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

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
Lattice QCD: significant
non-perturbative effects
RHIC: strongly interacting fluid
Non vanishing gluon condensate above deconfinement
David Miller,
Phys. Rep. (2007)
hep-ph/
Borsanyi et al.,
arXiv:

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

5. Assume that gluon condensates survive in cold QGP
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
mean field approximation
(“Walecka”)
Hard gluons are generated by intense quark sources
They have large ocupation numbers and become classical

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
soft
gluons
hard
gluons
quarks + 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 quark mass : hard coupling : 20 % of the vacuum value

14. Numerical results

15. Pressure and sound velocity

16. Pressure versus energy density

17. Comparison with the MIT bag model
F. Samarruca,
arXiV:
[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/
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:

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...