1. 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

2. 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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8. 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

9. L.P. Csernai

10. EoS, Viscosity !
L.P. Csernai

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

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

15. LHC
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16. 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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18. L.P. Csernai

19. 3-Dim Hydro for RHIC (PIC)X Z
L.P. Csernai

20. Pb+Pb 1.38+1.38 A Teed, central collision
PIC- hydro
Pb+Pb 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

21. Pb+Pb 1.38+1.38 A TeV, b= 70 % of b_max
PIC- hydro
A TeV
ATeV
Pb+Pb 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

22. Pb+Pb 1.38+1.38 A TeV, b= 50 % of b_max
PIC- hydro
A TeV
Pb+Pb 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

23. central
Freeze out
peripheral
Average temperature versus time in Pb+Pb collisions at 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

24. Dissipative expansion in numerical PIC hydro
[Sz. Horvat et al., PLB 2010]
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25. Entropy increase in FD expansion
High initial entropy Χ
[Sz. Horvat et al., PLB 2010]
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26. Fluid Dynamics  Equation of State & Transport Properties
Dynamical path
Quarkyonic
matter
Quarkyonic Matter [McLerran, Pisarski]
Quarks gainng mass, gluons are absorbed
L.P. Csernai

27. 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

28. 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/
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29. (!) FO T = Const.
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30. 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

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

32. 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

33. 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

34.  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

35. Observed Hadron FO
[Cleymans et al., PRL 81 (1998), PRC59 (1999), PRC73 (2006)]
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36. Mass change of constituent quarks
NJL model,
Sven Zschocke, [Li & Shakin PRD 66 (02)
Mass [MeV]
Massive constituent quarks
Light, current quarks
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37. 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

38. 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

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

40. 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
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41. SUMMARY
Initial state is decisive and can be tested by v1 & v 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

42. 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

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

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

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

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

47. Anti-flow (v1) at LHC
Initial energy density [GeV/fm3] distribution in the reaction plane, [x,y] for a Pb+Pb reaction at 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

48. Anti-flow (v1)
The energy density [GeV/fm3] distribution in the reaction plane, [x,z] for a Pb+Pb reaction at 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: (nucl-th)]
L.P. Csernai

49. 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

50. 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

51. 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 % 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

52. 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

53. 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

54. 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 % centrality (black stars).
L.P. Csernai

55. 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

56. 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

57. 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