Search for critical points by measuring spatial correlation lengths via multiplicity density fluctuations
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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.
12 pages, 4 figures, The 3rd edition of the International Workshop The Critical Point and Onset of Deconfinement
12 pages, 4 figures, The 3rd edition of the International Workshop The Critical Point and Onset of Deconfinement