Exploring critical fluctuation phenomenon according to net-proton multiplicity information entropy in AMPT model

Information entropy can be used for investigating the critical fluctuation phenomenon by describing multiplicity fluctuations in heavy-ion collisions. In this study, a multiphase transport (AMPT) model in the default version (AMPT-DEF) and with the string melting (AMPT-SM) were used as event generators to simulate the Au+Au reaction at different incident energies. Owing to the influence of the distribution bin number in extracting its information entropy, two methods, i.e., data binning and weighting factors, were proposed to correct the information entropy analysis. The comparison between information entropy and kurtosis also reflects the necessity to correct the information entropy analysis. The corrected information entropy of net-proton multiplicity was analyzed in central Au+Au collisions at sNN= 4.7, 6.4, 7.7, 8.8, 11.5, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 140, 170, and 200 GeV with the impact parameter b=3 fm. The results indicated that the fluctuations of net-proton multiplicity were essentially identical at collision energies ranging from sNN= 4.7 GeV to sNN= 200 GeV in the same model. No critical fluctuation phenomenon was found in the central Au+Au collisions simulated using the AMPT models, similar to the case of the AMPT model, which does not have. Comparing the information entropy of AMPT-SM to AMPT-DEF, the effect of partonic phase leads to a bigger fluctuation, indicating that the corrected information entropy can be a useful probe to explore the phase transition. The mid-rapidity net-proton multiplicity information entropy was also calculated, and the results led to the same conclusion. The corrected information entropy may be useful for investigating critical fluctuations, which is important for exploring critical endpoint.