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FLOW, FREEZE-OUT and EoS in relativistic heavy-ion collisions at NICA

L. Bravina for UiO heavy-ion theory group . FLOW, FREEZE-OUT and EoS in relativistic heavy-ion collisions at NICA . Physics at NICA (Dubna, Sept. 9-12, 2009) . Flow : how to quantify this phenomenon Connection to Equation of State

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FLOW, FREEZE-OUT and EoS in relativistic heavy-ion collisions at NICA

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  1. L. Bravina for UiO heavy-ion theory group FLOW, FREEZE-OUT and EoSin relativisticheavy-ioncollisions at NICA Physics at NICA (Dubna, Sept. 9-12, 2009)

  2. Flow: how to quantifythisphenomenon • Connection to Equationof State • Transverseflow at AGS and SPS energies • Freeze-outofhadrons in microscopicmodels • Flow and freeze-out • Thermalization, Equilibration and EoS at NICA • Summary of signals to study at NICA Content

  3. Flow: How to quantify it

  4. Ne W. Scheid, H. Muller, and W. Greiner, PRL 32, 741 (1974) H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980) M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A. Bethe, Nucl. Phys. A251, 502 (1975) G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, PRD 8, 4302 (1973) E. Glass Gold et al. Annals of Physics 6, 1 (1959) R. Lacey, QM’05 talk They are predicted to provide unprecedented access to the properties of Nuclear matter The idea to use collective flow to Probe the properties of nuclear matter is long-standing

  5. Definitions. Non-central Collisions (b>0 )

  6. DISTRIBUTIONS Rapidity dependence Transverse momentum dependence n=1,2,… Centrality dependence

  7. Motivation: connection to Equation of State

  8. DISAPPEARANCE OF DIRECTED FLOW Hung and Shuryak, PRL 75 (1995) 4003 In case of first order phase transition Braun-Munzinger, NPA 661 (1999) 261c

  9. DISAPPEARANCE OF DIRECTED FLOW Transition toQuark-Gluon Plasma leads to decrease in pressure and, therefore, to softening of the directed flow

  10. DIRECTED FLOW OF NUCLEONS AND FRAGMENTS Plastic Ball Collaboration introduced a slope parameter Directed flow ofnucleons and fragments haslinearslopeinnormaldirection => normal flow W. Reisdorf, H.G. Ritter Annu.Rev.Nucl.Part.Sci. 47 (1997) 663

  11. Transverse flow (between AGS and SPS) Directed flow

  12. DIRECTED FLOW OF NUCLEONS. 3-FLUID HYDRO The model predicts a local minimum in the excitation function of directed flow at energies between 10 and 20 AGeV (so far not been observed) J. Brachmann et al., PRC 61 (2000) 024909

  13. DIRECTED FLOW OF PIONS AND PROTONS AT 40 AGEV Softening of directed flow of protons at midrapidity C. Alt et al. (NA49), PRC 68 (2003) 034903

  14. DIRECTED FLOW OF PIONS AND PROTONS AT 158 AGEV Antiflow of protons in peripheral events C. Alt et al. (NA49), PRC 68 (2003) 034903

  15. SOFTENING OF DIRECTED FLOW

  16. COMPARISON WITH EXPERIMENTAL DATA E. Zabrodin et al. , PRC 63 (2003) 034902; L. Bravina et al., PRC 61 (2000) 064802

  17. SOFTENING OF DIRECTED FLOW L.Bravina et al., NPA 715 (2003) 665c Although the normal flow component is always larger than the antiflow one, in central rapidity window the antiflow can overshadow its normal counterpart

  18. DIRECTED FLOW IN DIFFERENT P_T - INTERVALS L.Bravina et al., PRC 63 (2001) 034902 The directed flow of high-pT pions (and other mesons) seems to have a normal slope

  19. CONCLUSIONS (DIRECTED FLOW )

  20. Elliptic flow

  21. ELLIPTIC FLOW OF PIONS AND PROTONS AT 40 AGEV Significant dip at midrapidity for proton flow in central events C. Alt et al. (NA49), PRC 68 (2003) 034903

  22. ELLIPTIC FLOW OF PIONS AND PROTONS AT 40 AGEV However, the dip at midrapidity disappears if one uses the {2} or {4} cumulant method C. Alt et al. (NA49), PRC 68 (2003) 034903

  23. Open question:

  24. Flow and freeze-out

  25. TIME EVOLUTION OF ELLIPTIC FLOW (RHIC) Au+Au @ 130 and 200 AGeV Analysis should be repeated at NICA enrgies

  26. ELLIPTIC FLOW AND FREEZE-OUT

  27. ELLIPTIC FLOW AND FREEZE-OUT L. B. et al., PLB 631 (2005) 109 Pions and nucleons are coming from different areas

  28. FREEZE-OUT OF HADRONS L. B. et al., PRC 60 (1999) 044905

  29. SEQUENTIAL FREEZE-OUT SPS L. B. et al., PRC 60 (1999) 044905 ; PLB 354 (1995) 196 AGS

  30. ABSENCE OF SHARP FREEZE-OUT

  31. CONCLUSIONS (FREEZE-OUT)

  32. Freeze-out at RHIC: UrQMD

  33. Freeze-out at RHIC: QGSM

  34. 5. Freeze-out at RHIC: UrQMD M.S. Nilsson, ”LHC and beyond” (Lund, Feb. 2009)

  35. freeze-out at RHIC: QGSM M.S. Nilsson , ”LHC and beyond” (Lund, Feb. 2009)

  36. Summary and perspectives • Collectivephenomena, such as directed and ellipticflow, should be studiedtogetherwiththefreeze-outconditions (i.e., femtoscopiccorrelations) • Wepropose to make modelpredictions (UrQMD, QGSM, HSD, AMPT, etc) ofdistributionspresented it this talk for NICA energy range

  37. EOS at NICA energies and roleofresonances L.Bravina(University of Oslo) in collaborationwith I.Arsene, J.Bleibel, M.Bleicher, G.Burau, A.Faessler, C.Fuchs, M.Nilsson, H.Stocker, K.Tywoniuk, E.Zabrodin or little Big Bang Strange Quark Matter’2008, Beijing, 09.10.2008

  38. Motivation: Equationof State Tricritical point is located around 10-40 GeV (LQCD) We have to explore this energy range to study the possible phase transition QGP can be formed already at low energies H. Stoecker, J. Phys. Conf. Ser. 50 (2006) 300 L. Bravina et al., PRC 60 (1999) 024904; 63 (2001) 064902

  39. Central cell: Relaxation to equilibrium

  40. EQUILIBRATION IN THE CENTRAL CELL Kinetic equilibrium: Isotropy of velocity distributions Isotropy of pressure Thermal equilibrium: Energy spectra of particles are described by Boltzmann distribution Chemical equlibrium:Particle yields are reproduced by SM with the same values of

  41. STATISTICAL MODEL OF IDEAL HADRON GAS input values output values Multiplicity Energy Pressure Entropy density

  42. PRE-EQUILIBRIUM STAGE Homogeneity of baryon matter Absence of flow The local equilibrium in the central zone is quite possible

  43. Models employed: UrQMD QGSM

  44. KINETIC EQUILIBRIUM Isotropy of velocity distributions Isotropy of pressure L.Bravina et al., PRC 78 (2008) 014907 Velocity distributions and pressure become isotropic for all energies

  45. KINETIC EQUILIBRIUM Isotropy of velocity distributions Isotropy of pressure L.Bravina et al., PRC 78 (2008) 014907 Velocity distributions and pressure become isotropic for all energies

  46. THERMAL AND CHEMICAL EQUILIBRIUM Boltzmann fit to the energy spectra Particle yields L.Bravina et al., PRC 78 (2008) 014907 Thermal and chemical equilibrium seems to be reached

  47. HOW DENSE CAN BE THE MEDIUM? ”Big” cell (V = 5x5x5 fm^3) “Small” cell (V => 0) Dramatic differences at the non-equilibrium stage; after beginning of kinetic equilibrium the energy densities and the baryon densities are the same for ”small” and ”big” cell

  48. Equation of State T vs. energy, etc

  49. ISENTROPIC EXPANSION Expansion proceeds isentropically (with constant entropy per baryon). This result supports application of hydrodynamics

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