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

CERN May HIC 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

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

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

CERN May HIC at the LHC Last Call for Predictions 5 “Soft Physics” measurements x t A A ΔωKΔωK p=(p 1 + p 2 )/2 q= p 1 - p 2 (QS) Correlation function Space-time structure of the matter evolution, e.g., T ch and μ ch soon after hadronization (chemical f.o.) Radial flow

CERN May 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).

CERN May HIC at the LHC Last Call for Predictions 7 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. Empirical observations and theoretical problems (2)

CERN May 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, (2002); S.V.Akkelin. Yu.S. : Phys. Rev. C 70, (2004); Phys.Rev. C 73, (2006); Nucl. Phys. A 774, 647 (2006) ; M.S. Borysova, Yu.S., Akkelin, Erazmus, Karpenko, Phys.Rev. C 73, (2006); N.S. Amelin, R. Lednicky, L. V. Malinina, T. A. Pocheptsov and Yu.S. Phys.Rev. C 73, (2006); Yu.S, Act Phys Pol B 37, 3343 (2006)

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

CERN May HIC at the LHC Last Call for Predictions 10 Evolution of T eff, APSD and particle density APSD and part. densities at hadronization time =7.24 fm/c (solid line) and at kinetic freeze -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]

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

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

CERN May HIC at the LHC Last Call for Predictions 13 Results and ideas 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.

CERN May HIC at the LHC Last Call for Predictions 14 Approximately conserved observables APSD - Phase-space density averaged over some hypersurface, where all particles are already free and over momen- 0. (Bertsch) tum at fixed particle rapidity, y=0. (Bertsch) t z Chemical. f.-o. Thermal f.-o. APSD is conserved during isentropic and chemically frozen evolution: n(p) is single-, n(p 1, p 2 ) is double (identical) particle spectra, correlation function is C=n(p 1, p 2 )/n(p 1 )n(p 2 ) p=(p 1 + p 2 )/2 q= p 1 - p 2 S. Akkelin, Yu.S. Phys.Rev. C (2004):

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

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

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

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

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

CERN May 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 (2004)); The is integral of motion; is conserved because of chemical freeze-out. 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 is fixed

CERN May 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 for central Pb+Pb (Au+Au) collisions from AGS to RHIC experiments measured near midrapidity. S. Kniege et al. (The NA49 Collaboration), J. Phys. G30, S1073 (2004).

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

CERN May 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 T H =T c (  B = 0). grows with A is fixed

CERN May 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 p max 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

CERN May HIC at the LHC Last Call for Predictions 25 Dynamical realization of general results Description of the hadronic observables within hydrodynamically motivated parametrizations of freeze-out. (Borysova, Yu.S., Akkelin, Erazmus, Karpenko, Phys.Rev. C 73, (2006) ) Peculiarities of the final stage of the matter evolution. (Amelin, Lednicky, Malinina, Pocheptsov and Yu.S., Phys.Rev. C (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)

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

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

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

CERN May HIC at the LHC Last Call for Predictions 29 Results : R o /R s

CERN May 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 with c s =0 :

CERN May 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.

CERN May HIC at the LHC Last Call for Predictions 32 Dynamical realization of freeze-out paramerization. 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. (Yu.S., Iu.A. Karpenko. Heavy Ion Phys. 25/1 (2006) 141–147)

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

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

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

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

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

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

CERN May 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

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

CERN May 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.

CERN May HIC at the LHC Last Call for Predictions 42 EXTRA SLIDES

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

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

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

CERN May HIC at the LHC Last Call for Predictions 46 R o /R s Using gaussian approximation of CFs, Long emission time results in positive contribution to Ro/Rs ratio Positive r out -t correlations give negative contribution to R o /R s ratio In the Bertsch-Pratt frame where Experimental data : Ro/Rs  1

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

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

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

CERN May HIC at the LHC Last Call for Predictions 50

CERN May HIC at the LHC Last Call for Predictions 51 Numerical 3D anisotropic solutions of relativistic hydro with boost-invariance: evolution of the effective radii