In this work, high-energy positive charged particles are distinguished using the Lobachevsky space or Hyperbolic space, which is defined as the total rapidity multiplied by hyperbolic cosines of the transverse and longitudinal rapidity of the particles. Experimental data from eight different types of interactions detected in the bubble chambers accumulated in the high-energy sector were used in the calculations. The weights used to construct the proton and positive pion distributions for each of the interacting secondary particles have been eliminated, allowing such studies to be performed such as particle counting and clustering.These weights do not include calculated weights at azimuth angles, near the center of the star, or without momentum measurements. We now have the opportunity to study positive pions and protons. The percentage of confused particles increases with the beam energy.
After the reconstruction, we conducted a study of the temperature of the charged particles produced by the p + p interaction of 205 GeV, where Tsallis temperatures are close to Hagedorn . On the other hand, Hagedor and temperatures are higher than Tsallis, which means that the unstable states exchange heat as they move to equilibrium
