Particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions

Yu. Karpenko

Bogolyubov Institute for Theoretical Physicsand

Kiev National Taras Shevchenko University

M.S. Borysova, Yu.M.Sinyukov, S.V.Akkelin, B.Erazmus, Iu.A.Karpenko, nucl-th/0507057 (to be published in Phys. Rev. C),

Yu.M. Sinyukov, Iu.A. Karpenko, nucl-th/0505041, nucl-th/0506002 (to be published in HIP)

Picture of evolution

Picture of evolution

Kpnd,

Hadronization

Initialstate

Pre-equilibratedstate

QGP and hydro Freeze-out

Hydro model

Sudden transition from local equilibrium to free streaming at some hypersurface

+ EoS p=p(ε)

ideal fluid :

(Ideal) hydrodynamics

Cooper-Frye prescription :

+ initial conditions

Continuous emission

Attempt to account nonzero emission time :(Blast-wave, Buda-Lund, …)

! No x-t correlations : at early times – only surface emission!! Emission function is not proportional to the l.eq. distribution function (Sinyukov et.al. PRL 2002)

Emission function “smeared” in :

Freeze-out

Space-like sectors Non-space-like sectors

Continuous emission

Enclosed freeze-out hypersurface, containing :

The idea of interferometry measurements

CF=1+cos qx|f(x,p)

p1

p2

x1

x2

q = p1- p2 , x = x1- x2

2

1 |q|

1/R02R0

f(x,p)

“General” parameterization at |q| 0 Podgoretsky’83, Bertsch-Pratt’95

Particles on mass shell & azimuthal symmetry 5 variables:q = {qx , qy , qz} {qout , qside , qlong}, pair velocity v = {vx,0,vz}

q0 = qp/p0 qv = qxvx+ qzvz

y side

x out transverse pair velocity vt

z long beam

Ri - Interferometry radii:

cos qx=1-½ (qx)2… exp(-Rx2qx

2 –Ry2qy

2 -Rz

2qz2)

Ro/Rs

Using gaussian approximation of CFs (q0),

Long emission time results in positive contribution to Ro/Rs ratioPositive rout-t correlations give negative contribution to Ro/Rs ratio

In the Bertsch-Pratt frame

where

Experimental data : Ro/Rs1

To describe Ro/Rs ratio with protracted particle emission, one needs positive rout-t correlations

The model of continuous emission

volumeemissio

n

surfaceemissio

n

Induces space-time correlations for emission points

(M.S.Borysova, Yu.M. Sinyukov, S.V.Akkelin, B.Erazmus, Iu.A.Karpenko,nucl-th/0507057, to be published in Phys. Rev. C)

Cooper-Frye prescription

Simplest modification of CFp(for non-space-like f.o. hypersurface):(Sinyukov, Bugaev)

Excludes particles that reenter the system crossing the outer side of surface in Cooper-Frye picture of emission.

Results : spectra

Results : interferometry radii

Results : Ro/Rs

Relativistic ideal hydrodynamics

+ EoS p=p(ε)

ideal fluid :

+(additional equations depicting charge conservation)

New hydro solution

The new class of analytic (3+1) hydro solutions (Yu.M.Sinyukov, Yu.A.Karpenko, nucl-th/0505041, nucl-th/0506002 - to be published in HIP)

For “soft” EoS, p=p0=const

Satisfies the condition of accelerationless :

(quasi-inertial flows similar to Hwa/Bjorken and Hubble ones).

New hydro solution

Is a generalization of known Hubble flow and Hwa/Bjorken solution with cs=0 :

Thermodynamical relations

Chemically equilibrated evolution

Chemically frozen case for particle number

Density profile for energy and quantum number (particle number, if it conserves):

with corresponding initial conditions.

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.

Freeze-out conditions

Impose a freeze-out at constant total energy density,

and presume that this HS is confined in a space-time 4-volume which belongs to the region of applicability of our solution with constant pressure.

Dynamical realization of enclosed f.o. hypersurface

Geometry :

Rt,max Rt,0 decreases with rapidity increase. No exact boost invariance!

Thermodynamics

Chemical potentials(T) for each particle sortSmoothly

decreases on

Observables from the latter calculations : spectra

Observables from the latter calculations : interferometry radii

Observables from the latter calculations : Ro/Rs ratio

Numerical hydro testing(T. Hirano, arXiv : nucl-th/0108004)

Conclusions

The continuous hadronic emission in A+A collisions can be taken into account by the (generalized) Cooper-Frye prescription for enclosed freeze-out hypersurface.

The phenomenological parameterization for enclosed hypersurface with positive (t-r) correlations can be reproduced by applying natural freeze-out criteria to the new exact solution of relativistic hydrodynamics.

The proton, pion an kaon single particle momentum spectra and pion HBT radii in central RHIC s=200 GeV Au+Au collisions are reproduced with physically reasonable set of the parameters that is similar in both approaches.

Conclusions

Successful description of data needs protracted hadronic emission (9 fm/c) from “surface” sector of the freeze-out hypersurface, and initial flows in transverse direction.

The fitting temperature is about 110 MeV on the “volume” part of hypersurface and 130-150 MeV on the “surface” part.

Thank you for your attention

Extra slides

Known relativistic hydro solutions

Hubble flow

Hwa/Bjorken solution

Biró solution

spherical symmetry

longitudinal boost invariance, cylindrical symmetry

longitudinal boost invariance

Kinetic description & sudden freeze-out

Duality in hydro-kinetic approach to A+A collisions (S.V. Akkelin, M.S. Borysova, Yu.M. Sinyukov, HIP, 2005)

Evolution of observables in a numerical kinetic model(N.S. Amelin, R. Lednicky, L.I. Malinina, Yu.M. Sinyukov, Phys.Rev.C); Yu.M.Sinyukov, proc. ISMD2005 & WPCF 2005