Generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>z</mml:mi></mml:math>-scaling in proton-proton collisions at high energies

New generalization of the $z$-scaling in inclusive particle production is proposed. The scaling variable $z$ is a fractal measure which depends on kinematic characteristics of the underlying subprocess expressed in terms of the momentum fractions ${x}_{1}$ and ${x}_{2}$ of the incoming protons. In the generalized approach, ${x}_{1}$ and ${x}_{2}$ are functions of the momentum fractions ${y}_{a}$ and ${y}_{b}$ of the scattered and recoil constituents carried by the inclusive particle and recoil object, respectively. The scaling function $\ensuremath{\psi}(z)$ for charged and identified hadrons produced in proton-proton collisions is constructed. The fractal dimensions and heat capacity of the produced medium entering definition of the variable $z$ are established to restore energy, angular, and multiplicity independence of $\ensuremath{\psi}(z)$. The proposed scheme allows a unique description of data on inclusive cross sections at high energies. Universality of the shape of the scaling function for various types of produced hadrons ($\ensuremath{\pi}$, $K$, $\overline{p}$, $\ensuremath{\Lambda}$) is shown. Results of the analysis of experimental data are compared with the next-to-leading order (NLO) QCD calculations in ${p}_{T}$ and $z$-presentations. The obtained results suggest that the $z$-scaling may be used as a tool for searching for new physics phenomena of particle production in high transverse momentum and the high multiplicity region at proton-proton colliders RHIC and LHC.