Particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions Yu. Karpenko Bogolyubov Institute for Theoretical Physics and Kiev National Taras Shevchenko University M.S. Borysova, Yu.M.Sinyukov, S.V.Akkelin, B.Erazmus, Iu.A.Karpenko, nucl- th/ (to be published in Phys. Rev. C), Yu.M. Sinyukov, Iu.A. Karpenko, nucl-th/ , nucl-th/ (to be published in HIP)

Picture of evolution

 K  p  n  d, Hadronization Initial state Pre-equilibrated state 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 q  x  |f(x,p) p 1 p 2 x1x1 x 2 q = p 1 - p 2,  x = x 1 - x 2  2 1 |q| 1/R 0 2R 0 f(x,p)

“General” parameterization at |q|  0 Podgoretsky’83, Bertsch-Pratt’95 Particles on mass shell & azimuthal symmetry  5 variables: q = {q x, q y, q z }  {q out, q side, q long }, pair velocity v = {v x,0,v z } q 0 = qp/p 0  qv = q x v x + q z v z y  side x  out  transverse pair velocity v t z  long  beam R i - Interferometry radii:  cos q  x  =1-½  (q  x) 2  …  exp(-R x 2 q x 2 –R y 2 q y 2 -R z 2 q z 2 )

R o /R s Using gaussian approximation of CFs (q  0), Long emission time results in positive contribution to R o /R s ratio Positive r out -t correlations give negative contribution to R o /R s ratio In the Bertsch-Pratt frame where Experimental data : Ro/Rs  1

To describe R o /R s ratio with protracted particle emission, one needs positive r out -t correlations

The model of continuous emission volume emission surface emission Induces space- time correlations for emission points (M.S.Borysova, Yu.M. Sinyukov, S.V.Akkelin, B.Erazmus, Iu.A.Karpenko, nucl-th/ , 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 : R o /R s

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/ , nucl-th/ to be published in HIP) For “soft” EoS, p=p 0 =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 c s =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 : R t,max R t,0 decreases with rapidity increase. No exact boost invariance!

Thermodynamics Chemical potentials  (T) for each particle sort Smoothly decreases on t :

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/ )

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 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