Upload
hortense-cook
View
213
Download
0
Tags:
Embed Size (px)
Citation preview
Sept 11- 14 WPCF-2008
Initial conditions and space-time scales in relativistic heavy ion
collisions
Yu. Sinyukov, BITP, Kiev
Based on: Yu.S. , I. Karpenko, A. Nazarenko J. Phys. G (Proc. QM-2008), in press
September 11-14
WPCF-2008 2
Expecting Stages of Evolution in Ultrarelativistic A+A collisions
Early thermalization at 0.5 fm/c
0.2?(LHC)
Elliptic flows
tRelatively small space-time
scales (HBT puzzle)
Early thermal freeze-out: T_th Tch
150 MeV
10-15 fm/c
7-8 fm/c
1-3 fm/c
September 11-14
WPCF-2008 3
Basic ideas for the early stage p
Hydrodynamic expansion: gradient pressure acts
Free streaming:
Gradient of density leads to non-zero
collective velocities
For nonrelativistic (massive) gas
At free streaming
So, even if an
d
:
Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko Braz.J.Phys. 37 (2007) 1031; Akkelin, Yu.S., Karpenko arXiv:0706.4066 (2007)(also in: Heavy-ion collisions at the LHC—Last call for predictions. J.Phys. G 35 054001 (2008))
September 11-14
WPCF-2008 4
t
x
outt
F. Grassi,Y. Hama, T. Kodama
Continuous emission Hydro-kinetic approach
is based on combination of Boltsmann equation and for hydro relativistic finite expanding system;provides evaluation of escape probabili- ties and deviations (even strong) of distri-bution functions from local equilibrium;accounts for conservation laws at the particle emission;
PROVIDE earlier (as compare to CF-prescription) emission of hadrons, because escape probability accounts for whole particle trajectory in rapidly expanding surrounding (no mean-free pass criterion for freeze-out)
Yu.S., Akkelin, Hama: PRL. 89, 052301 (2002); + Karpenko: PRC 78 034906 (2008).
Basic ideas for the late stage
September 11-14
WPCF-2008 5
Boost-invariant distribution function at initial hypersurface
CGC effective FT for transversally homogeneous system
Transversally inhomogeneous system: <transverse profile> of the gluon distribution proportional to the ellipsoidal Gaussian defined from the best fit to the density of number of participants in the collisions with the impact parameter b.
A.Krasnitz, R.Venugopalan PRL 84 (2000) 4309; A. Krasnitz, Y. Nara, R. Venugopalan: Nucl. Phys. A 717 (2003) 268, A727 (2003) 427;T. Lappi: PRC 67 (2003) 054903, QM 2008 (J.Phys. G, 2008)
If one uses the prescription of smearing of the -function as , then . As the result the initial local boost-invariant phase-space density takes the form
is the variance of a Gaussian weight over the color charges of partons
September 11-14
WPCF-2008 6
Developing of collective velocities in partonic matter at pre-thermal stage (Yu.S. Acta Phys. Polon.
B37, 2006)
Equation for partonic free streaming in hyperbolic coordinates between
Solution
where
September 11-14
WPCF-2008 7
Flows from non-equilibrated stage (at proper time = 1 fm/c)
fm/c
September 11-14
WPCF-2008 8
Initial parameters even being (quasi) isotropic at
becomes anisotropic at =1 fm/c.
Supposing fast thermalization near this time,
we use prescription:
Then for fm/c
the energy density profile:
with the Gaussian width fm; At supposed thermalization time :
is fitting parameter
September 11-14
WPCF-2008 9
Equation of State
EoS from LattQCD (in form proposed by
Laine & Schroder, Phys. Rev. D73, 2006) MeV
The EoS accounts for gradual decays of the resonances during the expansion of hadron gas consistiong of 359 particle species with masses below 2.6 GeV. We evaluate the change of the compositon of the system at each space-time point x due to resonance decays in accordance with the width of each resonance and its world line in Minkowski space.
MeV
September 11-14
WPCF-2008 10
Yu.S. , Akkelin, Hama: Phys. Rev. Lett. 89 , 052301 (2002); + Karpenko: to be published
*Is related to local
Hydro-kinetic approach
MODEL• is based on relaxation time approximation for relativistic finite expanding system;
• provides evaluation of escape probabilities and deviations (even strong) of distribution functions [DF] from local equilibrium;
3. accounts for conservation laws at the particle emission;
Complete algorithm includes: • solution of equations of ideal hydro [THANKS to T. Hirano for possibility to use code in 2006] ;• calculation of non-equilibrium DF and emission function in first approximation; [Corresponding hydro-kinetic code: Tytarenko,Karpenko,Yu.S.(to be publ.)]• Solution of equations for ideal hydro with non-zero left-hand-side that accounts for conservation laws for non-equlibrated process of the system which radiated free particles during expansion; • Calculation of “exact” DF and emission function; • Evaluation of spectra and correlations.
September 11-14
WPCF-2008 11
System's decoupling and spectra formation
Emission function
For pion emission
is the total collision rate of the pion, carrying momentum p with all the hadrons h in the system in a vicinity of point x.
is the space-time density of pion production caused by gradual decays during hydrodynamic evolution of all the suitable resonances H including cascade decays. We evaluate the compositon of the system at each space-time point x due to resonance decays in accordance with the width of each resonance and its world line in Minkowski space.
The cross-sections in the hadronic gas are calculated in accordance with UrQMD .
September 11-14
WPCF-2008 12
Rate of collisions for pions in expanding hadron gas depending on T and p
It accounts (in the way used in UrQMD) for pion cross sections with 359 hadron and resonance species with masses < 2.6 GeV. It is supposed that gas is in chemical equilibrium at Tch = 165 MeV and then is expanding. The decay of resonances into expanding liquid is taken into account.
September 11-14
WPCF-2008 13
Fitting parameterThe maximal initial energy density: fm/c; GeV/fm3
(the average energy density then is
that bring with it the value
at the thermalization time
This means that the best fit corresponds to
or
In CGC approach at RHIC energies the value is used (T. Lappi, Talk at QM2008, J.Phys. G, in press)
September 11-14
WPCF-2008 14
Pion emission density for RHIC energies in HKM
September 11-14
WPCF-2008 15
Emission densities at different Pt
September 11-14
WPCF-2008 16
Transverse spectra
September 11-14
WPCF-2008 17
Longitudinal interferometry radius
September 11-14
WPCF-2008 18
Side-radius
September 11-14
WPCF-2008 19
Out- radius
September 11-14
WPCF-2008 20
Conclusions
A reasonable description of the pionic spectra and HBT (except some an overestimate for ) in cental Au+Au
collisions at the RHIC energies is reached with the value of the fitting parameter or the average energy density at the initial time
The initial time fm/c and transverse width 5.3 fm (in the Gaussian approximation) of the energy density distribution are obtained from the CGC estimates.
The EoS at the temperatures corresponds to the lattice QCD calculations at
The used temperature of the chemical freeze-out MeV is taken from the latest results of particle number ratios analysis
(F. Becattini,Plenary talk at QM-2008).
The anisotropy of pre-thermal transverse flows in non-central collisions, bring us a hope for a successful description of the elliptic flows with thermalization reached at a relatively late time:1-2 fm/c.