z -Scaling: Search for Signatures of Phase Transition in Nuclear Matter

We present results of analysis of hadron production in p + p and Au + Au collisions obtained in the framework of z -scaling in searching for signatures of a phase transition in nuclear matter. The approach allows systematic analysis of experimental data on inclusive cross sections over a wide range of the collision energies, multiplicity densities, transverse momenta, and angles of various particles. The concept of the z ‑scaling is based on the principles of self-similarity, locality and fractality reflecting the general features of hadron interactions. The scaling function ψ (z) depends on the self-similarity variable z and is expressed by the inclusive cross-section and the multiplicity density of produced particles. The variable z is a function of the momentum fractions x_1 and x_2 of the colliding objects carried by interacting hadron constituents and depends on the fractions y_a and y_b of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart. There are three model parameters in the z -scaling approach. Structure of the colliding objects and fragmentation processes are characterized by the structural and fragmentation fractal dimensions δ and ϵ , respectively. The produced medium is described by a “specific heat” c . The discontinuity of the model parameters is discussed from the point of view of searching for phase transitions in nuclear matter.