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

Abstract

We present results of analysis of hadron production in $p + p$ and ${\text{Au}} + {\text{Au}}$ 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 $\psi (z)$ 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 $\epsilon$, 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.