F.S.N. and D.A. Fogaça

1. Gluon condensates and the equation of state of cold quark gluon plasmas F.S.N. and D.A. Fogaça IFUSP / BRAZIL arXiv:1012.5266

2. Introduction QCD phase diagram Hot QGP Cold QGP

3. Hot QGP Ideal gas of weakly interacting quarks and gluons (perturbative QCD) Equation of state from the MIT bag model RHIC: strongly interacting fluid Lattice QCD: significant non-perturbative effects Non vanishing gluon condensate above deconfinement David Miller, Phys. Rep. (2007) hep-ph/0608234 Borsanyi et al., arXiv:1011.4229

4. Cold QGP MIT Bag “Big Bag” Equation of state MIT bag model vacuum quarks

5. Our goal Assume that gluon condensates survive in cold QGP Naively: they go asymptotically to zero ... Non-trivial behavior: Metlitski, Zhitnitsky, Nucl. Phys. B (2005) Derive a simple EOS for the cold QGP Estimate the effects of the gluon condensates A2 and A4

6. QGP at large densities and zero temperature : Separation of the gluon fields in soft and hard modes: Soft gluons generate the condensates in the plasma Hard gluons are generated by intense quark sources They have large ocupation numbers and become classical mean field approximation (“Walecka”)

7. Infinite matter: soft and hard fields are uniform ! Soft gluons Quarks Hard gluons

8. The effective Lagrangian : Uniform fields: Field decomposition :

9. A^4 A^3 A^2 mass term for the hard gluons A^1 A^0

10. Expectation values of the soft gluons in the “vacuum” : dimension 4 gluon condensate is a parameter ! dimension 2 gluon condensate is a parameter ! dynamical gluon mass

11. The effective Lagrangian quarks + hard gluons soft gluons hard gluons Equations of motion hard coupling g is a parameter ! Energy - momentum tensor

12. The equation of state When the two EOS coincide From B we can infer the value of the condensate in the QGP ! MIT Bag Model

13. Parameters 20 % of the vacuum value 15 % of the vacuum value quark mass : hard coupling :

14. Numerical results

15. Pressure and sound velocity

16. Pressure versus energy density

17. Comparison with the MIT bag model F. Samarruca, arXiV:1009.1172 [nucl-th]

18. Comparison with the MIT bag model More energy More pressure Harder EOS Hard gluons!

19. Comparison with the MIT bag model

20. Conclusion Simple approach to dense and cold QGP Gluon field decomposition = soft + hard Mean field approximation Bag constant Weak gluon condensates in QGP Massive gluons Richer version of the MIT bag model with classical hard gluons Condensates make the EOS softer

21. Back ups

27. But we can estimate the Laplacian : Compute the Lagrangian, energy-momentum tensor and obtain the EOS :

28. Gluon condensate in a hot QGP : David Miller, Phys. Rep. (2007) hep-ph/0608234 Gluon condensate in dense and cold QGP ? Naively: goes asymptotically to zero ! Non-trivial behavior: Metlitski, Zhitnitsky, Nucl. Phys. B (2005)

29. Introduction RHIC (2003) : evidence of the strongly interacting QGP (sQGP) non-perturbative effects ! How to include non-perturbative effects in the equation of state ? Finite temperature: lattice QCD Finite density: models ! Our model: effects of the gluon condensates in the QGP !

31. Borsanyi et al., arXiv:10114229

32. The equation of state From B we can infer the value of the condensate in the QGP ! MIT Bag Model

36. Finite temperature: Finite density ?

38. É difícil acreditar...