1. 1 Asymptotics in Relativistic Nuclear Physics A.Malakhov Joint Institute for Nuclear Research, Dubna The 1 st CBM-Russia-JINR Collaboration Meeting, Dubna, May 19-22, 2009

2. 2 A.M.Baldin and L.A.Didenko. Fortschr. Phys. 38 (1990) 4, 261-332. I + II → 1 + 2 + 3 + … b ik = - (u i – u k ) 2 u i = p i /m i i, k = I, II, 1, 2, 3, …. u k = p k /m k A.M.Baldin, A.I.Malakhov, and A.N.Sissakian. Physics of Particles and Nuclei, Vol.32. Suppl. 1, 2001, pp.S4-S30.

3. 3 Classification of relativistic nuclear collisions on b ik b ik ~ 10 -2 classic nuclear physics 0.1  b ik < 1 intermediate domain b ik >> 1 nuclei should be considered as quark-gluon systems

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5. 5 e E·d  /dp 3 = C·exp(-T/T 0 ) p + Cu →   (180 0 ) + …

6. 6 Beam + Target Beam energy (A  GeV) Intensity (1/sec) Target (mg/cm 2 ) Cross- section (mb/sr  cm 2 ) Yield (1/sec) Number of events (1/day) J/  Si + Si 610 9 3010 -10 10 -4 10 Ta + Ta 610 9 3010 -7 10 -3 100 A.G.Litvinenko, A.I.Malakhov, P.I.Zarubin. JINR Rapid Communications №1- 93, p.27

7. 7 Correlation Depletion Principle (CDP) CDP was offered by N.N.Bogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r, t). The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized. CDP in Relativistic Nuclear Physics was suggested by A.M.Baldin in four-velocity space. Due to complementary of r ik and b ik this principle is quite opposite to the Bogolyubov CDP. The Bogolyubov CDP is valid for |r i - r k | 2 →  while the Baldin CDP is fulfilled for |r i - r k | 2 → 0 (or b ik →  ) according to the asymptotic freedom.

8. 8 W | → W α · W β b αβ →  α = I, β = II I + II → 1 + … d 2 σ /db II 1 dx 1 → F I · F II (b II 1, N 1 ) b II 1 = (u II – u 1 ) 2 N 1 – cumulative number

9. 9 V α - middle point of system u i - four-velocity of particle i in the system u k - four-velocity of particle k in the system b αi << b αk Example of the Isolated system: W α and W β (F I and F II ) The important example of the Isolated system → JETS b αi = - (V α – u i ) 2 b αk = - (V α – u k ) 2 Isolated system

10. 10 Invariant definition of hadron jets The jet is a claster of hadrons with small relative b ik. The jet axis (a unit four-vector): The summation is performed over all the particles belonging to a selected particle group (claster). It is possible to determine the squared four- velocity with respect to the axis: V = Σ(u i /√(Σu i ) 2 V o 2 – V 2 = 1 b k = - (V – u k ) 2 i

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14. 14 Distribution of π – mesons on b k in jets of hadron- hadron and hadron-nucleus collisions at high energies are UNIVERSAL. They do not depend either on the colliusion energy, or on the type of fragmenting system. This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum.

15. 15 For jets : ~ 1 For hadrons: << 1 The jet is well allocated if the condition satisfies: b s I > b s II >

16. 16 Automodelity Principle b ik →  asymptotic regimes → decreasing of the probability distributions (cross-sections) W and factorization (DCP). Asymptotic regimes → automodelity distributions W. Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables → similarity parameters.

17. 17 Automodelity W, i.e. the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear, intermediate and a quark-gluon) → HYPOTHESIS demanding an experimental substantiation.

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20. 20 А. М. Балдин, А. А. Балдин. Phys.of Element. Part. and Atomic Nuclei, V.29, 1998.

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24. 24 I + II → 1 + … (N I P I + N II P II – p 1 ) 2 = (N I m 0 + N II m 0 + Δ) 2 Δ is the mass of the particle providing conservation of the barion number, strangeness and other quantum numbers

25. 25 Baldin A.M., Malakhov A.I. JINR Rapid Communications, No.1(87)-98, 1998, pp.5-12.

26. 26 PREDICTIONS

27. 27 Asymptotics s/(2m I m II )  (u I u II ) = ch2Y   П  min = (m T /2m 0 )[1+  √1+(  2 -m 1 2 )/m T 2 ] N   0

28. 28 The analytical representation for П leads to the following conclusions: There is the limiting value of П at high energies The effective number of nucleons involved in the reaction decreases with increasing collision energy Probability of observation of antinuclei and fragments in the central rapidity region is small Strange particles yield increases with increasing collision energy The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising

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30. 30 A 2 = min [-Σ(V α – u k ) 2 - Σ(V β – u i ) 2 ], A 3 = min [-Σ(V α – u k ) 2 - Σ(V β – u i ) 2 - Σ(V γ – u j ) 2 ], …………………. etc. K i K i j

31. 31 Distribution of jet axes is well described QCD as result of the production of quarks and gluons (i.e. color charges). In other words → studying of jets is studying of deformation of vacuum by a color charge, studying of the deconfinment.

32. 32 Observability of particles from which can consist quarks Observability of short-lived particles is based on two necessary criteria: 1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors: σ = σ p · W d Where W d is interpreted as the decay probability (or secondary interaction probability) a suggested particle, σ p its production cross section. 2) Universality of W d or similarity of the W d properties in various reactions. I + II → Jet α + Jet β σ = σ p · W α (b k )· W β (b k )

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34. 34 Conclusion CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions

35. 35 Thank you !