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Matter evolution in A+A collisions in the light of recent ALICE LHC results Yu. M. Sinyukov Bogolyubov Institute for Theoretical Physics NPQCD May 3 - 6, 2011

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Soft Physics measurements 2 xLxL 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: Landau, 1953 p p1p1 p2p2 Long Side Out BW lengths of homogeneity in expanding system Radial flow xTxT

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The evidences of space-time evolution of the thermal matter in A+A collisions: Rough estimate of the fireball lifetime for Au+Au Gev: In p+p all femto-scales are A+A is not some kind of superposition of the of order 1 fm ! individual collisions of nucleons of nuclei The phenomenon of space-time evolution of the strongly interacting matter in A+A collisions Particle number ratios are well reproduced in ideal gas model with 2 parameters: T, for collision energies from AGS to RHIC: thermal+chemical equilibrium What is the nature of this matter at the early collision stage? Whether does the matter becomes thermal?

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Collective expansion of the fireball. Observation of the longitudinal expansion: It was conformed by NA35/NA49 Collaborations (CERN), 1995 ! Observation of transverse (radial) collective flows: Effective temperature for different particle species (non-relativistic case) : radial collective flow Observation of elliptic flows: HYDRODYNAMICS !

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Does hydro work at LHC 5 The ALICE experiment suggests that the quark-gluon plasma remains a strongly coupled liquid, even at temperatures that are 30% greater than what was available at RHIC. The plot shows the elliptic flow parameter v2 (a measure of the coupling in the plasma) at different heavy-ion collision energies, based on several experiments (including the new data from ALICE [1] ) E. Shuryak, Physics 3,105 (2010) [1] K. Aamodt et al. (ALICE Collaboration), Phys. Rev. Lett. 105, 252302 (2010). ?

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6 Expecting Stages of Evolution in Ultrarelativistic A+A collisions Early thermalization at 0.5 fm/c 0.2?(LHC) Elliptic flows t Relatively small space-time scales, R out /R side ~ 1 (HBT puzzle) Early thermal freeze-out: T_th Tch 150 MeV 8-20 fm/c 7-8 fm/c 1-3 fm/c or strings

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7 Interferometry radii Borysova, Yu.S., Akkelin,Erazmus, Karpenko: PRC 73, 024903 (2006)

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8 Duration of particle emission is taken into account by means of enclosed freeze-out hypersurface: v i =0.35 volume emission surface emission

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9 Ro/Rs ratio and initial flows

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Collective velocities developed between =0.3 and =1.0 fm/c Collective velocity developed at pre-thermal stage from proper time tau_0 =0.3 fm/c by supposed thermalization time tau_th = 1 fm/c for scenarios of partonic free streaming and free expansion of classical field. The results are compared with the hydrodynamic evolution of perfect fluid with hard equation of state p = 1/3 epsilon started at. Impact parameter b=0. Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko Braz.J.Phys. 37 (2007) 1031. Yu.S., Nazarenko, Karpenko: Acta Phys.Polon. B40 1109 (2009). Central collisions

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Collective velocity developed at pre-thermal stage from proper time =0.3 fm/c by supposed thermalization time tau_i = 1 fm/c for scenarios of partonic free streaming. The results are compared with the hydrodynamic evolution of perfect fluid with hard equation of state p = 1/3 epsilon started at. Impact parameter b=6.3 fm. Collective velocities and their anisotropy developed between =0.3 and =1.0 fm/c Non-central collisions b=6.3 fm

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13 Hydrodynamic expansion: gradient pressure acts Free streaming: Gradient of density leads to non-zero collective velocities For nonrelativistic gas So, even if and : Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko Braz.J.Phys. 37 (2007) 1031. :at For thermal and non-thermal expansion In the case of thermalization at later stage it leads to spectra anisotropy Basic ideas for the early stage: developing of pre-thermal flows

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Summary-1 Yu.S., Nazarenko, Karpenko: Acta Phys.Polon. B40 1109 (2009) 14 The initial transverse flow in thermal matter as well as its anisotropy are developed at pre-thermal - either partonic, string or classical field (glasma) - stage with even more efficiency than in the case of very early perfect hydrodynamics. Such radial and elliptic flows develop no matter whether a pressure already established. The general reason for them is an essential finiteness of the system in transverse direction. The anisotropy of the flows transforms into asymmetry of the transverse momentum spectra only of (partial) thermalization happens. So, the results, first published in 2006, show that whereas the assumption of (partial) thermalization in relativistic A + A collisions is really crucial to explain soft physics observables, the hypotheses of early thermalization at times less than 1 fm/c is not necessary.

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15 Akkelin, Yu.S. PRC 81, 064901 (2010) If some model (effective QCD theory) gives us the energy-momentum tensor at time, one can estimate the flows and energy densities at expected time of thermalization, using hydrodynamic equation with (known) source terms. This phenomenological approach is motivated by Boltzmann equations, accounts for the energy and momentum conservation laws and contains two parameters: supposed time of thermalization and initial relaxation time. where IC:Eqs: Matching of nonthermal initial conditions and hydrodynamic stage

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t x T ch Locally (thermally & chemically) equilibrated evolution and initial conditions (IC) IC for central Au+Au collisions The effective" initial distribution is the one which being used in the capacity of initial condition bring the average hydrodynamic results for fluctuating initial conditions: I. Initial rapidity profiles: and are only fitting parameters in HKM is Glauber-like profile II. is CGC-like profile where

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Equation of state in (almost) equilibrated zone 18 EoS from LattQCD (in form proposed by Laine & Schroder, Phys. Rev. D73, 2006). MeV Crossover transition, LattQCD is matched with an ideal chemically equilibrated multicomponent hadron resonance gas at Particle number ratios are baryon number and strangeness susceptibilities F. Karsch, PoS CPOD07:026, 2007

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t x T ch

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Cooper-Frye prescription (CFp) t z t r CFp gets serious problems: Freeze-out hypersurface contains non-space-like sectors artificial discontinuities appears across Sinyukov (1989), Bugaev (1996), Andrelik et al (1999); cascade models show that particles escape from the system about whole time of its evolution. Hybrid models (hydro+cascade) and the hydro method of continuous emission starts to develop.

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Hybrid models: HYDRO + UrQMD ( Bass, Dumitru (2000) ) t z t r The problems: the system just after hadronization is not so dilute to apply hadronic cascade models; hadronization hypersurface contains non-space-like sectors (causality problem: Bugaev, PRL 90, 252301, 2003); The average energy density and pressure of input UrQMD gas should coincide with what the hadro gas has just before switching. At r-periphery of space-like hypsurf. the system is far from l.eq. t HYDRO UrQMD The initial conditions for hadronic cascade models should be based on non-local equilibrium distributions

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Possible problems of matching hydro with initially bumping IC The example of boost-invariant hydroevolution for the bumping IC with four narrow high energy density tubes (r= 1 fm) under smooth Gaussian background (R=5.4 fm) RIDGES?

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Continuous Emission Hydrokinetic approach t x F. Grassi, Y. Hama, T. Kodama (1995) The evolution of the single finite system of hadrons cannot be split into the two compo- nents: expansion of the interacting locally equi- librated medium and a free stream of emitted particles, which the system consists of. Such a splitting, accounting only for the momentum- energy conservation law, contradicts the unde- rlying dynamical equations such as a Boltzmann one. Yu.S., Akkelin, Hama: PRL 89, 052301 (2002 )

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Yu.S., Akkelin, Hama: PRL 89, 052301 (2002); + Karpenko: PRC 78, 034906 (2008). Hydro-kinetic approach MODEL is based on relaxation time approximation for emission function of relativistic finite expanding system; provides evaluation of emission function based on escape probabilities with account of deviations (even strong) of distribution functions [DF] from local equilibrium; o accounts for conservation laws: back reaction of the particle emission to the hydro-evolution at the particle emission; Complete algorithm includes: solution of equations of ideal hydro; calculation of non-equilibrium DF and emission function in first approximation; solution of equations for ideal hydro with non-zero left-hand-side that accounts for conservation laws for non-equilibrium process of the system which radiated free particles during expansion; Calculation of exact DF and emission function; Evaluation of spectra and correlations.

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and are G(ain), L(oss) terms for p. species Boltzmann eqs (differential form) Probability of particle free propagation (for each component ) Boltzmann equations and probabilities of particle free propagation

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84 Boltzmann eqs (integral form) Spectra and Emission function Index is omitted everywhere Spectrum Relax. time approximation for emission function (Yu.S., Akkelin, Hama PRL, 2002) For (quasi-) stable particles

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Kinetics and hydrodynamics below T ch =165 MeV For hadronic resonances & where

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Equation of state in non-equilibrated zone EoS MeV Pressure and energy density of multi- component Boltzmann gas At hypersurface the hadrons are in chemical equilibrium with some barionic chemical potential which are defind from particle number ratio (conception of chemical freeze-out). Below we account for the evolution of all N densities of hadron species in hydro calculation with decay resonances into expanding fluid, and compute EoS dynamically for each chemical composition of N sorts of hadrons in every hydrodynamic cell in the system during the evolution. Using this method, we do not limit ourselves by chemically frozen or chemically equilibrated evolution, keeping nevertheless thermodynamically consistent scheme.

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EoS used in HKM calculations for the top RHIC energy The gray region consists of the set of the points corresponding to the different hadron gas compositions at each occurring during the late nonequilibrium stage of the evolution.

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88 System's decoupling and spectra formation Emission function For pion emission is the total collision rate of the pion, carrying momentum p with all the hadrons h in the system in a vicinity of point x. is the space-time density of pion production caused by gradual decays during hydrodynamic evolution of all the suitable resonances H including cascade decays The cross-sections in the hadronic gas are calculated in accordance with UrQMD.

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Iu. Karpenko, Yu.S. PRC 81, 054903 (2010)

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PARAMETERS for the RHIC TOP ENERGY In CGC approach at RHIC energies this energy density corresponds to the value Fitting parameter at In CGC approach at RHIC energies the value is used (T. Lappi, J.Phys. G, 2008) Max initial energy density Initial transverse flows Glauber IC 16.5 GeV/fm 3 0.22 CGC IC 19.5 GeV/fm 3 0.21 Parameter absorbs unknown portion of the prethermal flows, the viscosity effects in the QGP and, in addition, the event-by-event fluctuations of the initial conditions which also lead to an increase of the effective transverse flows in the observed inclusive spectra.

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Pion, kaon and proton emission densities (Gaussian IC, vacuum c.s.) 93 T=145 MeV T=80 MeV At the point of maximal pion emission P

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Conclusion for RHIC The HKM allows one to restore the initial conditions and space-time picture of the matter evolution in central Au + Au collisions at the top RHIC energy. The analysis, which is based on a detailed reproduction of the pion and kaon momentum spectra and measured femtoscopic scales, demonstrates that basically the pictures of the matter evolution and particle emission are similar at both Glauber and CGC IC with, however, different initial maximal energy densities: it is about 20% more for the CGC IC. The process of decoupling the fireballs created in Au + Au collision lasts from about 8 to 20 fm/c, more than half the fireballs total lifetime. The temperatures in the regions of the maximal emission are different at the different transverse momenta of emitting pions: T 75–110 MeV for pT = 0.2 GeV/c and T 130–135 MeV for pT = 1.2GeV/c. A comparison of the pion and kaon emissions at the same transverse mass demonstrates the similarity of the positions of emission maxima, which could point out to the reason for an approximate m T -scaling.

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Iu. Karpenko, Yu.S. PLB 688, 50 (2010) Predictions for LHC and comparison with the ALICE results

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essentially non-flat initial energy density distributions (Gaussian, Glauber, CGC); more hard transition EoS, corresponding to cross-over (not first order phase transition!); fairly strong transverse flow at the late stage of the system evolution. It is caused by: developing of flows at very early pre-thermal stage; additional developing of transv. flow due to shear viscosity (Teaney, 2003); effective increase of transv. flow due to initially bumping structure (Grassy, Hama, Kodama – 2008) ; + correct description of evolution and decay of strongly interacting and chemically/thermally non-equilibrated system after hadronisation! Karpenko, Yu.S. PRC 81, 054903 (2010) The following factors allows to describe the space- time scales of emission and Rout/Rside ratio: Akkelin, Hama, Karpenko, Yu.S, PRC 78, 034906 (2008)

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Initial conditions for different collision energies Fitting parameter at Glauber IC Max initial energy density Initial transverse flows SPS top energy 9.0 GeV/fm 3 0.17 RHIC top energy 16.5 GeV/fm 3 0.25 LHC-1 40 GeV/fm 3 0.25 LHC-2 40 GeV/fm 3 0.25 Parameter absorbs unknown portion of the prethermal flows, the viscosity effects in the QGP and, in addition, the event-by-event fluctuations of the initial conditions which also lead to an increase of the effective transverse flows in the observed inclusive spectra. For sqrt(s)=2.76 ATeVFor LHC-1

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Pion spectra at top SPS, RHIC and two LHC energies in HKM

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Side- radii at top SPS, RHIC and two LHC energies in HKM The ALICE Collaboration, Phys. Lett. B696, 328 (2011)

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Out- radii at top SPS, RHIC and two LHC energies in HKM 100

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- Long-radii at top SPS, RHIC and two LHC energies in HKM ~20% less

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Out-to-side ratio

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Comparison with others model predictions

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The ratio as function on initial energy density 12 1 2 At some p For details see Iu. Karpenko, Yu.S. PLB 688, 50 (2010)

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Emission functions for top SPS, RHIC and LHC energies

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LHC HBT Puzzle (?)

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Hybrid HKM (first results) 107

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Nantes July 15, 2009 108 Role of non-dissipative stage in formation of large Vint at LHC

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Conclusion for femtoscopy at LHC The main mechanisms, that were considering as explaning the paradoxical behavior of the interferometry scales, are conformed experimentally by ALICE LHC. In particular, decrease of ratio with growing energy and saturation of the ratio at large energies happens due to a magnification of positive correlations between space and time positions of emitted pions and a developing of pre-thermal collective transverse flows. Some underestimate of overall value of the radii (interferometry volume probably can be solved in HKM by switching to UrQMD at the temperatures 130-140 MeV. Viscosity in QGP should be included in the model. Non-thermal stage at the late times play an important role at LHC. Event by event analysis.

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THANK YOU ! 110

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BACK UP SLIDES

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Momentum transverse spectra of protons in HKM for top RHIC energy and different types of profiles (CGC and Glauber) of initial energy density without and with including of the mean field effect for protons (12% of the proton transverse rapidity field off in the interval (0-1))

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Generalized Cooper-Frye prescription: IF for each momentum p, there is a region of r where the emission function has a sharp maximum with temporal width. The width of the maximum, which is just the relaxation time ( inverse of collision rate), should be smaller than the corresponding temporal homogeneity length of the distribution function: (1% accuracy!!!) Then the momentum spectra can be presented in Cooper-Frye form despite it is, in fact, not sadden freeze-out and the decaying region has a finite temporal width. Also, what is important, such a generalized Cooper-Frye representation is related to freeze-out hypersurface that depends on momentum p and does not necessarily encloses the initially dense matter. Akkelin, Hama, Karpenko, Yu.S, PRC 78, 034906 (2008) Yu.S., Akkelin, Karpenko Act. Phys. Polon. 40, 1025 (2009)

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The pion emission function for different pT in hydro-kinetic model (HKM) The isotherms of 80 MeV is superimposed.

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The pion emission function for different pT in hydro-kinetic model (HKM). The isotherms of 135 MeV (bottom) is superimposed.

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Transverse momentum spectrum of pi in HKM, compared with the sudden freeze-out ones at temperatures of 80 and 160 MeV with arbitrary normalizations.

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Dnepropetrovsk May 3 2009 NPQCD-2009 117 Saddle point approximation Emission density Spectrum where Normalization condition Eqs for saddle point : Physical conditions at

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Dnepropetrovsk May 3 2009 NPQCD-2009 118 Cooper-Frye prescription Spectrum in new variables Emission density in saddle point representation Temporal width of emission Generalized Cooper-Frye f-la

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Nov 3-6 RANP08 119 Generalized Cooper-Frye prescription: 119 r t 0 Escape probability Yu.S. (1987)-particle flow conservation; K.A. Bugaev (1996) (current form)

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Nov 3-6 RANP08 120 Momentum dependence of freeze-out Here and further for Pb+Pb collisions we use: initial energy density EoS from Lattice QCD when T< 160 MeV, and EoS of chemically frozen hadron gas with 359 particle species at T< 160 MeV. Pt-integrated

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Dnepropetrovsk May 3 2009 NPQCD-2009 121 Conditions for the utilization of the generalized Cooper-Frye prescription i)For each momentum p, there is a region of r where the emission function has a sharp maximum with temporal width. ii) The width of the maximum, which is just the relaxation time ( inverse of collision rate), should be smaller than the corresponding temporal homogeneitylength of the distribution function: 1% accuracy!!! iii) The contribution to the spectra from the residual region of r where the saddle point method is violated does not affect essentially the particle momentum spectrum. Then the momentum spectra can be presented in Cooper-Frye form despite it is, in fact, not sadden freeze-out and the decaying region has a finite temporal width. Also, what is very important, such a generalized Cooper-Frye representation is related to freeze-out hypersurface that depends on momentum p and does not necessarily encloses the initially dense matter. iiii) The escape probabilities for particles to be liberated just from the initial hyper-surface t0 are small almost in the whole spacial region (except peripheral points)

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122 Conclusions The CFp might be applied only in a generalized form, accounting for the direct momentum dependence of the freeze-out hypersurface corresponding to the maximum of the emission function at fixed momentum p in an appropriate region of r.

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