XI HADRON PHYSICS March, 22-27, 2010, São Sebastião, Brazil

Transcription

1 XI HADRON PHYSICS March, 22-27, 2010, São Sebastião, Brazil

2 Non-linear waves in the Quark Gluon Plasma F. Navarra and D.A. Fogaça IFUSP L.G. Ferreira Filho UERJ / Resende based on: D.A. Fogaça and F.S. Navarra, Phys. Lett. B639 (2006) 629, B645 (2007) 408 Nucl. Phys. A790 (2007) 619c D.A. Fogaça, L.G. Ferreira Filho and F.S. Navarra, Nucl. Phys. A819 (2009) 150 see also poster by L. G. Ferreira Filho

3 Introduction 2004: EVIDENCE of the perfect fluid at RHIC (measurement of eliptic flow v 2 ) 2005: evidence of waves and Mach cones in the QGP (double bump structure in the away side jets) LHC: precision tests of this fluid detailed studies of waves in the QGP! Interesting times for hydrodynamics!

4 Hydrodynamics (perfect fluid) Energy-momentum conservation Euler Baryon number conservation continuity Entropy conservation

5 Hydrodynamics of bulk matter Initial conditions Equation of state Freeze-out prescription Event - by - event fluctuations Good description of spectra d d N p T d N dη, and others... Viscous hydrodynamics Study of waves in QGP Waves: perturbations generated by fast moving partons in the plasma

6 Hydrodynamics of perturbations amplitude << wavelength I) Linearization Expand around equilibrium : Neglect : Obtain : solution: spherical waves speed of sound

7 Perturbations caused by supersonic motion spherical waves pile up and form a conical front v

8 Supersonic motion in the QGP π π supersonic quark QGP π π unquenched jet 2 =1/ c s 3

9 Simulations Temperature profile Torrieri, Noronha, Betz, Gyulassy arxiv: nucl-th

10 II) Beyond linearization (perturbations may be not so small) Define dimensionless variables : Expand Euler and continuity equations around equilibrium : Insert in Euler and continuity equations Rewrite the equations as power series in σ R.C. Davidson, Methods in non-linear plasma theory (1972) Each must vanish

11 Differential equation depends on the equation of state! Euler EOS: If: Korteweg - de Vries (KdV) If: 2... = 0 Breaking wave equation

12 KdV has an exact soliton solution: stable and localized pulse! in water : in cold nuclear matter: ρ 1 soliton x Fowler, Raha, Weiner, PLB (1982)

13 How to get the Laplacian? In nuclear matter mean field theory (non-linear Walecka) : Mean field Lagrangian Equations of motion Usually: 2 V0 = 0 and

14 But we can estimate the Laplacian : 2 V 0 = g m V 2 V 2 ρ B Compute the Lagrangian, energy-momentum tensor and obtain the EOS :

15 In QCD : There can be no preferred color! No simple way to have KdV solitons! Breaking waves!

16 Breaking wave equation :

17 QGP equation of state MIT Bag Model

18 Zero Temperature Compact stars Baryon rich system Sound = perturbation in the baryon density Euler v ρ B Expand and in powers of σ

19 Initial condition: ρ = 1 A sech 2 ( x B ) Numerical solution: increasing A the wave breaks earlier decreasing B the wave breaks earlier

20 A

21 7A

22 Heavy ion collisions Zero baryon number High Temperature Sound = perturbation in the energy density Entropy conservation Euler v ε σ Expand and in powers of

23 Initial condition: ε 1 = A sech 2 ( x B ) Numerical solution: increasing T the wave breaks earlier

24 B

25 0.4 B

26 T

27 2T

28 2T 0.2 A

29 If the pulse lives longer more energy goes foreward and less energy goes to the conical wave! weaker wake Torrieri, Noronha, Betz, Gyulassy stronger wake arxiv: nucl-th

30 Summary Improve hydrodynamics: small effects might be observable Non-linear effects may appear: solitons and shocks Simple way to obtain KdV in QHD in cold and warm nuclear matter It does not work for QCD: breaking waves We have tested a simple QGP EOS : compact stars: long living perturbations in baryon density hot QGP: long living, far reaching pulses in energy density Propagation of pulses depend on initial amplitude, width and medium temperature These pulses might be in the head of Mach cones...

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40 Grandezas fundamentais: Densidade: ρ = m V massa (Kg) 3 volume ( m ) (massa específica) Compressibilidade: facilidade em mudar de volume Líquido = fluido incompressível ρ constante Gás = fluido compressível ρ varia Essa distinção depende mais das forças intermoleculares.

41 XI HADRON PHYSICS March, 22-27, 2010, São Sebastião, Brazil

42 π π supersonic quark π π unquenched jet

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44 É difícil acreditar...

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