Corrections for regular identification of high energy positive particles in experimental data using lobachevsky space




Lobachevsky space, Hagedorn approach, Tsallis approach


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.


Download data is not yet available.
PDF 20


N. A. Chernikov (Dubna, JINR) “Lobachevsky geometry and relativistic nuclear physics” Dubna, 1997.

A. A. Baldin, E. G. Baldina, E. N Kladnitskaya, O. V. Rogachevsky, “Analysis of experimental data on relativistic nuclear collisions in Lobachevsky space”, Phys.Part.Nucl.Lett. 1 (2004), 171-177, Pisma Fiz.Elem.Chast.Atom.Yadra 2004 (2004) 119, pp. 7-16.

R. Togoo, T. Tulgaa, A. Tursukh, O. V. Rogachevsky, M. Sovd and J. Shinebayar “A possibity to identify positive particles produced from the inelastic interactions detected by propane bubble chamber”, Proc. of Mongolian Academy of Sciences,Vol. 56, No. 1(217),Ulaanbaatar, 2016, pp. 5-12.

R. Togoo, M. Sovd, T. Tulgaa, A. Tursukh, B. Khurelbaatar, O. V. Rogachevsky and J. Shinebayar “Coloumb interaction in C+C collisions at 4.2 A GeV/c momentum” Proc. Of the Institute of Physics and Technology, № 44, Ulaanbaatar, 2018.

Imran Khan and Kh. K. Olimov “Spectral Temperatures of Δ0(1232) Resonances Produced in p12C and d12C Collisions at 4.2 GeV/c per Nucleon” ISSN 1063-7788, Physics of Atomic Nuclei, 2013, Vol. 76, No. 7, pp. 883–887.

R. Hagedorn and J. Rafelski, “Hot Hadronic Matter and Nuclear Collisions” Phys. Lett. B 97, 136 (1980).

Li-Li Li, Fu-Hu Liu “Kinetic Freeze-Out Properties from Transverse Momentum Spectra of Pions in High Energy Proton-Proton Collisions”, MDPI Physics 2 (2020) 2, pp. 277-308,

Hagedorn,R. “Multiplicities, $p_T$ Distributions and the Expected Hadron $to$ Quark - Gluon Phase Transition”, Riv.Nuovo Cim. 6N10 (1983), pp. 1-50,

Hagedorn, R., “Statistical thermodynamics of strong interactions at high-energies” Nuovo Cim.Suppl. 3 (1965), pp. 147-186.

Field, R. D. and Feynman, R. P., “A Parametrization of the Properties of Quark Jets” Phys. B 136, pp. 1-76 (1978).

G. Wilk and Z. Wlodarczyk, “Interpretation of the Nonextensivity Parameter q in Some Applications of Tsallis Statistics and Lévy Distributions” Phys. Rev. Lett. 84, 2000,

Grzegorz Wilk (Warsaw, Inst. Nucl. Studies), Zbigniew Wlodarczyk (Jan Kochanowski U.) “Consequences of temperature fluctuations in observables measured in high energy collisions” Published in: Eur.Phys.J.A 48 (2012),

A. I. Bondarenko, R. A. Bondarenko, E. N. Kladnitskaya, “Study of nucleus-nucleus interactions with complete destruction of the target nucleus with momentum 4.2-GeV/c per nucleon” Dubna, JINR, R1-96-292, 1996.




How to Cite

Ravdandorj, T., Narankhuu, K., & Janchiv, S. (2023). Corrections for regular identification of high energy positive particles in experimental data using lobachevsky space. Proceedings of the Mongolian Academy of Sciences, 62(04), 21–27.