CCNU-UiB-CIAE Workshop, May 2011 中国—挪威 研讨会， 2011年 5月 Theoretical Studies of Collective Dynamics using Multi-module approach Laszlo P. Csernai, University of Bergen, Norway CCNU, Wuhan, China, May 5, 2011

Several Years of Collaboration NSFC - RCN Prof. Dai-Mei Zhou, CCNU Prof. Ben-hao Sa, CIAE Prof. Chun-bin Yang, CCNU Prof. Xu Cai, CCNU Dr. Yun Cheng, CCNU Dr. Yu-liang Yan, CIAE Miss Du-juan Wang, CCNU/UoB Experimentalists: Prof. Dai-cui Zhou, CCNU, …. Prof. Laszlo P. Csernai, UoB Prof. Joakim Nystrand, UoB Dr. Csaba Anderlik, UoB/U-C Dr. Szabolcs Horvat, (UoB) Miss Astrid Skålvik, UoB Experimentalists: Prof. Dieter Röhrich, UoB … Other theorists: Prof. Daniel D. Strottman, LANL Prof. Volodynyr Magas, U Barcelona Prof. Igor Mishustin, FIAS Dr. Bernd R. Schlei, GSI … L.P. Csernai

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Scheid, Ligensa, Greiner; Phys.Rev.Lett. 21 (1968) 1479, Scheid, Greiner; Z. Phys. 226 (1969) 364. G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, Phys. Rev. D8 (1973) 135. L.P. Csernai

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EoS, Viscosity ! L.P. Csernai

H.G. Ritter H. Gutbrod A. Poskanzer Plastic Ball & Wall 1984 H.G. Ritter H. Gutbrod A. Poskanzer L.P. Csernai

[Westfall et al. PRL (1976)] L.P. Csernai

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LHC L.P. Csernai

TODAY – Elliptic flow at LHC Flow is stronger than ever before, Dominant at higher energies, Quark number scaling indicates that flow is created in QGP L.P. Csernai

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3-Dim Hydro for RHIC (PIC) X Z L.P. Csernai

Pb+Pb 1.38+1.38 A Teed, central collision PIC- hydro Pb+Pb 1.38+1.38 A Teed, central collision Lagrangian fluid cells, moving, ~ 5 mill. MIT Bag m. EoS FO at T ~ 250 MeV, but calculated much longer! GeV/fm3 ..\zz-Movies\LHC-Ea_b0_m5_tf45.mov L.P. Csernai

Pb+Pb 1.38+1.38 A TeV, b= 70 % of b_max PIC- hydro A TeV ATeV Pb+Pb 1.38+1.38 A TeV, b= 70 % of b_max Lagrangian fluid cells, moving, ~ 5 mill. MIT Bag m. EoS FO at T ~ 200 MeV, but calculated much longer, until pressure is zero for 90% of the cells. Structure and asymmetries of init. state are maintained in nearly perfect expansion. ..\zz-Movies\LHC-Ec-1h-b7-A.mov L.P. Csernai

Pb+Pb 1.38+1.38 A TeV, b= 50 % of b_max PIC- hydro A TeV Pb+Pb 1.38+1.38 A TeV, b= 50 % of b_max Lagrangian fluid cells, moving, ~ 5 mill. MIT Bag m. EoS FO at T ~ 200 MeV, but calculated much longer. Transverse velocuty leads to significant v2 ! Max v2 at LHC ..\zz-Movies\LHC-uv-b05.mov L.P. Csernai

central Freeze out peripheral Average temperature versus time in Pb+Pb collisions at 1.38+1.38 ATeV, for impact parameters, b = 0, 0.1, 0.2, … 0.7 b_max from the top (0.00) down (0.7). L.P. Csernai

Dissipative expansion in numerical PIC hydro [Sz. Horvat et al., PLB 2010] L.P. Csernai

Entropy increase in FD expansion High initial entropy Χ [Sz. Horvat et al., PLB 2010] L.P. Csernai

Fluid Dynamics  Equation of State & Transport Properties Dynamical path Quarkyonic matter Quarkyonic Matter [McLerran, Pisarski] Quarks gainng mass, gluons are absorbed L.P. Csernai

Elliptic flow / Sources of v2 1) Anisotropic flow from initial state eccentricity (finite b  spatial v anti-correlation) 2) EoS of the matter 3) Initial state surface layer [RC Hwa, CB Yang ] 4) Recombination from local anisotropic f(x,p) and the collision integral [D Molnar, CM Ko et al.,] (!) MD models may include 1, (2), (3), 4  Description of NCQ scaling is a complex issue !!! L.P. Csernai

Constituent quark number scaling of v2 (KET ) CNQ scaling Constituent quark number scaling of v2 (KET ) Collective flow of hadrons can be described in terms of constituent quarks. Observed nq – scaling  Flow develops in quark phase, there is no further flow development after hadronization R. A. Lacey (2006), nucl-ex/0608046. L.P. Csernai

(!) FO T = Const. L.P. Csernai

Linear pt dependence of flow (?) (!) FO T = Const. V2 from few source models [Huovinen et al. 2001]  v2 (pt) rises linearly at high pt (Bjorken Model) L.P. Csernai

NCQ - Importance of Initial State FO [w/Mishustin] Take 3 sources only: As Ac= 42 100 Ts=100 vx=0.5 Tc=172 Tcrit – 2%  1 As Ac= 50 100 Ts=100 vx=0.2 Tcr=122 Tcrit + 2%  0 T (x)   u(x) Hadron flow does not show NCQ scaling !! As Ac= 20 100 Ts=150vx=0.25 Tc=180 As Ac= 20 100 Ts=180 vx=0.4 Tc=150 L.P. Csernai

Note that: Thermal equilibrium among different mass particles does not lead to NCQ scaling. Sources of different T do not lead to linearly increasing V2(pt) spectra. L.P. Csernai

Hadronization via recombination Momentum distribution of mesons in simple recombination model: Local fq(pµuµ) is centered at the local u, & meson Wigner function: momentum conservation comoving quark and antiquark: for the momentum distribution of mesons we get: flow moments: for baryons, 2 3 [MolnarD-NPA774(06)257] L.P. Csernai

 Elliptic flow of mesons: For baryons: Scaling Variables of Flow: 1st step: Flow asymmetry: V2 / n q  V2 scales with nq i.e., flow develops in QGP phase, following the common flow velocity, u, of all q-s and g-s. Mass here does not show up (or nearly the same mass for all constituent quarks). Then flow asymmetry does not change any more. In a medium pT is not necessarily conserved, K ET = mT – m might be conserved  scaling in the variable K ET [J. Jia & C. Zhang, 2007] L.P. Csernai

Observed Hadron FO [Cleymans et al., PRL 81 (1998), PRC59 (1999), PRC73 (2006)] L.P. Csernai

Mass change of constituent quarks NJL model, Sven Zschocke, [Li & Shakin PRD 66 (02) Mass [MeV] Massive constituent quarks Light, current quarks L.P. Csernai

End point of adiabatic expansion of CQs Endpoints are still above the FO energy of EH/NH ~ 1 GeV. Viscous dissipation & rapid recombination to mesons and baryons, with using part of the latent heat, can increase the final T to the observed FO temperatures. Adiabatic expansion, end points when energy reaches E/N=1.2 GeV (including the B-field) L.P. Csernai

v2 scaling – few sources Collective flow (v2) – Spatial anticorrelation Velocities change in coalescence Baryons gain more flow energy from Bcgd. (FEM/q)/ (FEB/q) = 2/3  vM = 0.21  vB= 0.26 Mesons Baryons ! Three sources (one warmer central source) yields scaling beyond 1 GeV ! ThEM/ThEB = TM / TB = 2/3  TM = 152 MeV,  TB=228 MeV L.P. Csernai

Freeze-out hypersurface Central collision Strong expansion Longitudinal Transverse ring, which freezes out fast ..\zz-Movies\LHC_mov1_b0-250sm.mov L.P. Csernai

Freeze-out hypersurface b=70% Isotherm FO hypersurf. at temperature of 250 MeV Elliptic flow is visible in the x-direction! Beam directed peaks are not exp.observable v2 v2 ..\zz-Movies\LHC_mov1_b7-250sm.mov L.P. Csernai

SUMMARY Initial state is decisive and can be tested by v1 & v2 v2 dominates in more peripheral collisions Viscosity is important both in hydro and in the initial dynamics Numerical viscosity should be taken in correction !!! CNQ scaling indicates QGP, modifies F.O. description to Const. Quarks. This requires, however, Modified BTE or molecular dynamics description FO leads to acceleration ! (simplified approach eliminates this) L.P. Csernai

Numerical solution from hydro to parton Distribution of T-μ in each cells by solving the boundary condition QGP Parton phase Partons Partons QGP QGP YunCheng- 10th Dec 2010

Preliminary results at transition time Pseudorapidity distribution of the charged particles at the transition time. YunCheng- 10th Dec 2010

Preliminary results at transition time Pseudorapidity distribution of the charged particles at different transition times. b=30% YunCheng- 10th Dec 2010

Preliminary results comparing with data PT distribution of the charged hardons at final detection. Compared with STAR data. YunCheng- 10th Dec 2010

Preliminary results comparing with data Pseudorapidity distribution of the charged particles in central collisions. Compared to PHOBOS data. YunCheng- 10th Dec 2010

Anti-flow (v1) at LHC Initial energy density [GeV/fm3] distribution in the reaction plane, [x,y] for a Pb+Pb reaction at 1.38 + 1.38 ATeV collision energy and impact parameter b = 0.5_bmax at time 4 fm/c after the first touch of the colliding nuclei, this is when the hydro stage begins. The calculations are performed according to the effective string rope model. This tilted initial state has a flow velocity distribution, qualitatively shown by the arrows. The dashed arrows indicate the direction of the largest pressure gradient at this given moment. L.P. Csernai

Anti-flow (v1) The energy density [GeV/fm3] distribution in the reaction plane, [x,z] for a Pb+Pb reaction at 1.38 + 1.38 A.TeV collision energy and impact parameter b = 0.5b_max at time 12 fm/c after the formation of the hydro initial state. The expected physical FO point is earlier but this post FO configuration illustrates the flow pattern. [LP. Csernai, VK. Magas, H. Stocker, D. Strottman, arXiv: 1101.3451 (nucl-th)] L.P. Csernai

Anti-flow (v1) The calculated charged particle multiplicity, N_ch, as a function of FO time (assuming a t_FO = const: FO hyper-surface), for different impact parameters, b = 0.0; 0.1; 0.2; … 0.7 b_max. The indicated (b0, b1, ... b7) FO times for different impact parameters reproduce the measured charged particle multiplicities, N_ch, in the corresponding centrality bins. The visible fluctuations arise from the feature of the PIC method, that the volume increases by one cell when a marker particle crosses the boundary. Thus at the initial state with relatively few cells and large relative surface, this leads to fluctuations. L.P. Csernai

Anti-flow (v1) Using the Cooper-Frye FO formula, we can obtain the v_n(pt) and v_n(y) flow components, for massless pions: Conservation laws are satisfied at a constant time FO hyper-surface. L.P. Csernai

Anti-flow (v1) The v_1 & v_2 parameter calculated for ideal massless pion Juttner gas, versus the transverse momentum, p_t, for b = 0.7b_max, at t = 8 fm/c FO time. The magnitude of v_2 is comparable to the observed v_2 at 40-50 % centrality. The v_2 value is slightly below the experimental data, which can be attributed to integral over the whole rapidity range, while the experiment is only for η < 0.8. The v1 peak appears at positive rapidity, in contrast to lower energy calculations and measurements. L.P. Csernai

Anti-flow (v1) The v_1 parameter calculated for ideal massless pion Juttner gas, versus the transverse momentum, p_t for b = 0.5 – 0.7 b_max, at t = 10=8 fm/c FO time (thin blue/thick red line). The magnitude of v_1 is increasing with impact parameter and it is about 3%, at b = 0.7 b_max. L.P. Csernai

Anti-flow (v1) Initial state CM rapidity fluctuations were taken into account Vs_1 (pt) is not sensitive to the initial state y_CM fluctuations L.P. Csernai

Anti-flow (v1) The v_2 parameter calculated for ideal massless pion Juttner gas, versus the transverse momentum, p_t for b = 0.7 b_max, at t = 8 fm/c FO time. The magnitude of v_2 is comparable to the observed v_2 at 40-50 % centrality (black stars). L.P. Csernai

Anti-flow (v1) The vS_1 flow parameter calculated according to the eq. (4) for ideal massless pion Juttner gas, versus the transverse momentum, p_t for b = 0.7 b_max, at t = 8 fm/c FO time. L.P. Csernai

Anti-flow (v1) The v_1 & v_2 parameters calculated for ideal massless pion Juttner gas, versus the rapidity y for b = 0.7 b_max, at t = 8 fm/c FO time. Full curve presents semi analytical calculations according to eq. (2); the v_1 peak appears at positive rapidity, in contrast to lower energy calculations and measurements. The dash-dotted and dotted curves present v_1 & v_2 calculated taking into account initial CM rapidity fluctuations. L.P. Csernai

Anti-flow (v1) FD calculations suggest measurable v_1(y) and vS_1 (pt)- flows at LHC. These flow parameters are very sensitive to the initial state y_CM-fluctuations, which can and should be measured by ALICE. The most important our prediction is that the v_1 peak moves to "forward" direction, in contrast to lower energies. This is a result of our tilted and moving initial state, in which the effective "angular momentum" from the increasing beam momentum is superseding the expansion driven by the pressure. L.P. Csernai