Local multiplicity fluctuations as a signature of critical hadronization in heavy-ion collisions at TeV energies

In central Pb-Pb collisions at LHC the multiplicity of particles produced is so high that it should become feasible to examine the nature of transition from the deconfined quark-gluon state to the confined hadron state by methods that rely on the availability of high multiplicity events. We consider four classes of the transition process ranging from critical behavior to totally random behavior, depending on whether or not there is clustering of quarks and on whether or not there is contraction of dense clusters due to confinement. Fluctuations of bin multiplicities in each event are quantified, and then the event-by-event fluctuations of spatial patterns are analyzed. A sequence of measures are proposed and are shown to be effective in capturing the essence of the differences among the classes of simulated events. It is demonstrated that a specific index has a low value for critical transition but a larger value if the hadronization process is random.