D. Toivonen, M. Tokarev JINR, Dubna Z-scaling & High- pT and cumulative particle production in pp and pA collisions at high energies Z XXXII International Symposium on Multiparticle Dynamics Alushta, Crimea, Ukraine, September, 2002

Content Introduction Z-scaling & basic principles - self-similarity, locality, fractality Z-scaling & properties - energy and angular independence, power law High- hadron production in pp and pD Cumulative particle production in pA Summary

Motivation & Goals The numerous experimental data on high-pT hadron, direct photon and jet production obtained at U70, ISR, SpS and Tevatron reveal scaling properties in Z-presentation. The general concept of Z-scaling is based on the fundamental symmetry principles of self-similarity, locality and fractality. Therefore the violation of Z-scaling is suggested to use as a signature of new physics phenomena in pp, pA and AA interactions at high-pT. To include in joint analysis new high-pT data sets to verify the properties of Z-scaling. To perform the analysis of cumulative processes of particle production in the framework of Z-presentation.

Z-scaling & Symmetry Self-similarity The dropping of certain dimensional quantities or parameters out of a physical picture interaction. Locality The momentum-energy conservation law is locally valid for interacting constituents. Fractality The internal structure of colliding objects, interaction of their constituents and formation mechanism of real particles reveal self-similarity and are described by the power law. The general concept of Z-scaling is based on the fundamental principles of self-similarity, locality and fractality.

Z-scaling New presentation of experimental data revealing scaling properties radial scaling variable Feynman variable transverse mass

Scaling variable Z is the measure of constituent interaction is the multiplicity density of charged particles are the momentum fractions are the anomalous fractal dimensions, is the energy of constituent sub-process

Scaling function is the collision energy is the multiplicity particle density is the inelastic cross section is the pseudorapidity is the rapidity is the inclusive cross section Normalization equation

Physical meaning of and o The scaling variable is the formation length revealing the property of a fractal measure o The scaling function is the probability density to form a particle with the formation length I.Zborovsky, hep-ph/ I.Zborovsky et al., JINR E

Properties of Z-scaling Energy independence of Angular independence of Power behavior, A-dependence of,

Energy independence of Z-scaling The scaling function has the same shape for different collision energy Angular independence of Z-scaling The scaling function has the same shape for different angles of produced particles Z-presentation and power law The scaling function in the high- range reveals the power behavior

Z (a) The dependence of cross section of meson production on transverse momentum. (b) The corresponding scaling function. - Energy independence of - Angular independence of - Power law J.W. Cronin et.al., Phys. Rev. D11 (1975) D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. M.Tokarev Yu.Panebratsev I.Zborovsky G.Skoro JINR E Z-scaling and energy dependence of -meson production in pp collisions at high-

Z (a) The dependence of cross section of meson production on transverse momentum. (b) The corresponding scaling function. Experimental data are taken from: J.W. Cronin et.al., Phys. Rev. D11 (1975) D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. D.E. Jaffe et al., Phys. Rev. D40 (1989) Z-scaling and energy dependence of -meson production in pp collisions at high-

A-dependence of Z-scaling The scaling transformations of and allow us to compare scaling functions for different nuclei M.Tokarev, Yu.Panebratsev, I.Zborovsky, G.Skoro JINR E ; Int. J. Mod. Phys. A16 (2001) 1281.

A-dependence of Z-scaling Z J.W. Cronin et al., Phys. Rev. D11 (1975) D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. M.Tokarev Yu.Panebratsev I.Zborovsky G.Skoro JINR E Int.J.Mod.Phys. A16 (2001) 1281 The shape of the scaling function is the same for different nuclei from D to Pb Energy independence of Power law at high-z A-dependence of

Z (a) The dependence of cross section of meson production on transverse momentum. (b) The corresponding scaling function. - Energy independence of - Angular independence of - Power law J.W. Cronin et.al., Phys. Rev. D11 (1975) D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. D.E. Jaffe et al., Phys. Rev. D40 (1989) Z-scaling and energy dependence of -meson production in pD collisions at high-

plot The plot allows us to determine the kinematical range where the scaling can be violated. The plot can be used as a joint kinematical and dynamic criterion to select domain where new physical phenomena can be found.

Summary I Results of data analysis on inclusive cross sections of high-pT charged hadron production in p-p and p-D collisions at high energies do not give indications of Z-scaling violation. The mechanism of particle formation is described by the scaling function over a wide kinematical range. The power law at is observed. is used to determine the kinematical region preferable to search for the scaling violation.

Cumulative particle production in p-A & Z-scaling The kinematical region for h-A and A-A interactions forbidden for particle production in nucleon-nucleon collision is called the cumulative region. 4-momentum conservation law & baryon, strange, charm numbers

Kinematical boundary for pion backward hemisphere production in p-A pDLiBeTa

Z (a) The dependence of cross section of meson production on particle momentum. (b) The corresponding scaling function. Experimental data are taken from: N.A. Nikiforov et al., Phys. Rev. C22 (1980) 700. J.W. Cronin et.al., Phys. Rev. D11 (1975) D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. D.E. Jaffe et al., Phys. Rev. D40 (1989) Z-scaling, cumulative and high- -meson production in pTa collisions

Angular dependence of multiplicity particle density in backward hemisphere particle production in p-A Li, Be, C, Al, Cu, Ta Angular dependence of A-dependence of The ratio and at and.

plot The kinematical range for the process where the scaling can be violated

Summary New analysis of high-pT data on charged hadrons produced in p-p and p-D collisions were performed. The obtained results confirm the general properties of z-scaling. Data z-presentation of backward hemisphere particle production in pA collisions was presented. The angular dependence of multiplicity particle density for different nuclei (Li, Be, C, Al, Cu, Ta) was found. Comparison of scaling functions for high-pT and cumulative data sets was performed. Available experimental data on high-pT particle spectra give no indication on z-scaling violation. The change of fractal dimension is suggested to use as the quantitative measure of the scaling violation.

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D. Toivonen, M. Tokarev JINR, Dubna Search for Z-scaling violation in pp and pA collisions at high energies XVI International Seminar on High Energy Physics Problems “Relativistic Nuclear Physics & Quantum Chromodynamics” JINR, Dubna, June 10-15, 2002 Z

D. Toivonen, M. Tokarev JINR, Dubna Z XVI International Conference on Particles and Nuclei (PANIC02) Osaka, Japan, September 30 - October 4, 2002 Z-scaling, high-pT and cumulative particle production in p-A collisions at high energies