The Study Of Dependence Of Entropy Index On The Width And Shape Of Multiplicity Distributions

A new development further along the non-linear phenomena in high energy collisions was made by Cao and Hwa in the event by event analysis. They proposed to measure the phase space patterns in multiparticle system by event factorial moments. In this thesis, the erraticity of event factorial moments in pseudorapidity space of multiparticle production with the simulation of a random cascading model has been studied in some detail.We investigated the dependence of erraticity behavior, which refers to the phenomena that the fluctuations of event factorial moments increase with decreasing phase space scale, on the shape and width of multiplicity distribution. A new form of multiplicity distribution, which has the advantage of being able to change the average and width freely by using two controlling parameters is introduced. With this distributions in hand the dependence of entropy index, proposed by Cao and Hwa as a characteristic of the degree of event-by event fluctuations, on the width and shape of multiplicity distributions are studied in some details using Monte Carlo method and compared with the results from NA22 experiment. It is found that the entropy index is insensitive to the shape of multiplicity distribution but decreases with the increase of the distribution width. The latter observation contradicts the expectation that entropy index μq measures the event-by-event fluctuations of factorial moments. The reason of this contradiction could be explained as the following. Looking into the definition of μq, more carefully, we can see that it is the derivative of ψg(p) at a certain point p =1. There is noguarantee for μq to be a monotonically increasing function of ψq Therefore, the failure for μq as a measurement of the event-by-event fluctuations is understandable. It is necessary to find another appropriate quantity for this purpose.Therefore, the appropriate quantity for characterizing the event-by-event fluctuation of factorial moments is discussed in some detail . Looking into the definition of the event factorial moment, we propose to use the erraticity exponent ψ (2) to characterize the event to event fluctuations at q=2. It has then shown using Monte Carlo method that erraticity exponent ψ2(2) increases with the increasing of multiplicity-distribution width just as expected, while the entropy index μ2 behaves in an opposite way. Therefore , ψ2(2) is a good variable for characterizing the event-by-event fluctuation at q=2, while the entropy index μ2 may has its own right to work as a signal for chaotic property, is inappropriate for the study of event-by-event fluctuation.Erraticity analysis provide new opportunity in measuring event by event fluctuations in high energy nuclear collisions. Applying erraticity analysis to high multiplicity sample at RHIC and LHC energy is recommended. Event by event analysis will help identify phase transition in high energy nuclear collisions, whether it is first order or a soft cross over.