CERN May 30 2007

Heavy Ion Collisions at the LHC

Last Call for Predictions

Initial conditions and space-time scales in relativistic heavy ion

collisions

Yu. Sinyukov, BITP, Kiev(with participation of Yu. Karpenko, S.Akkelin)

CERN May 30 2007

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Expecting Stages of Evolution in Ultrarelativistic A+A collisions

t

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“Soft Physics” measurements

xt

A

A

ΔωK

p=(p1+ p2)/2

q= p1- p2

(QS) Correlation function

Space-time structure of the matter evolution, e.g.,

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Approximately conserved observables

APSD - Phase-space density averaged over some hypersurface , where all particles are already free and over momen- tum at fixed particle rapidity, y=0. (Bertsch)0. (Bertsch)

t

z

Chemical. f.-o.

Thermal f.-o.

APSD is conserved during isentropic and chemically frozen evolution (including a free streaming):

n(p) is single- , n(p1, p2 ) is double

(identical) particle spectra,

correlation function is C=n(p1, p2

)/n(p1)n(p2 ) p=(p1+ p2)/2

q= p1- p2

S. Akkelin, Yu.S. Phys.Rev. C 70 064901 (2004):

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The averaged phase-space density. LHC prediction = 0.2-0.3

Non-hadronic

DoF

Limiting HagedornTemperature

S. Akkelin, Yu.S: Phys.Rev. C 73, 034908 (2006); Nucl. Phys. A 774, 647 (2006)

CERN May 30 2007

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Energy dependence of the interferometry radii

Energy- and kt-dependence of the radii Rlong, Rside, and Rout for central Pb+Pb (Au+Au) collisions from AGS to RHIC experiments measured near midrapidity. S. Kniege et al. (The NA49 Collaboration), J. Phys. G30, S1073 (2004).

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HBT PUZZLE

The interferometry volume only slightly increases with collision energy (due to the long-radius growth) for the central collisions of the same nuclei.

Explanation:

only slightly increases and is saturated due to limiting Hagedorn temperature TH =Tc (B = 0).

grows with

A is fixed

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HBT PUZZLE & FLOWS

Possible increase of the interferometry volume with due to geometrical volume grows is mitigated by more intensive transverse flows at higher energies:

, is inverse of temperature

Why does the intensity of flow grow?

More more initial energy density more (max) pressure pmax

BUT the initial acceleration is ≈ the same

HBT puzzle Intensity of collective flows grow

Time of system expansion grows:

Initial flows (< 1-2 fm/c) develop

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Ro/Rs ratio and initial flows

M.Borysova, Yu.S., S.Akkelin, B.Erazmus, Iu.Karpenko,Phys.Rev. C 73, 024903 (2006)

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Developing of collective velocities in partonic matter at pre-thermal stage (Gyulassy, Karpenko, Yu.S., Nazarenko, BJP (2007)

Distribution function at initial hypersurface 0=1

Venagopulan, 2003, 2005; Kharzeev 2006

Equation for partonic free streaming:

Solution

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Transverse velocities at: =1 fm/c; Gaussian profile, R=4.3 fm

1st order phase transition

Crossover

IC at =0.1 (RHIC) and 0.07 (LHC) fm/c for Glasma from T. Lappy (2006)

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Equation of States

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Freeze-out hypersurface for LHC energies

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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;• calculation of non-equilibrium DF and emission function in first approximation;• 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.

CERN May 30 2007

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Emission at RHIC top energy

EXTRA SLIDES

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Emission at LHC energy Sqrt(s) = 5.5 TeV

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Emission function at large pT

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Transv. spectra of pions (blue line is prediction)

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Long –radii for pions (blue line is prediction)

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Side- radii for pions (blue line is prediction)

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Out –radii for pions (blue line is prediction)

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Out-to-Side ratio for pions (blue line is prediction)

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Conclusions The relatively small increase of interferometry radii with energy,

as compare with expectations, are caused by

increase of transverse flow due to longer expansion time;

developing of initial flows at early pre-thermal stage;

more hard transition EoS, corresponding to cross-over;

non-flat initial (energy) density distributions, similar to Gaussan;

early (as compare to CF-prescription) emission of hadrons, because

escape probability account for whole particle trajectory in rapidly expanding surrounding (no mean-free pass criterion for freeze-out)

The hydrokinetic approach to A+A collisions is proposed. It allows one to describe the continuous particle emission from a hot and dense finite system, expanding hydrodynamically into vacuum, in the way which is consistent with Boltzmann equations and conservation laws, and accounts also for the opacity effects.

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Last Call for Predictions24

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