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

Abstract

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.

Study of Anomalous Fractal Dimensions and Scaling Exponent in Ginzburg--Landau Phase Transition in 14.5 $A$\,GeV/$c$ $^{28}$Si--AgBr Interactions

“…7are essentially independent of the nature of the GL parameters. Such a behaviour was experimentally observed in the study of photon number fluctuations of a single-mode laser at the threshold of lasing [52,55], confirming that it is a phase transition problem describable by GL theory [56]. On the theoretical side, it has also been found that using 2-dimensional Ising model to simulate quark-hadron phase transition and the resulting scaling behaviour of F q is in agreement with Eqs.…”

“…The scaling exponent can be used to investigate the presence of second-order phase transition in the hadronization process in high energy nuclear interactions. Hwa and Yang [52] have reviewed many papers on local behaviours of multiplicity fluctuations of the systems undergoing a second-order phase transition describable by the Ginzburg-Landau theory. These are then connected to the distribution of clusters produced that can be used to simulate initial configurations before start of hadronization.…”

“…An important feature of this method is that it does not only detect large non-statistical fluctuations but also filters out statistical ones. It is worth mentioning that if a multiplicity distribution is written as a convolution of Poisson and dynamical distributions and the underlying dynamics is trivial, then F q must be unity for all q values [52]. Any deviation from unity may be then a measure of non-trivial dynamical fluctuations, and F q (δ) ∝ δ −φq representing power-law behaviour would suggest a dynamics that is not characterized by a particular scale [1,2].…”

“…Details of calculations of the parameters of GL theory and critical exponent, ν, can also be found in Refs. [52,58].…”

Sensitivity of Multiplicity Fluctuations to Rapidity in High-Energy Nucleus-Nucleus Interactions

“…Thus, the study of fluctuations has become an important tool in envisaging the process of phase transition in relativistic nuclear interactions [16]. A great deal of work [17][18][19][20][21][22][23] has been carried out in this field over a wide range of energies. Earlier, it has been suggested [24] that the deconfinement should result in the non-monotonous trends in the behavior of multiplicity fluctuations, which could act as an indicator for the observance of the critical point [25].…”