Search for fractality and phase transition in p–p collisions at LHC energy

Abstract

In this paper, a detailed study of the multiplicities of charged particles produced in [Formula: see text]–[Formula: see text] collisions, at [Formula: see text][Formula: see text]TeV, has been carried out. Analysis of UrQMD generated events along pseudo–rapidity ([Formula: see text]), azimuthal angle ([Formula: see text]) and [Formula: see text]-[Formula: see text] phase spaces is made with the help of scaled factorial moment method. The results have also been compared with the UrQMD events with finite impact parameter ([Formula: see text]) and minimum bias (MB) conditions. From the intermittency exponent ([Formula: see text]), the anomalous fractal dimension [Formula: see text] is derived and the variations of [Formula: see text] with order [Formula: see text] are investigated. The observed intermittent fluctuations are manifested by various parameters such as anomalous fractal dimension [Formula: see text], degree of multifractality ([Formula: see text]), critical exponent ([Formula: see text]), Levy index ([Formula: see text]) and multifractal specific heat. In the framework of Ginzburg–Landau theory, the second-order phase transition in the light of scaled factorial moment method has also been carried out to search for the quark-hadron phase transition. It is observed that the intermittent type of fluctuations are strong enough in [Formula: see text]-[Formula: see text] space compared to the one-dimensional [Formula: see text] space and [Formula: see text] space. The data reflects the signature of multifractality in [Formula: see text] space and [Formula: see text]-[Formula: see text] space. Whereas in case of [Formula: see text] space, it shows the evidence of monofractality. It is also interesting to note that the values of critical exponents for all impact parameters indicate the apparent existence of quark hadron phase transition except for MB events. However, no such behaviour is observed in [Formula: see text] space. From the knowledge of generalized fractal dimension [Formula: see text], multifractal specific heat is derived from scale factorial moment analysis in case of one-dimensional [Formula: see text] space, [Formula: see text] space and two-dimensional [Formula: see text]-[Formula: see text] space.