Energy dependence of femtoscopy scales in A+A collisions and predictions for LHC

1. Energy dependence of femtoscopy scales in A+A collisions and predictions for LHC Yu. M. Sinyukov Bogolyubov Institute for Theoretical Physics, Kiev In collaboration with Yu. Karpenko Workshop on Particle Correlations and Femtoscopy: WPCF-2010 Kiev, 14-18 September, 2010

2. 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 What is the nature of this matter atthe early collision stage? Whether does the matter becomes thermal? Particle number ratios are well reproduced inideal gas model with 2 parameters: T, for collision energies from AGS to RHIC: thermal+chemical equilibrium

3. 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 particlespecies (non-relativistic case) : radial collective flow • Observation of elliptic flows: HYDRODYNAMICS !

4. Expecting Stages of Evolution in Ultrarelativistic A+A collisions t Relatively small space-time scales (HBT puzzle) 8-20 fm/c Early thermal freeze-out: T_th Tch 150 MeV 7-8 fm/c Elliptic flows 1-3 fm/c Early thermalization at 0.5 fm/c 0.2?(LHC) or strings 4

5. Pre-thermal transverse flow 5

6. Collective velocities developed between =0.3 and =1.0 fm/c Central collisions 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 freestreaming and free expansion of classical field. The results are compared with thehydrodynamic evolution of perfect fluid with hard equation of state p = 1/3 epsilon startedat.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) .

7. Collective velocities and their anisotropy developed between =0.3 and =1.0 fm/c Non-central collisions b=6.3 fm 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 freestreaming. The results are compared with thehydrodynamic evolution of perfect fluid with hard equation of state p = 1/3 epsilon startedat.Impact parameter b=6.3 fm.

8. Basic ideas for the early stage: developing of pre-thermal flows Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko Braz.J.Phys. 37 (2007) 1031. For nonrelativistic gas For thermal and non-thermal expansion at : Hydrodynamic expansion: gradient pressure acts So, even if : and Free streaming: Gradient of density leads to non-zero collective velocities In the case of thermalization at later stage it leads to spectra anisotropy 8

9. Summary-1 Yu.S., Nazarenko, Karpenko: Acta Phys.Polon. B40 1109 (2009) • 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.

10. Phenomenological model of pre-thermal evolution Akkelin, Yu.S. PRC81, 064901 (2010) Matching of nonthermal initial conditions and hydrodynamic stage • 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 . Eqs: IC: where

11. HydroKinetic Model (HKM) of A+A collisions I. Matter evolution in chemically equilibrated space-time zone 11

12. Locally (thermally & chemically) equilibrated evolution and initial conditions (IC) t Tch 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: x is Glauber-like profile I. Initial rapidity profiles: Yu. Karpenko talk at this Workshop: where II. is CGC-like profile and are only fitting parameters in HKM

13. Equation of state in (almost) equilibrated zone 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 Yu. Karpenko talk at this Workshop: Particle number ratios F. Karsch, PoS CPOD07:026, 2007 are baryon number and strangeness susceptibilities 13

14. HKM II. Evolution of the hadronic matter in non-equlibrated zone. t Decay of the system and spectra formation Tch x

15. “Soft Physics” measurements A x Landau, 1953 t ΔωK Cooper-Frye prescription (1974) A p=(p1+ p2)/2 q= p1- p2 QS correlation function Space-time structure of the matter evolution: Long p1 p Out p2 BW Side 15

16. Cooper-Frye prescription (CFp) t t z 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.

17. Hybrid models: HYDRO + UrQMD (Bass, Dumitru (2000)) t t t UrQMD HYDRO z r The initial conditions for hadronic cascade models should be based on non-local equilibrium distributions • 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.

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

20. Continuous Emission “The back reactionof the emission on the fluid dynamics is not reduced justto energy-momen-tum recoiling of emitted particles on theexpan-ding thermal medium, but also leads to a re-arrangementof the medium, producing a devia-tion of its state from thelocal equilibrium, ac-companied by changing of the localtemperature, densities, and collective velocity field. Thiscomplex effect is mainly a consequence of the fact that theevolution of the single finite system of hadrons cannot be splitinto the two compo-nents: expansion of the interacting locallyequi-librated medium and a free stream of emitted particles,which the system consists of. Such a splitting, accountingonly for the momentum-energy conservation law, contradictsthe unde-rlying dynamical equations such as a Boltzmannone.” t x F. Grassi, Y. Hama, T. Kodama (1995) Akkelin, Hama, Karpenko, Yu.S PRC 78 034906 (2008)

21. Yu.S. , Akkelin, Hama: PRL89 , 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 escape probabilities and deviations (even strong) • of distribution functions [DF] from local equilibrium; • 3. accounts for conservation laws 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.

22. Boltzmann equations and probabilities of particle free propagation Boltzmann eqs (differential form) and are G(ain), L(oss) terms for p. species Probability of particle free propagation (for each component ) 22

23. Spectra and Emission function Boltzmann eqs (integral form) Index is omitted everywhere Spectrum Relax. time approximation for emission function (Yu.S. , Akkelin, Hama PRL, 2002) For (quasi-) stable particles 23

24. Kinetics and hydrodynamics below Tch =165 MeV For hadronic resonances & where

25. 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. 25

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

27. System's decoupling and spectra formation Emission function For pion emission isthetotalcollisionrateofthepion, carrying momentump withallthehadronshinthesysteminavicinityofpointx. isthespace-timedensityofpionproductioncausedbygradualdecaysduringhydrodynamicevolutionofallthesuitableresonancesHincludingcascadedecays The cross-sections in the hadronic gas are calculated in accordance with UrQMD . 27

28. The following factors reduces space-time scales of the emission and Rout/Rside ratio: Akkelin, Hama, Karpenko, Yu.S, PRC 78, 034906 (2008) 28 • 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)

29. Energy dependence of space-time scales Iu. Karpenko, Yu.S. PLB 688, 50(2010)

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

31. Long- radii at top SPS, RHIC and two LHC energies in HKM

32. Side- radii at top SPS, RHIC and two LHC energies in HKM

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

34. Out- to side- ratio at top SPS, RHIC and two LHC energies in HKM

35. Emission functions for top SPS, RHIC and LHC energies

36. The ratio as function on in-flow and energy At some p 2 1 2 1

37. Conclusion • The main mechanisms that lead to the paradoxical behavior of the interferometry scales, are exposed. • 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. • The process of decoupling the fireballs created in Au + Au collision at RHIC energies lasts from about 8 to 20 fm/c, more than half the fireball’s 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. • At LHC energies the decay of the central part of the fireball is estimated as from 10 to 27 fm/c.

38. BACK UP SLIDES

39. 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))

40. Saddle point approximation Spectrum Emission density where Normalization condition Eqs for saddle point : Physical conditions at NPQCD-2009 40 Dnepropetrovsk May 3 2009

41. Cooper-Frye prescription Spectrum in new variables Emission density in saddle point representation Temporal width of emission Generalized Cooper-Frye f-la NPQCD-2009 41 Dnepropetrovsk May 3 2009

42. Generalized Cooper-Frye prescription: t 0 Escape probability r RANP08 42 Yu.S. (1987)-particle flow conservation; K.A. Bugaev (1996) (current form) 42 Nov 3-6

43. Momentum dependence of freeze-out Here and further for Pb+Pb collisions we use: initial energy density Pt-integrated EoS from Lattice QCD when T< 160 MeV, and EoS of chemically frozen hadron gas with 359 particle species at T< 160 MeV. RANP08 43 Nov 3-6

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

45. The pion emission function for different pT in hydro-kinetic model (HKM). The isotherms of135 MeV (bottom) is superimposed.

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

47. Conditions for the utilization of the generalized Cooper-Frye prescription • 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 relaxationtime ( 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 saddlepoint methodis violated does not affect essentially theparticle momentum spectrum. 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) 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 necessarilyencloses the initially dense matter. NPQCD-2009 47 Dnepropetrovsk May 3 2009

48. “Soft Physics” measurements A x Landau, 1953 t ΔωK Cooper-Frye prescription (1974) A p=(p1+ p2)/2 q= p1- p2 QS correlation function Space-time structure of the matter evolution: Long p1 p Out p2 BW Side 48

49. 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 functionat fixed momentum p in an appropriate regionof r.