Fluctuation of Gaps in Hadronization at Phase Transition

Abstract

Event-by-event fluctuations of hadronic patterns in heavy-ion collisions are studied in search for signatures of quark-hadron phase transition. Attention is focused on a narrow strip in the azimuthal angle with small $\Delta y$. The fluctuations in the gaps between particles are quantified by simple measures. A scaling exponent $\alpha$ is shown to exist around $T_c$. An index $\xi$ is shown to characterize the critical fluctuation; it is a numerical constant $\xi=0.05\pm0.01$. All the measures considered in this gap analysis are experimentally observable. Whether or not the theoretical predictions, based on simulations using 2-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.