Study On The Scaling Properties Of Factorial Moments Of CEPC Energy Region In E~+e~- Collision

This article first briefly introduces the history and current status of particle physics,high-energy physics experiments,and e~+e~- collision experiments,introduces some important concepts and theories in the study of high energy collisions and fractals;secondly,a brief introduction to the event generator,simulation method and basic model of the e~+e~- collisions is made,including the simulation of the CEPC experimental device,the most commonly used Monte Carlo simulation method and two classic models-Jetset7.4 model and Herwig5.9 model;Then,systematically reports on the relevant research work we have conducted.The internal processes of high-energy collision experiments show their complex nonlinear characteristics.In this paper,based on the CEPC project,a Monte Carlo simulation generator is used to generate the data sample of the e~+e~- collision events at center-of-mass energy 250 GeV,and the fractal theory is used to study its nonlinear characteristics.In the study,we use factorial moments to eliminate statistical fluctuations,and use fractal theory to analyze and study the nonlinear dynamic characteristics of high-energy e~+e~-collisions.First,we calculate the one-dimensional normalized factorial moment(NFM)of the multi-particle final state and extract the saturation index of the system.It is found that the saturation indices in the three directions are not equal,indicating that the phase space of the multi-particle final state system is anisotropic and its fractal structure should be self-affine;however,the contraction rate in each direction satisfies a specific relationship,ie,the contraction rate is conserved,and there is a double Hurst index phenomenon,this shows that the anomalous scale characteristics of NFM can be observed both in isotropic and anisotropic segmentation of the final phase space.Second,three-dimensional factorial moment analysis is performed on the system.We separately perform isotropic segmentation and anisotropic segmentation on the phase space of the multi-particle final states to calculate the distribution of three-dimensional factorial moments.It is found that in both cases,the logarithmic distribution of the three-dimensional factorial moments has a good scaling characteristic,which confirms that in the CEPC energy region of high-energy e~+e~- collisions,the final particle phase space does self-affine fractal structure,and the corresponding dynamic fluctuations are anisotropic.At the same time,we conduct a comparative study of the nonlinear characteristics of particle(?~+)with its corresponding anti-particle(?~-)and find that under the multi-particle final states in the CEPC energy region of the e~+e~- collision,the particle(?~+)and anti-particle(?~-)have exactly the same non-linear characteristics,that is,they all exhibit anisotropic dynamic fluctuation characteristics.In addition,we also calculate the parameter,an effective fluctuation strength ?_eff ,which describes the fluctuating strength or intermittent intensity in high-energy collisions.It is found that as the order increases,?_eff decreases.Also,the effective fluctuation strength ?_eff in heavy-ion Au-Au collisions is smaller than that of hadron-hadron collisions,and is much smaller than for e~+e~- collision.