Search for critical points by measuring spatial correlation lengths via multiplicity density fluctuations

Abstract

The nature of phase boundaries in the QCD phase diagram has not been satisfactorily explored by experiments. Based on the Ginzburg-Landau free energy with a spatially inhomogeneous term as a function of a scalar order parameter, it is possible to determine spatial correlation lengths from measured two point correlation functions in general, where a spatially dependent multiplicity fluctuation from the mean value is taken as the order parameter. The divergence of the correlation lengths can be a robust signature of a critical system as well as the disappearance of $<q\bar{q}>$ condensations. Simultaneous observations of such observables can probe the nature of the phase boundary conclusively. In this letter, a present result from the PHENIX experiment will be reported. We will focus whether a critical behavior of the phase transition exists or not by searching for increases of pseudo-rapidity correlation lengths as a function of the number of participant nucleons with dominantly low $p_t$ charged particles where instant fluctuations such as high $p_t$ jets are expected to be negligible. The result shows a non monotonic increase in the correlation lengths which can be a symptom of the critical behavior.