Further development of the HydroKinetic Model (hHKM) and

description of the RHIC and LHC A+A data

Yu. M. Sinyukov

Bogolyubov Institute for Theoretical Physics

Kiev

In collaboration with Iu. Karpenko

Tokyo WPCF-2011 20-24 September

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HydroKinetic Model(HKM)

of A+A collisions

I. Matter evolution in chemically

equilibrated space-time zone

t

r_

outt

Tch

Locally (thermally & chemically) equilibrated evolution and initial

conditions (IC)

IC for central Au+Au collisionsThe “effective" initial distribution is the one which

being used in the capacity of initial condition bring the averagehydrodynamic results for fluctuating initial conditions:I.

Initial transv. rapidity profiles:

and are only fitting parameters in HKM

is Glauber-like profile

II. is CGC-like profile where

Equation of state in (almost) equilibrated zone

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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

t

x

outt

Tch

HKMII. Evolution of the

hadronic matter in non-equlibrated zone.

Decay of the system and spectra formation

Hybrid models: HYDRO + UrQMD (Bass, Dumitru (2000))

t

z

t

r

constr

constzt

at

: 22hadr 0zat )(:hadr 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);

An opacity for the particles moving inside the system is ignored.

At r-periphery of space-like hypsurf. the system is far from l.eq.

)(r

t

HYDRO

UrQMD

UrQMDhadrhadr

The initial conditions for hadronic cascade models should be based on non-local equilibrium distributions

Hybrid Hydrokinetics

Yu.S., Akkelin, Hama: PRL 89 , 052301 (2002); + Karpenko: PRC 78, 034906 (2008); Karpenko, Yu.S. 81, 054903 (2010)

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; UrQMD

Complete algorithm includes: • solution of equations of ideal hydro;• calculation of non-equilibrium DF and emission function in first approximation;o 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;o Calculation of “exact” DF and emission function; UrQMD o Evaluation of spectra and correlations.

Boltzmann eqs (integral form)

Basic equations in HKM

Relax. time approximation for emission function (Yu.S. , Akkelin, Hama PRL, 2002)

where

Hydro equations (4 eqs)

Equations for decays of resonances into fluid (359 eqs)

EoS for where

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.

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

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 energydensity

Initial transverse flows

Glauber IC 16.5 GeV/fm3 0.22

CGC IC 19.5 GeV/fm3 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.

Iu. Karpenko, Yu.S. PLB 688, 50 (2010)

Predictions for LHC and comparison with the ALICE results

essentially non-flat initial energy density distributions (Gaussian, Glauber, CGC);

more hard 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) ;

+ An account for chemically/thermally non-equilibrium evolution of

strongly interacting system and its gradual decay 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)

Initial conditions for different collision energies

Fitting parameter at

Glauber IC Max initial energydensity

Initial transverse flows

SPS top energy

9.0 GeV/fm3

0.17

RHIC top energy

16.5 GeV/fm3 0.25

LHC-1 40 GeV/fm3 0.25

LHC-2 40 GeV/fm3 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 ATeV

For LHC-1

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

Side- radii at top SPS, RHIC and predictions for the two LHC

energies in HKM

The ALICE Collaboration, Phys. Lett. B696, 328 (2011)

Out- radii at top SPS, RHIC and predictions for the two LHC energies in HKM

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Long-radii at top SPS, RHIC and predictions for the two LHC energies in HKM

~20% less

Out-to-side ratio. Predictions for LHC.

Comparison of Ro/Rs results from ALICE LHC with model predictions (figures from ALICE Coll. paper)

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Ro/Rs ratio and initial flows (2006)

The ratio as function on initial energy

density

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1

2

At some p

For details see Iu. Karpenko, Yu.S. PLB 688, 50 (2010)

More energy density, more pre-thermal flows stronger t-r correlations at surface freeze-out less ratio.

Emission functions for top SPS, RHIC and LHC energies

LHC HBT Puzzle (?)

In the case of isentropic and chemically frozen expansion of hadron-resonance gas the interferometry scales mostly defined by the initial sizes and does not change much with energy increase : Akkelin, Yu.S. : PRC 70 . 064901 (2004); PRC 73 034908 (2006)

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x

y

¿

HKM

UrQMD

Hybrid HKM (hHKM): matching of HKM and UrQMD at the space-like hypersurface

A dissipation in the systems is responsible for formation of the HBT radii: Yu.S. et al PRL 89 , 052301 (2002)

Femtoscopy scales for RHIC and LHC in hHKM

See details in Poster 234: Karpenko, Yu.S., Werner “First results from hHKM for RHIC and LHC”

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Suppression parameter and transverse spectra of charged particles in hHKM

¸

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Role of non-dissipative stage in formation of large Vint at LHC

hHKM

Vi nt(A;dN=dy)

Conclusion for femtoscopy at LHC

The main mechanisms, that were considering as explaining 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 plays an important role at LHC.

The comparison of vs for pp and AA collisions conforms probably the result of Akkelin, Yu.S. : PRC 70 . 064901 (2004); PRC 73 034908 (2006) that the interferometry volume depends not only on multiplicity but also on initial size of colliding systems.

Vint dN=d́

THANK YOU !

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