Speaker
Description
The status of $z$-scaling theory is reviewed. Basic physical principles such as self-similarity, locality, and fractality are discussed. The microscopic scenario of interactions of hadrons and nuclei at a constituent level in terms of dimensionless variables is studied.
The structure of the colliding objects and fragmentation process in final state is described by fractal dimensions $\delta_1, \delta_2$ and $\epsilon_a, \epsilon_b$, respectively. The fractal dimensions and the model parameter $c$ interpreted as a specific heat of the produced medium are found from the scaling behavior of the dimensionless function $\psi(z)$, which depends on a self-similarity variable~$z$. The scaling variable $z$ is given in terms of the momentum fractions $x_1,x_2,y_a$, and $y_b$ that define a selected constituent sub-processes. The principle of maximal entropy is used to determine the momentum
fractions taking into account the momentum conservation for the selected binary interaction. Applicability of the $z$-scaling approach for the description of polarization processes is illustrated. The equivalence of the minimal resolution principle with respect to the constituent sub-processes and the maximal fractal entropy $S_{\delta, \epsilon}$ is shown. The principle of maximum entropy together with the assumption of the fractal self-similarity of hadron structure and fragmentation processes leads to the preservation of a scale-dependent quantity - fractal cumulativity, characterizing hadron interactions at a constituent level. The fractal cumulativity is a property of a fractal-like object (or fractal-like process) with fractal dimension $D$ to form a "structural aggregate" with certain degree of local compactness which carries its momentum fraction $\zeta$.
The conservation law for the fractal cumulativity is formulated.
The crossing symmetry for the part of the entropy $S_{\delta, \epsilon}$ dependent only on the fractal dimensions in high resolution limit is discussed.
