EVOLUTION OF ENERGY DENSITY FLUCTUATIONS IN A+A COLLISIONS

1. EVOLUTION OF ENERGY DENSITY FLUCTUATIONS IN A+A COLLISIONS Its possible account in the framework of the 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

2. Outline • Motivation • Hydro-kinetic approach • Calculation details • Energy density evolution • Transverse velocity • Conclusions

3. Ridge-like structure in A + A collisions STAR CollaborationPhys.Rev.C80:064912,2009 Near-side correlation structure in Au + Au and d + Au collisions at √SNN= 200 GeV • At large pttrig the near-side correlation • structure can be factored into • a jet-like peak, with properties similar to correlations in p + pcollisions • an elongated contribution that is approximately independent of Δη, which we therefore call the ridge.

4. Motivation • Schenke B.,. et al., QGP collective effects and jet transport // J. Phys. G: Nucl. Part. Phys. – 2008. – Vol. 35. – P. 104109 - 104112. • Dumitru A., et.al., Glasma flux tubes and the near side ridge phenomenon at RHIC // Nucl. Phys. - 2008. – Vol. A 810. – P. 91 - 115. • Y. Hama et al. Hydrodynamics: Fluctuating Initial Conditions and Two-particle Correlations // Acta Phys.Polon. - - 2009. - 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 otheris 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.

5. Yu.Sinyukov , Akkelin, Hama: PRL89 , 052301 (2002); + Karpenko: PRC 78, 034906 (2008). Hydro-kinetic 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.

6. Initial conditions 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. 1 tube: Eb=90 GeV/fm3; R=5,4fm; E0=270 Gev/fm3; R0=3fm; a0=1fm; 4 tubes: Eb=85 GeV/fm3;R=5,4fm; Ei=250 GeV/fm3; Ri=5,6 fm; ai=1 fm; 10 tubes: Eb=25 GeV/fm3; R=5,4fm; R0=0fm; R1,2,3=2,8fm; Ri,i>3=4,7fm; ai=1fm; Ei=4Eb·Exp(-Ri2/R2).

7. Energy density distribution with smooth initial energy density distribution Тch = 165 MeV; τ0 = 0.2 fm/с; Eb =17 GeV/fm3; R=5,4 fm; τ = 1.0fm/с. ε, GeV

8. One longitudinally tube-like fluctuation -spike in the middle of transverse plane Configuration with spike of energy density in the middle with R=1 fm/с, and maximum 270 Gev/fm3

9. One-tube: spike displaced in transverse plane ε, Gev/fm3 Y, fm X, fm ε, Gev/fm3 ε, Gev/fm3 Y, fm Y, fm X, fm X, fm

11. 10 tubes ε, GeV/fm3 ε, GeV/fm3 Y, fm X, fm Y, fm X, 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(-Ri2/R2).

12. Averaged transverse velocity • 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.

13. Averaged transverse velocity 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%

14. Conclusions • 3D Hydro code was developed and applied for an analysis of the evolution of transversally bumping and longitudinally tube-like initial conditions with the aim to study the fluctuations at the final stage. • The traces of the initial fluctuations remain after evolution at the later times that should lead to a non-trivial structure in observed particle correlations and, probably, to ridges. • Strong fluctuations in initial energy density distribution do not result in anomalously big fluctuations of the mean transverse momenta of observed particles. • The further studies of this issue and description of observed spectra 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 as a formation of the particle momentum at the decoupling stage.

15. Thank you!