\ensuremath{\xi}=0.05\ifmmode\pm\else\textpm\fi{}0.01.$ All the measures considered in this gap analysis are experimentally observable. Whether or not the theoretical predictions, based on simulations using a two-dimensional Ising model, are realistic for heavy-ion collisions, analysis of the experimental data suggested here should be carried out, since the existence of a scaling behavior is of interest in its own right.