Study of Non-Statistical Fluctuations in Relativistic Nuclear Collisions Shafiq AHMAD  , M. AYAZ AHMAD, M. IRFAN and M. ZAFAR Department of Physics, Aligarh Muslim University, Aligarh-202002, India (Received December 8, 2005; accepted March 20, 2006; published June 12, 2006) An attempt is made to study the existence of non-statistical fluctuations of relativistic particles using the method of scaled factorial moments (SFMs) in the interactions of 28 Si and 12 C nuclei at 4.5 A GeV/c with nuclear emulsion. The experimental result has also been compared with FRITIOF generated data. The analysis of SFMs gives an evidence for an intermittency pattern of fluctuations. The increasing trend of anomalous fractal dimensions, d q , of the pseudo-rapidity distribution with the order of the moment, q observed in the present study supports a self-similar cascade mechanism. The results for experimental data are quite consistent with those obtained for FRITIOF data. Finally, it can be concluded that no universality in the values of the multifractal specific, c, is found for our data. KEYWORDS: Intermittency, fluctuations and relativistic nuclear collisions DOI: 10.1143/JPSJ.75.064604 1. Introduction The unusually large non-statistical particle density fluc- tuations in small phase space regions have attracted a lot of attention in relativistic nuclear collisions to understand the mechanism of particle production. Several theoretical and experimental groups have suggested different methods to identify the existence of non-statistical fluctuations. Bialas and Peschanski 1) were the first to introduce the most suitable method known as scaled factorial moments (SFMs) to study the non-statistical fluctuations in the distributions of rela- tivistic shower particles produced in high-energy collisions. The proposal of these factorial moments was made in analogy with the phenomenon known as intermittency in the hydrodynamics of turbulent fluid flow. In high-energy physics, the power law behaviour of the scaled factorial moment is known as intermittency. One of the possible characteristics of the scaled factorial moment analysis is that it can detect and characterize the dynamical fluctuation and it is also capable of filtering out the statistical noise. In this method, the scaled factorial moments, F q , are computed as a function of decreasing phase space size. The values of F q for purely statistical fluctuation saturate with decreasing phase space size, whereas in dynamical fluctuation, F q mo- ments are supposed to increase with decreasing phase-space size and exhibit a power law behaviour of normalized factorial moments, F q . However, ordinary multiplicity mo- ments (hn q i=hni q ) method is used to demonstrate different features of multiplicity distributions and is unable to reveal the existence of dynamical fluctuation due to significant contribution of the purely statistical fluctuations. The possibility of observing a new state of quark matter 2) has developed a lot of interest in the study of relativistic nucleus–nucleus collisions. The recent lattice QCD calcu- lations 3) predict a phase transitions of nuclear matter of confined hadrons into a quark–gluon plasma (QGP) at a sufficiently high temperature (200 – 220 MeV), high energy density of the order of 3 GeV/fm 3 and/or high baryon density (> 0:5/fm 3 ). It is widely believed that the strong interacting matter in these violent collisions undergo a transition, temporarily, to a deconfined quark–gluon plasma (QGP). Initially, there was a strong speculation that the origin of intermittent type of non-statistical fluctuation was thought to be the result of the phase transitions from QGP to normal hadronic matter in relativistic nucleus–nucleus collisions. But there is no experimental evidence for the formation of quark–gluon plasma in low energy nucleus– nucleus collisions. Further, no conclusive evidence for the formation of quark–gluon plasma has been found in nucleus–nucleus collisions at ultra-relativistic energies al- so. 4) Therefore the interpretation of intermittency can no longer be related with QGP formation. Only future experi- ments would clarify the situation. It has been suggested that the Bose–Einstein (BE) interference 5) and presence of random cascade mechanism or short-range correlations may be responsible for the origin of intermittency. There is a strong feeling that the BE interference can play a role in dynamical fluctuations. This correlation arises due to the symmetric wave functions of identical bosons in BE statistics. Increase in the value of the factorial moments, F q , with decreasing phase-space size could be explained on the basis of the above correlations between equal charged particles. The phenomenon of intermittency would be stronger for equal charged particles than for all charged particles. Analysis of some experimental results 6–8) shows that BE effect cannot be considered as the main source of intermittency, especially in e þ e  annihilation, 9) lepton– hadron 10) and hadron–hadron collisions. 11) No such data are available for nuclear collisions. However, EMU01 data ex- clude the possibility of BE correlations as a dominant source of intermittency in heavy ion collisions. 12) It has been observed that the intermittent behaviour is clearly explained due to short-range correlations 12,13) for lower order of moments. The intermittency has also been observed in a variety of collision processes and therefore it may be considered as a general property of multiparticle production. However, no single mechanism could explain the observed intermittency in various collision processes. So a detailed study is required to understand the intermittency more rigorously. An attempt has been made to investigate some interesting features of the scaled factorial moments observed in the interactions of 28 Si and 12 C nuclei with emulsion at 4.5 A GeV/c. The dependence of the intermittency index,  q , on  E-mail: sahmad2004amu@yahoo.co.in Journal of the Physical Society of Japan Vol. 75, No. 6, June, 2006, 064604 #2006 The Physical Society of Japan 064604-1