EVOLUTION OF ENERGY EVOLUTION OF ENERGY DENSITY FLUCTUATIONS IN DENSITY FLUCTUATIONS IN

A+A COLLISIONSA+A COLLISIONS

Its possible account in the Its possible account in the framework offramework of

the hydrokinetic approachthe hydrokinetic approach

M. S. Borysova 1,2, In collaboration with Yu. Karpenko 2 and Yu.M. Sinyukov 2

1 Kyiv Institute for Nuclear Research, Kyiv, Ukraine 2 Bogolubobov Institute for Theoretical Physics, Kyiv, Ukraine

WPCF 14.09.2010

OutlineOutline

MotivationMotivationHydro-kinetic approachHydro-kinetic approachCalculation detailsCalculation detailsEnergy density evolutionEnergy density evolutionTransverse velocityTransverse velocityConclusionsConclusions

STAR Collaboration Phys.Rev.C80:064912,2009

At large pttrig the near-side correlation

structure can be factored into• a jet-like peak, with properties similar to

correlations in p + p collisions• an elongated contribution that is

approximately independent of Δη, which we therefore call the ridge.

Ridge-like structure in A Ridge-like structure in A + A collisions+ A collisions

Near-side correlation structure inAu + Au and d + Au collisions at √SNN = 200 GeV

MotivationMotivation

1.1. Schenke B.,. et al.Schenke B.,. et al., QGP collective effects and jet transport // J. Phys. G: Nucl. Part. Phys. – , QGP collective effects and jet transport // J. Phys. G: Nucl. Part. Phys. – 2008. – Vol. 35. – P. 104109 - 104112.2008. – Vol. 35. – P. 104109 - 104112.

2.2. Dumitru A., et.al.,Dumitru A., et.al., Glasma flux tubes and the near side ridge phenomenon at RHIC // Glasma flux tubes and the near side ridge phenomenon at RHIC // Nucl. Nucl. Phys. Phys. - 2008. – Vol. A 810. – P. 91 - 115.- 2008. – Vol. A 810. – P. 91 - 115.

3.3. Y. Hama Y. Hama et al. et al. Hydrodynamics: Fluctuating Initial Conditions and Two-particle Correlations // Hydrodynamics: Fluctuating Initial Conditions and Two-particle Correlations // Acta Phys.Polon.Acta Phys.Polon. - - - - 20092009. -. - B40:931-936 B40:931-936..

• In recent publications strikingly different explanations are proposed [1-3]. One of them explore a final-state effect as the origin of the ridge [1]. The other is that correlations over several rapidity units can only originate at the earliest stages of heavy ion collisions when pre-thermal matter is produced [1,2].

• Then due to fluctuations of energy density distribution in colliding nuclei the longitudinally boost-invariant and transversally inhomogeneous bumping structure of the matter can be formed.

• With the aim to investigate this issue the evolution in time of energy density profiles with different initial configurations were considered.

YuYu..SSinyukov , inyukov , Akkelin, HamaAkkelin, Hama: : PPRLRL 8989 , 052301 (2002) , 052301 (2002); ; + Karpenko: PRC + Karpenko: PRC 7878, 034906 (2008)., 034906 (2008).

Hydro-kinetic Hydro-kinetic approach approach

MODEL• provides evaluation of escape probabilities and deviations of distribution functions [DF] from local equilibrium;

• is based on relaxation time approximation for relativistic finite expanding system;

• accounts for conservation laws at the particle emission;

Complete algorithm includes: • solution of equations of ideal hydro, using Harten Lax Van Leer (HLLE)

method;• 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-equilibrium process of the system which radiated free particles during expansion• Calculation of emission function; • Evaluation of spectra and correlations.

Initial conditionsInitial conditions

ti

iiN

i

a

yyxx

iR

yx

b eEeEE0

)()(2

22

2

22

222iii yxR

Eb=90 GeV/fm3; R=5,4fm; E0=270 Gev/fm3; R0=3fm; a0=1fm;

Eb=85 GeV/fm3; R=5,4fm; Ei=250 GeV/fm3; Ri=5,6 fm; ai=1 fm;

Eb=25 GeV/fm3; R=5,4fm; R0=0fm; R1,2,3=2,8fm; Ri,i>3=4,7fm; ai=1fm; Ei=4Eb·Exp(-Ri

2/R2).

1 tube:4 tubes:

10 tubes:

Bjorken-type initial conditions at τ0 = 0.2 fm/с : boost-invariance of the system in longitudinal direction, initial longitudinal flow without transverse collective expansion.

Energy density Energy density distribution with smooth distribution with smooth

initial energy density initial energy density distributiondistribution

ТТchch = 165 = 165 MeV;MeV;ττ00 = 0.2 = 0.2 fmfm/с/с;;EEbb =17 GeV =17 GeV//fmfm33;; R=5,4 fm R=5,4 fm;; ττ = = 11..00 fmfm/с/с..

ε, G

eV

One longitudinally tube-like One longitudinally tube-like fluctuation -spike in the fluctuation -spike in the

middle of transverse planemiddle of transverse plane

Configuration with spike of energy density in the middle with R = 1 fm/с, and maximum 270 Gev/fm3

One-tube: One-tube:

spike spike displaced in displaced in transverse transverse

planeplane

ε, Gev/fm3ε, Gev/fm3

ε, Gev/fm3

X, fm X, fm

X, fm

Y, fm Y, fm

Y, fm

10 tubes10 tubesε, GeVGeV//fmfm33

X, fmY, fm

ε, GeVGeV//fmfm33

X, fmY, fm

Eb=25 GeV/fm3; R=5,4fm; R0=0fm; R1,2,3=2,8fm; Ri,i>3=4,7fm; ai=1fm; Ei=4Eb·Exp(-Ri

2/R2).

Averaged transverse Averaged transverse velocityvelocity

Transverse velocity radial profiles, averaged over azimuth angle for different slices of time: 1, 2 and 3 fm/c •without fluctuations, •1-tube in the center,•1-tube shifted, •10-tubes.

Vr, 10 tubes, no tubes and 1 tube, 2 fm/c.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

R, fm

Vr

Vr, 10 tubes, no tubes and 1 tube, 1 fm/c.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

R, fm

Vr

Vr_10 tbs (1 fm/c)

Vr no tbs (1 fm/c)

Vr_1 tb (1 fm/c)

Vr_1 tb_c (1 fm/c)

Vr, 10 tubes, no tubes and 1 tube, 3 fm/c.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

R, fm

Vr

Averaged transverse Averaged transverse velocityvelocity

ττ, fm/c, fm/c <V<VRR>>centeredcentered

<V<VRR>>shiftedshifted

11 0.110238 0.0808824

22 0.238913 0.187978

33 0.347213 0.290372

1010 0.70941 0.720137

The totally averaged transverse velocities for the cases - one tube in the center and one shifted tube.

At early time the corresponding fluctuations in the transverse velocity averaged over azimuth angle and radius are approximately 30% while at the later times it is only 3%

ConclusionsConclusions3D Hydro code was developed and applied for an analysis of the 3D Hydro code was developed and applied for an analysis of the evolution ofevolution of transversally bumping and longitudinally tube-like initial transversally bumping and longitudinally tube-like initial conditions with the aim to study the fluctuations at the final stage. conditions with the aim to study the fluctuations at the final stage.

The traces of the initial fluctuations remain after evolution at the later The traces of the initial fluctuations remain after evolution at the later times that should lead to a non-trivial structure in observed particle times that should lead to a non-trivial structure in observed particle correlations and, probably, to ridges.correlations and, probably, to ridges.

Strong fluctuations in initial energy density distribution do not result in Strong fluctuations in initial energy density distribution do not result in anomalously big fluctuations of the mean transverse momenta of anomalously big fluctuations of the mean transverse momenta of observed particles.observed particles.

The further studies of this issue and description of observed spectra The further studies of this issue and description of observed spectra and correlations could be done in the frameworks of the HKM, which and correlations could be done in the frameworks of the HKM, which will allow one to describe all the stages of the system evolution as well will allow one to describe all the stages of the system evolution as well as a formation of the particle momentum at the decoupling stage.as a formation of the particle momentum at the decoupling stage.

Thank youThank you!!