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Interferometry signatures of new states in hydrodynamic picture of A+A collision

Interferometry signatures of new states in hydrodynamic picture of A+A collision. Yu. Sinyukov, BITP, Kiev. Thermodynamic QCD diagram of the matter states. The thermodynamic arias

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Interferometry signatures of new states in hydrodynamic picture of A+A collision

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  1. Interferometry signatures of new states in hydrodynamic picture of A+A collision Yu. Sinyukov, BITP, Kiev Heavy Ion Collisions at the LHC Last Call for Predictions

  2. Thermodynamic QCD diagram of the matter states • The thermodynamic arias occupied by different forms of the matter Theoretical expectations vs the experimental estimates HIC at the LHC Last Call for Predictions

  3. UrQMD Simulation of a U+U collision at 23 AGeV HIC at the LHC Last Call for Predictions

  4. Expecting Stages of Evolution in Ultrarelativistic A+A collisions t HIC at the LHC Last Call for Predictions

  5. “Soft Physics” measurements A x t ΔωK A p=(p1+ p2)/2 q= p1- p2 Tch and μchsoon after hadronization (chemical f.o.) (QS) Correlation function Space-time structure of the matter evolution, e.g., Radial flow HIC at the LHC Last Call for Predictions

  6. Empirical observations and theoretical problems (1) EARLY STAGES OF THE EVOLUTION • An satisfying description of elliptic flows at RHIC requires the earlier thermalization, , and perfect fluidity. • The letter means an existence of a new form of thermal matter: asymptotically free QGP strongly coupled sQGP. ? PROBLEM: How does the initially coherent state of partonic matter – (CGC-?) transform into the thermal sQGP during extremely short time ~ ½ fm/c (problem of thermalization). HIC at the LHC Last Call for Predictions

  7. Empirical observations and theoretical problems (2) LATE STAGES OF THE EVOLUTION: • No direct evidence of (de)confinement phase transition in “soft physics” except (?) for: NA49 + Gadzidzki/Gorenstein However: it needs asymp. free QGP (+ light quarks) • HBT PUZZLE. 1.The behavior of the interferometry volumes only slightly depends on the collision energy: slightly grows with and . 2. HIC at the LHC Last Call for Predictions

  8. Way to clarify the problems Analysis of evolution of observables in hydrodynamic and kinetic models of A+A collisions Yu.S., S.V.Akkelin, Y. Hama: Phys. Rev. Lett. 89, 052301(2002); S.V.Akkelin.Yu.S. : Phys. Rev. C 70 , 064901 (2004); Phys.Rev. C 73, 034908 (2006); Nucl. Phys. A 774, 647(2006); M.S. Borysova, Yu.S., Akkelin, Erazmus, Karpenko, Phys.Rev. C 73, 024903 (2006); N.S. Amelin, R. Lednicky, L. V. Malinina, T. A. Pocheptsov and Yu.S. Phys.Rev. C 73, 044909 (2006); Yu.S, Act Phys Pol B 37, 3343(2006) HIC at the LHC Last Call for Predictions

  9. (2+1) n.-r. model with longitudinal boost-invariance [Akkelin, Braun-Munzinger, Yu.S. Nucl.Phys. A (2002)] • Momentum spectrum • Effective temperature • Interferometry volume • Spatially averaged PSD • Averaged PSD (APSD) HIC at the LHC Last Call for Predictions

  10. Evolution of Teff , APSD and particle density APSDand part. densities at hadronization time =7.24 fm/c (solid line) and at kineticfreeze -out =8.9 fm/c (dashed line). The dot-dashed line corresponds to the “asymptotic” time =15 fm/c of hydrodynamic expansion of hadron-resonance gas [Akkelin, Braun-Munzinger, Yu.S. Nucl.Phys. A2002] HIC at the LHC Last Call for Predictions

  11. Numerical UKM-R solution of B.Eq. with symmetric ICfor the gas of massive (1 GeV) particles [Amelin,Lednicky,Malinina, Yu.S. (2005)] HIC at the LHC Last Call for Predictions

  12. Longitudinal (x) and transverse (t) CF and correspondent radii for asymmetric initial coordinate distribution. R2 HIC at the LHC Last Call for Predictions

  13. Results andideas • The approximate hydro-kinetic duality can be utilized in A+A collisions • Interferometry volumes does not grow much even if ICs are quite asymmetric: less then 10 percent increase during the evolution of fairly massive gas. • Effective temperature of transverse spectra also does not change significantly since heat energy transforms into collective flows. • The APSD do not change at all during non-relativistic hydro- evolution, also in relativistic case with non-relativistic and ultra-relativistic equation of states and for free streaming. • The main idea to study early stages of evolution is to use integrals of motion - the ''conserved observables'' which are specific functionals of spectra and correlations functions. HIC at the LHC Last Call for Predictions

  14. Approximately conserved observables t Thermal f.-o. • APSD - Phase-space density averaged over some hypersurface , where all particles are already free and over momen- tum at fixed particle rapidity,y=0. (Bertsch) Chemical. f.-o. n(p) is single- , n(p1, p2 ) is double (identical) particle spectra, correlation function is C=n(p1, p2)/n(p1)n(p2) z p=(p1+ p2)/2 q= p1- p2 • APSD is conserved during isentropic and chemically frozen evolution: S. Akkelin, Yu.S. Phys.Rev. C 70 064901 (2004): HIC at the LHC Last Call for Predictions

  15. The averaged phase-space density Non-hadronic DoF Limiting Hagedorn Temperature HIC at the LHC Last Call for Predictions

  16. The statistical errors The statistical uncertainties caused by the experimental errors in the interferometry radiiin the AGS-SPS energy domain. The results demonstrate the range of statistical signicance ofnonmonotonic structures found for a behavior of pion averaged phase-space densities as functionof c.m. energy per nucleon in heavy ion collisions. HIC at the LHC Last Call for Predictions

  17. Rapidity densities of entropy and number of thermal pions vs collision energy (bulk) viscosity HIC at the LHC Last Call for Predictions

  18. Anomalous rise of pion entropy/multiplicities and critical temperature HIC at the LHC Last Call for Predictions

  19. The interferometry radii vs initial system sizes HIC at the LHC Last Call for Predictions

  20. The interferometry radii vs initial system sizes • Let us consider time evolution (in  ) of the interferometry volume if it were measured at corresponding time: • for pions does not change much since the heat energy transforms into kinetic energy of transverse flows (S. Akkelin, Yu.S. Phys.Rev. C 70 064901 (2004)); • The <f> is integral of motion; • is conserved because of chemical freeze-out. is fixed Thus the pion interferometry volume will approximately coincide with what could be found at initial time of hadronic matter formation and is associated with initial volume HIC at the LHC Last Call for Predictions

  21. Energy dependence of the interferometry radii Energy- and kt-dependence of the radii Rlong, Rside, and Rout forcentral Pb+Pb(Au+Au) collisions from AGS to RHICexperiments measurednear midrapidity. S. Kniege et al. (The NA49 Collaboration), J. Phys. G30, S1073 (2004). HIC at the LHC Last Call for Predictions

  22. Interferometry volumes and pion densities at different (central) collision energies HIC at the LHC Last Call for Predictions

  23. HBT PUZZLE • The interferometry volume only slightly increases with collision energy (due to the long-radius growth) for the central collisions of the same nuclei. Explanation: • only slightly increases and is saturated due to limiting Hagedorn temperature TH =Tc (B = 0). • grows with A is fixed HIC at the LHC Last Call for Predictions

  24. HBT PUZZLE & FLOWS • Possible increase of the interferometry volume with due to geometrical volume grows is mitigated by more intensive transverse flows at higher energies: ,  is inverse of temperature • Why does the intensity of flow grow? More more initial energy density  more (max) pressure pmax BUT the initial acceleration is ≈ the same HBT puzzle Intensity of collective flows grow Time of system expansion grows Initial flows (< 1-2 fm/c) develop HIC at the LHC Last Call for Predictions

  25. Dynamical realizationof general results • Description of the hadronic observables within hydrodynamically motivated parametrizations of freeze-out. (Borysova, Yu.S., Akkelin, Erazmus, Karpenko, Phys.Rev. C 73, 024903 (2006)) • Peculiarities of the final stage of the matter evolution. (Amelin, Lednicky, Malinina, Pocheptsov and Yu.S., Phys.Rev. C 73 044909 (2006)) • Hydrodynamic realizations of the final stages. (Yu.S., Iu.A. Karpenko. Heavy Ion Phys. 25/1 (2006) 141–147). • Peculiarities of initial thermodynamic conditions for corresponding dynamic models and • How to reach these initial conditions at pre-thermal (partonic) stage of ultra-relativistic heavy ion collisions (Akkelin, Gyulassy, Karpenko, Yu.S., Nazarenko, Werner) HIC at the LHC Last Call for Predictions

  26. The model of continuous emission (M.S.Borysova, Yu.S., S.V.Akkelin, B.Erazmus, Iu.A.Karpenko, Phys.Rev. C 73, 024903 (2006)) volume emission Induces space-time correlations for emission points surface emission Vi =0.35 fm/c HIC at the LHC Last Call for Predictions

  27. Results : spectra HIC at the LHC Last Call for Predictions

  28. Results : interferometry radii HIC at the LHC Last Call for Predictions

  29. Results : Ro/Rs HIC at the LHC Last Call for Predictions

  30. New hydro solutions: Yu.S., Karpenko: Heavy Ion Phys. 25/1 (2006) 141–147. The new class of analytic (3+1) hydro solutions For “soft” EoS, p=const Is a generalization of known Hubble flow and Hwa/Bjorken solution withcs=0 : HIC at the LHC Last Call for Predictions

  31. Thermodynamical quantities Density profile for energy and quantum number (particle number, if it conserves): with corresponding initial conditions. HIC at the LHC Last Call for Predictions

  32. Dynamical realization of freeze-out paramerization. (Yu.S., Iu.A. Karpenko. Heavy Ion Phys. 25/1 (2006) 141–147) • Particular solution for energy density: System is a finite in the transverse direction and is an approximately boost-invariant in the long- direction at freeze-out. HIC at the LHC Last Call for Predictions

  33. Dynamical realization of enclosed f.o. hypersurface Geometry : Rt,max Rt,0 decreases with rapidity increase. Approximate boost invariance HIC at the LHC Last Call for Predictions

  34. Numerical 3D anisotropic solutions of relativistic hydro with boost-invariance: freeze-out hypersurface HIC at the LHC Last Call for Predictions

  35. Pion emission function in transverse plane of Bjorken hydrodynamic tube intergrated over at HIC at the LHC Last Call for Predictions

  36. Developing of collective velocities in partonic matter at pre-thermalstage (Gyulassy, Karpenko, Yu.S., Nazarenko) • Distribution function at initial hypersurface 0=1 Venagopulan, 2003, 2005; Kharzeev 2006 • Equation for partonic free streaming: • Solution HIC at the LHC Last Call for Predictions

  37. Transverse velocities =3 fm/c =3 fm/c =1.5 fm/c =1.5 fm/c Landau-Lifshitz Eckart HIC at the LHC Last Call for Predictions

  38. Anisotropy of DF, =3 fm/c HIC at the LHC Last Call for Predictions

  39. Components of energy-momentum tensor in the comoving reference frame T_tt T_yy T_xx T_zz HIC at the LHC Last Call for Predictions

  40. Developing of transverse velocities: free streaming vs hydro HIC at the LHC Last Call for Predictions

  41. Conclusions • The plateau founded in the APSD behavior vs collision energy at SPS is associated, apparently, with the deconfinement phase transition at low SPS energies; a saturation of this quantity at the RHIC energies indicates the limiting Hagedorn temperature for hadronic matter. • It is shown that if the cubic power of effective temperature of pion transverse spectra grows with energy similarly to the rapidity density (that is roughly consistent with experimental data), then the interferometry volume is only slightly increase with collision energy. • An increase of initial of transverse flow with energy as well as isotropization of local spectra at pre-thermal stage could get explanation within partonic CGC picture. HIC at the LHC Last Call for Predictions

  42. EXTRA SLIDES HIC at the LHC Last Call for Predictions

  43. Interferometry volumes and pion densities at different (central) collision energies HIC at the LHC Last Call for Predictions

  44. The chemical potential HIC at the LHC Last Call for Predictions

  45. The statistical errors The statistical uncertainties caused by the experimental errors in the interferometry radiiin the AGS-SPS energy domain. The results demonstrate the range of statistical signicance ofnonmonotonic structures found for a behavior of pion averaged phase-space densities as functionof c.m. energy per nucleon in heavy ion collisions. HIC at the LHC Last Call for Predictions

  46. Ro/Rs Using gaussian approximation of CFs, where In the Bertsch-Pratt frame • Long emission time results in positive contribution to Ro/Rs ratio • Positive rout-tcorrelations give negative contribution to Ro/Rs ratio Experimental data : Ro/Rs1 HIC at the LHC Last Call for Predictions

  47. (2+1) n.-r. model with longitudinal boost-invariance [Akkelin, Braun-Munzinger, Yu.S. Nucl.Phys. A (2002)] • Momentum spectrum • Effective temperature • Interferometry volume • Spatially averaged PSD • Averaged PSD (APSD) HIC at the LHC Last Call for Predictions

  48. A numerical solution of the Boltzmann equation with the asymmetric initial momentum distribution. HIC at the LHC Last Call for Predictions

  49. Asymmetric initial coordinate distribution and scattered R.M.S. HIC at the LHC Last Call for Predictions

  50. HIC at the LHC Last Call for Predictions

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