particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions
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Particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions. Yu. Karpenko Bogolyubov Institute for Theoretical Physics and Kiev National Taras Shevchenko University - PowerPoint PPT PresentationTRANSCRIPT
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