Flow fluctuation and event plane correlation from E-by-E Hydrodynamics and Transport Model Victor Roy Central China Normal University, Wuhan, China Collaborators : LongGang Pang, Gung-You Qin, & Xin-Nian Wang 1

Outline Motivation Ideal Hydrodynamics and Transport model Event plane correlation Comparison of v n distribution from experiment and model simulation Summary 2

Motivation Initial state © S Bass Space-time evolution Hydrodynamics / Transport Observed hadrons momentum distribution of the observed hadrons Directed flow Elliptic flow Triangular Flow Flow harmonics are important observables for measuring transport coefficient of the Quark Gluon plasma 3

Azimuthal angle event plane flow harmonics: theoretical model study 3+1D Ideal Hydro AMPT L Pang et al PhysRevC J Xu et al Phys.Rev.C83,034904(2011) Pb+Pb 2.76 TeV

200 GeV 1/4  <  /s < 6(1/4  ) 2.76 TeV 1/4  <  /s < 4(1/4  ) The extracted value of shear viscosity over entropy density ratio is model dependent. The main uncertainty coming from initial condition. Importance of Initial condition 5

Charged hadrons V 2 from viscous hydro, TeV, LHC GlauberCGC V 2 (p T ) value largely depends on the initial condition and hence also the extracted value of  /s 6 Importance of Initial condition V Roy et al, Journal of Physics G, Nucl. Part. Phys. 40, (2013) p T (GeV)

7 ATLAS Probability distribution of v 2 P(v n ) will allow us to better estimate the transport coefficient and initial condition in HIC Event-by-event distribution of flow harmonics

We are asking a different question For the similar initial condition what will be the difference in v n distribution if the system evolves according to (1) Hydrodynamics (macroscopic) 3+1d Ideal hydro (2) Transport (Microscopic) AMPT L Pang et al PhysRevC Zi wei lin et al PhysRevC

9 Event-Plane Correlation in HIC R S Bhalerao et al PhysRevC Event plane correlation  an important observable which may provide the crucial information about the initial state of HIC Z qiu et al Our study is focused on the event plane correlation in the longitudinal direction 2+1 D hydro AMPT Phys.Lett. B717 (2012)

10 Importance of longitudinal Fluctuation Tube like initial conditionLongitudinal fluctuation IC -No rapidity dependence -Used in most of the existing 3+1D hydrodynamics model Event planes at different pseudo-rapidity are same -More close to real situation -Observables are rapidity dependent -Used in our 3+1 D ideal hydrodynamics model Event plane correlation may depends On pseudo-rapidity

The other question we are asking How does the event planes varies along the pseudo-rapidity in case of longitudinal fluctuating initial condition. Can the event plane correlation possibly help us to extract shear viscosity of QGP? We will discuss results from both (1) Hydrodynamics (macroscopic) 3+1d Ideal hydro (2) Transport (Microscopic) AMPT L Pang et al PhysRevC Zi wei lin et al PhysRevC

3+1D Ideal hydrodynamics with longitudinal fluctuating initial condition Initial Condition Energy Momentum tensor is calculated from the position and momentum of the initial parton on a fixed proper time surface QGP phase Hadronic Phase Freeze-out  T f =137 MeV Number of event for each centrality ~500 EoS (Lattice QCD+HRG) Chemical Equilibrium, s95p-v1 HIJING (MC Glauber model) Energy density in XY Parton density along spatial-rapidity TIMETIME L Pang et al PhysRevC

A Multiphase Transport Model AMPT (string melting,2.25t7d) Initial condition Excited string and mini-jet fragmented to partons QGP phase Parton freeze-out, Hadron formation via coalescence Hadronic phase Hadron freeze-out Number of events for Each centrality = Parton cross section=1.5, 20 mb Zhang’s Parton Cascade two parton collision only A Relativistic Transport B-B,B-M,M-M elastic and inelastic processes HIJING (Glauber model) X (fm) Distribution of participating nucleons In a typical non-central Au+Au collision. TIMETIME Average over all charged particle In a given event Zi wei lin et al PhysRevC

14  =0  Event planes at different pseudo-rapidity We are calculating the event average of  0.5  n-th order event plane

15  =0  Event planes at different pseudo-rapidity We are calculating the event average of -- 0.5  n-th order event plane

16 Event Plane correlation: tube like and longitudinal fluctuating IC -Blue triangle  Boost invariant tube like initial condition -Red Circle  Initial condition with longitudinal fluctuation -The longitudinal fluctuation introduces the event plane de-correlation Au+Au 200 GeV : Ideal hydrodynamics

17 Second order event plane correlation for 20-25% Pb+Pb collision Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Event planes are more correlated for QGP with lower viscosity Resolution factor is used to correct the effect of finite multiplicity In the infinite multiplicity limit R(  )  1

18 Second order event plane correlation for 20-25% Pb+Pb collision Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Green circles  Ideal hydrodynamics Ideal hydro  similar to  =1.5 mb

19 Third order event plane correlation for 20-25% Pb+Pb collision Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Third order event plane correlation also shows the similar viscosity dependence

20 Third order event plane correlation for 20-25% Pb+Pb collision Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Green circles  Ideal hydrodynamics Ideal hydro matches with the AMPT result for  =1.5 mb

21 Second order event plane correlation for 5-10% Pb+Pb collision Higher correlation for sigma 20 mb Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb

22 Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Green circles  Ideal hydrodynamics Second order event plane correlation for 5-10% Pb+Pb collision

23 Third order event plane correlation for 5-10% Pb+Pb collision Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Central collision   3 correlation less sensitive to QGP viscosity

24 Third order event plane correlation for 5-10% Pb+Pb collision Red triangles  AMPT,  =1.5 mb Blue Star  AMPT,  20 mb Green circles  Ideal hydrodynamics Central collision   3 correlation less sensitive to QGP viscosity

Let us look at event-by-event distribution of V n -We are using the same initial condition for hydro & transport model which explained the event averaged v 2 (p T ) at LHC. (slide 3) 25

26 Comparison of  2 and v 2 for Pb+Pb collision from MC Glauber  2 distribution is scaled to match the mean value with v 2  2 from MC Glauber model is wider than experimental v 2 distribution

27 Comparison of scaled v 2 distribution from AMPT and Experiment Scaled distribution of v 2 from AMPT is wider than the experimental distribution, roughly follows the  2 distribution Parton cross section 1.5 mb

28 Comparison of  3 and v 3 for Pb+Pb collision from MC Glauber Scaled  3 from MC Glauber model is similar to experimental v 3 distribution

29 Comparison of scaled v 3 distribution from AMPT and Experiment Parton cross section 1.5 mb

30 Comparison of  4 and v 4 for Pb+Pb collision from MC Glauber

31 Comparison of scaled v 4 distribution from AMPT and Experiment Parton cross section 1.5 mb

32 v n distribution for two different partonic cross section -Red circles  Experimental data -Continuous line   =1.5 mb -Broken line   =20 mb Viscosity changes the distribution

33 Scaled distribution is less Sensitive to the viscosity Good observable for study initial condition Scaled v n distribution two different partonic cross section

34 Scaled v n distribution from ideal hydrodynamics Ideal hydro  Similar to AMPT Negligible effect of viscosity Scaled v n distribution mostly depends only on initial condition

Conclusion Event plane correlation decreases with increasing pseudo-rapidity. Correlation increases for larger partonic cross section in transport model, in other words, the correlation is higher for less viscous QGP. Ideal hydrodynamics with the same initial condition shows similar event plane correlation like transport model. Both Ideal hydrodynamics and transport model initialized with MC Glauber model fails to explain experimental v 2 distribution. -Higher harmonics are well explained. QGP viscosity has negligible effect on scaled distribution of v n 35

Initial condition Initial eccentricity of n-th order Varies event by event 0-5% Event-By-Event distribution of  n Event averaged  n Hydro  eccentricity calculated from partons on fixed proper time surface. AMPT  from the distribution of participant nucleon Teaney et al. PhysRevC

Extra Slides AMPT version used for the analysis: 2.25t7d (String Melting) (Parameter set A ) Event plane definition :  = V 2 |  =0 Particles from this region are used for calculating event plane 37

Formula’s used in hydrodynamics simulation Energy momentum tensor calculated from the initial parton momentum and spatial distribution 38

Formula’s used in AMPT simulation 39 Schenke et al

40 Dependence of multiplicity on cross section in AMPT J Xu et al Phys. Rev. C 83,