Interferometry For The Inhomogeneous Pion Sources

RHIC HBT puzzle is an experimental phenomenon which can not be explainedwith existing theory. We analyse the cause of the HBT puzzle and use inhomogeneoussource as an explanation to such puzzle. We develop a method for detecting the inho-mogeneity of the sources produced in ultra-relativistic heavy ion collisions, throughevent-by-event correlations.By analyzing the relationship between HBT radii and the emitting sources, wefind that the key to solve the HBT puzzle is shortening the lifetime of the source.We improve the granular model and get the results of HBT interferometry which canagree with experimental data well. We also find that the lifetime of the source canbe shortened by increasing its surface area, which is the basis for the inhomogeneoussource.Using the NeXSPheRIO model, we find two important characters at the initialcondition of the system: 1) The initial energy distribution of the source is very irregu-lar; 2) The initial energy distribution are different event-by-event even with the sameimpact parameters. Usual hydrodynamic model do not have such characters, whichwe use for analyzing in this article.We find that the source is inhomogeneous in space and time, which is causedby the irregular distribution of the initial energy. The formation of such structure isindependent of the equation of state. We consider that the initial condition of the usualhydrodynamic model is equal of the average effect of different real initial conditions.This effect can make the surface area smaller and the lifetime longer. As a result, the"HBT puzzle"appeared.As the system also has the character that its initial energy distribution are differ-ent event-by-event even with the same impact parameters. Using this character, wedevelop a method for detecting the inhomogeneity of the sources through event-by-event interferometry. The results of imaging analysis indicate that the relative sourcefunctions for different events for the inhomogeneous granular sources are differenteven with the same impact parameter. This difference is more evident for the eventswith large impact parameter. By comparing the difference of the correlation functions, we find that the increasing degree of such difference with the number of pions is moreevident as the impact parameter increasing. This character is only belong to the in-homogeneous sources and can be regarded as the signals of the detection of sourceinhomogeneity in experiment.