| One of the most important tasks of Physics is to study the inner structure of matters. From the assumption of atom in ancient to discovery of electron, proton and neutron, until the level of quark-gluon, it can be seen that each basic cell of a certain time will be replaced by the next deeper inner structure, and in future we will have a deeper and deeper acquaintance with the basic particles. Quantum Chromodynamics (QCD) successfully describes the strong interactions between quark-gluon, and it has two distinct characters:asymptotic freedom and color confinement. Due to "color confinement", we could not find free quarks or gluons. And in experiments, the quark and gluon would freeze out into hadrons in such a short time that one can only detect the final state hadrons, instead of them. One important way to study the inner structure of matters is through collisions of high energy particles. Last century people had carried out the high energy collisions experiments widely, ranged from the electron-positron collisions, proton-proton collisions, hardon-hardon collisions, to the recently heavy ion collisions. The particles in collisions are becoming more and more complex, as well as the higher and higher energy. On the other hand, using the model to simulate the collision process is also anther important research method in high energy physics. The modeling method is cost much less, compared with the expensive experimental device in CERN or BNL. Besides, this method always attempts to found a completed mechanism for high energy collisions, which is a beneficial exploring on the research. Therefore, the modeling simulation is a beneficial and significant complement for the high energy collision experiment. This thesis would adopt the AMPT model, based on the Monte Carlo method, to simulate the heavy ion collisions. Using the modeling results, the scaling properties in collisions can be explored. This thesis firstly briefly introduces the significant concepts and theory in the research of intermittency and fractal in high energy collisions, the AMPT model which would be used in simulation of heavy ion collisions, and some physical variables used in this thesis. Finally, the relevant research work would be reported in details.The complexity of high energy collisions forced people to resort to the help of nonlinear theory, such as fractal theory. The study of fractal of final state system needs to observe the behavior of probability moment, however the limit particle production in early high energy collision experiments led to the occurrence of statistical fluctuation, which would interfere the observation of probability moment in final state phase-space. Therefore, people introduced the factorial moment to suppress the statistical noises, and then the true dynamical fluctuation is revealed.The previous experimental results showed that the final multiparticle phase-space of electron-positron collisions is self-similar fractal, and the hadron-hadron collisions corresponds to the self-affine fractal. So, which kind of fractal does the final state phase-space of heavy ion collision correspond to? Is there any different fractal properties in heavy ion collisions compared with the previous collision experiments? We will use the Monte Carlo model to simulate the collision process, generate collision events, and then analyze the data with method of NFM(Normalization Factorial Moment).First we using the AMPT model to generate5000Au-Au collision events at200Gev. Then we seltect the phase-space variables as rapidity, transverse momentum and azimuthal angle. Then the1-d,2-d and3-d NFM can be obtained, with isotropic partitioning of final state phase-space. Fitting the one-dimensional NFM with saturation equation, we can obtain the saturation exponents along with the three direction (y, p,,<p) in phase space, and calculate the Hurst exponents. The result shows that Hurst exponents are identical, and equals to one, which means the final state phase-space is isotropic. So with isotropic partitioning of phase space, and calculate two dimensional NFM. The results of2-d NFM’s fitting show that the double-log distribution of2-d NFM with partition number M has a good scaling feature, which preliminarily indicates that the final state system of heavy ion collisions is self-similar fractal. Besides, it is found that the scaling feature of2-d NFM along a certain phase-space plane is better than those in the other plane, which may be the effect of non-integer partitioning. The fitting of3-d NFM also indicates good scaling feature, and the intermittency exponents of each order obtained in fitting can be used to calculate the effective fluctuation strength aeff, which would be constant with different order q and can be used to reflect the strength of fluctuation or intermittency in high energy collisions. After comparison, it is found that effective fluctuation strength in heavy ion collisions is smaller than that in hadron-hadron and electron-positron collisions. Further more, the NFM’s scaling is discussed with the formula Fq∝Fβ2. According this formula, we draw the double-log figure of3-d NFM, which also shows good scaling feature and checks the conclusion of self-similar fractal in heavy ion collisions. If a certain region in phase space can be described by Ginzburg-Landua type of phase transition, then the NFM has a relation with q as the formula βq∝(q-1)v, and v=1.304. Here we introduce the parameter v, which can characterize all the intermittency exponents in specific cases. So according to the intermittency exponents obtained in analysis of2-d and3-d NFM, parameter v in different dimensions are calculated, and are found to be identical within error ranges, which reveal that v is a parameter independent with dimension and phase-space direction. However, they are all larger than1.304which is typical value of Ginzburg-Landau phase transition, which is not in accordance with former conclusion that effective fluctuation strength in heavy ion collisions is larger than that in hadronic and leptonic collisions. Maybe it is because the AMPT does not include phase transition.It is known that hadronization of partons may occur at different times in the evolution of the system and may populate different pt intervals, depending on the time of hadronization. So we split the transverse momentum into small intervals, which could avoid the overlapping of multiplicities of hadron production in a given event, and yield different v values. It is expected that the value of v in high pt would be larger than the low pt, due to the existence of jets effects in high pt. According to the double-log distribution of2-d NFM on (y,φ) plane in each pt interval, we can qualitatively see the increasing intermittency or fluctuation with increasing transverse momentum. However, due to the limited events, there occur large vibration and error ranges in distribution of high pt intervals, which make it impossible to determine the v value quantitatively. Therefore we adopt the a special NFM, whose partition number M equals to one, to observe the fluctuation property of system. The results shows the special NFM increases rapidly with the increasing of transverse momentum, as is expected before. |
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