Study Of Energy Dependence Of Fractal Feature In Electron-positron Collisions

This thesis introduces the significant theories in research on intermittency and fractal behavior in high energy collision, and models for high energy e+e- collision simulation and technology for data analysis; and also introduces our corresponding research in detail.Self-affine fractal had been observed in high energy e+e- collisions just at the Z0 decay energy scale. However neither the fractal feature, nor the energy dependence of the fractal feature of the e+e- collision system has been studied at any other center-of-mass energy scale. This thesis focuses on the energy dependence of the fractal behavior of e+e- collisions by generating the e+e- collision events using the Monte Carlo simulation Jetset7.4. From 30 GeV to 200 GeV,18 energies are chosen as the c.m. energy of e+e- collisions. And in the thrust coordinate system, choose the rapidity y, transverse momentum pt, azimuthal angleφas the variables in the phase space. With isotropic partition of the chosen phase space, calculate the three-dimensional normalized factorial moments (NFM). The calculated results show that, at various c.m. energies, the three-dimensional NFM behaves abnormal scaling with the partition numbers on the phase space, which indicates high energy e+e- collision final state multiparticle systems have self-similar fractal feature at various c.m. energy. Also, the intermittency exponents have been measured at various c.m. energies, and it has been observed as depending on the c.m. energy. That is, the intermittency exponent increases with the raise of the c.m. energy; and when the c.m. energy is lower than 80 GeV, the intermittency exponent increases rapidly with the raise of the c.m. energy; when the c.m. energy is greater than 80 GeV, the intermittency exponent increase and then saturate with the raise of the c.m. energy. Moreover, with the decline of the c.m. energy, all intermittency distribution curves converge nearly to the zero point, which indicates that the dynamical fluctuation trends to zero when the e+e- collision c.m. energy is low enough.To further study the fractal feature of the e+e- collision final state phase space, calculate the one-dimensional NFMs of the three phase space variables, and measure their energy dependence. Still, generate e+e- collision events at 17 different c.m. energies with Jetset7.4, and calculate the one-dimensional NFMs of the three phase space variables, i.e. y, pt,φ, respectively. After fitting the results with saturation equation, the saturation exponents show that, the energy dependence of the three phase space variables are quite different. The saturation exponent of the NFM of y rises with the increase of the c.m. energy, the saturation exponent of the NFM of pt, declines with the increase of the c.m. energy, and the saturation exponent of the NFM ofφnearly keeps constant with the increase of the c.m. energy. Except for the Z0 decay energy scale, the three saturation exponents of the one-dimensional NFM are unequal to each other, which indicate that the three-dimensional phase space should be anisotropic. Since the abnormal scaling behavior of the three-dimensional NFM has been observed under the isotropic partition of the phase space, it's necessary to further study the Hurst exponent of phase space, the saturation exponent of the NFM, the abnormal scaling feature of the NFM and the fractal feature of the high energy collision final state phase space. It is shown that the three-dimensional NFM behaves abnormal scaling with the increase of the partition numbers of the phase space; both under the anisotropic partition according to the shrinking factors, which indicated by the Hurst exponents and calculated using the saturation exponents; and under the isotropic partition, which means all the Hurst exponents equal to one. This indicates that a special double-Hurst-exponent phenomenon exists in multiparticle final state phase space in high energy e+e- collision. That is, when isotropic partition is taken on the phase space, the three-dimensional NFM abnormal scaling behavior can be observed, which corresponds to one group of Hurst exponents being equal to one; and the other group of Hurst exponents are calculated from the MC simulation data, which results in three unequal Hurst exponents.Double-Hurst-exponent phenomenon is a strange one. So we research and discuss this phenomenon from the theory of the dynamical fluctuation. After analyzing the relation between the Hurst exponent and the shrinking factors along the phase space variable directions, find that when the overall shrinking factor conserves, isotropic partition can lead to NFM scaling behavior even in an essential anisotropic phase space. This indicates that once the system fits the shrinking factor conservation, it maybe exist double-Hurst-exponent phenomenon. So it won't determine the fractal feature exactly that the partition way of the phase space and the NFM abnormal scaling behavior. After research on the three saturation exponents of the one-dimensional NFM, the Hurst exponent, and the three-dimensional NFM scaling feature, we propose a criteria to determine the fractal feature in the high energy collision multiparticle final state phase space. That is, when the three Hurst exponents are all equal to one, the system is self-similar fractal; otherwise, it should be self-affine fractal. To examine our proposed criteria and the existence of the double-Hurst-exponent, we use the published hadron-hadron collision and e+e- collision experiments'reports, which supports our results; meanwhile we use the Jetset7.4 and Herwig5.9 to simulate e+e- collision events, which also keep agreement to our results. In conclusion, our results show that, high energy hadron-hadron collision final state particles system is self-affine fractal; the high energy e+e- collision final state multiparticle system is self-similar fractal when the c.m. energy is 91.2 GeV, and is self-affine fractal when the c.m. energy is not 91.2 GeV.Finally, we study on the energy dependence of the Levy stability and multi fractal spectrum of the high energy e+e- collision multiparticle system. The research on the Levy exponent, Renyi dimension, and the multi fractal spectrum at various c.m. energies shows that:at different c.m. energies the high energy e+e- collision multiparticle system fits the Levy stability; the Levy exponent depends on the c.m. energy, i.e. the Levy exponent declines with the increase of the c.m. energy; the multi fractal spectrum and the Renyi dimension depends weakly on the c.m. energy, i.e. the fractal dimension nearly not changed with the increase of the c.m. energy, the information dimension and the correlation dimension declines with the increase of the c.m. energy when the c.m. energy is lower that 80 GeV, and then keeps unchanged with the increase of the c.m. energy.