$Z$ scaling in proton-nucleus collisions at high energies

New scaling, z scaling, in the inclusive particle production in $\mathrm{pA}$ collisions is studied. The concept of z scaling is based on fundamental principles such as self-similarity, locality, scale relativity, and fractality reflecting the general features of particle interactions. The scaling function $H_A\mathrm{}\left(z\right)\mathrm{}$ is expressed via the invariant cross section ${\mathrm{Ed}}^3\sigma {/dq}^3$ and the average multiplicity density $dN/d\eta$ of particles produced at pseudorapidity $\eta =0\mathrm{}$ in the corresponding nucleon-nucleon interaction. The dependence of $H_A\mathrm{}\left(z\right)\mathrm{}$ on scaling variable $z$, the center-of-mass energy $\sqrt{s},$ and the atomic number A is investigated. It is shown that the available experimental data on cross sections in $\mathrm{pA}$ collisions confirm the scaling properties of the function $H_A\mathrm{}\left(z\right).$ The obtained results can be of interest for future experiments at BNL relativistic heavy-ion collider and CERN large hadron collider in searching for new physical phenomena in $pp,$ $pA,$ and $\mathrm{AA}$ collisions.