Kaon and pion femtoscopy in the hydrokinetic model of ultrarelativistic heavy-ion collisions

1. Kaon and pion femtoscopy in the hydrokinetic model of ultrarelativistic heavy-ion collisions Yu. M. Sinyukov Bogolyubov Institute for Theoretical Physics, Kiev Talk at the X GDRE Workshop “Heavy Ion with Ultrarelativistic Energies” SUBATRECH, Nantes, June 17 2010

2. OUTLOOK • 0.Evidences of collective/hydrodynamic behavior of the matter formed A+A . • I. Thermalization (is early thermalization really needed?), IC, HBT-puzzle and all • that… • II. The transition from very initial nonthermal state in HIC to • hydrodynamic stage. Phenomenological approach. • III. Matter evolution at chemically equilibrated stage. • IV. Matter evolution at non-equilibrated stage. HydroKinetic Model (HKM). • V. System’s decay and spectra formation. Whether it possible to apply Cooper-Frye prescription for continuously emitting and not equilibrated system? If possible, how? • VI. The HKM results for the top RHIC energies. Pion and kaon femtoscopy • VII. Energy dependence of the interferometry scales: SPS, RHIC, LHC

3. 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

6. Collective expansion of the fireball. • Observation of the longitudinal boost-inv. 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 !

7. 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 7

8. Pre-thermal transverse flow 8

9. 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) .

10. 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.

11. 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 11

12. 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.

13. 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

14. HydroKinetic Model (HKM) of A+A collisions I. Matter evolution in chemically equilibrated space-time zone 14

15. 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: where II. is CGC-like profile and are only fitting parameters in HKM

16. 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 Particle number ratios F. Karsch, PoS CPOD07:026, 2007 are baryon number and strangeness susceptibilities 16

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

18. “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 18

19. 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.

20. 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.

21. Possible problems of matching hydro with initially bumping IC RIDGES? 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)