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Non-Perturbative Effects for the Quark Gluon Plasma Equation of State

Non-Perturbative Effects for the Quark Gluon Plasma Equation of State. Oleg A. Mogilevsky. Viktor. V. Begun, Mark I. Gorenstein Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine. Begun, Gorenstein, O.A. M., Ukr. J. Phys. (2010) and Int. J. Mod. Phys. E (2011).

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Non-Perturbative Effects for the Quark Gluon Plasma Equation of State

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  1. Non-Perturbative Effects for the Quark Gluon Plasma Equation of State Oleg A. Mogilevsky • Viktor. V. Begun, Mark I. Gorenstein • Bogolyubov Institute for Theoretical Physics, • Kiev, Ukraine Begun, Gorenstein, O.A.M., Ukr. J. Phys. (2010) and Int. J. Mod. Phys. E (2011)

  2. Lattice results for the QCD EoSin the SU(3) gluodynamics Boyd et al, PRL 1995 NPB 1996 • Thep(T)is verysmallatTcand rapidlyincreasesat T > Tc • AthighTthe system behaves asidealmasslessgas • The constant is about10% smallerthan the SB limit • Both and approach their limiting valuefrom below • The interaction measure demonstrates a prominentmaximumatT = 1.1 Tc Oleg Mogilevsky

  3. Quasi-particle approach The thermodynamic relation leads to the equation for B* where Interacting gluons are treated as a gas of non-interacting quasi-particles with gluon quantum numbers, but with mass m(T) and particle energy Oleg Mogilevsky

  4. The modified SB constant The modified SB constant σ = 4.73 < σSBallows to fit the high temperature behavior of pressure and energy density. This requires κ(a) ~ 0.9 and a ~ 0.84 Oleg Mogilevsky

  5. Bag Model For non-interacting massless constituents and zero values of all conserved charges: With negative values of B one obtains a good fit of for T > Tc, but finds a disagreement for Oleg Mogilevsky

  6. C – Bag Model R.D. Pisarsky, PRD 2006 Prog. Theor. Phys. Suppl. 2007 Oleg Mogilevsky

  7. Linear Term in pressure Bag C – Bag The thermodynamical relation is the 1st order differential equation. Its general solution involves an arbitrary integration constant A Oleg Mogilevsky

  8. A – Bag Model The term −AT gives a negative contribution to p(T) and guarantees both a correct high temperature behavior of and its strong drop at T near Tc. The A-BM, gives essentially the same values of the model parameters , B, and A either one starts from fitting of or from Oleg Mogilevsky

  9. Interaction Measure A = 0 C = 0 C –Bag A – Bag The C-BM gives no maximum. The requirement of a maximum makes the fit worse at T > 2Tc, whereas the A-BMgives the maximum either one fits the pressure or the interaction measure. Oleg Mogilevsky

  10. Possible Physical Origin of the A-Bag Model the modified gluon dispersion relation where M is a QCD mass scale corresponds to effective mass which is large at low k, and provides an infrared cut-off at k ~ M It gives power corrections of relative order for and for Gribov, Nucl.Phys.B 1978; Zwanziger, Phys. Rev. Lett. 2005 Karsch, Z. Phys. C 1988; Rischke, et. al. Phys. Lett. B 1992. Oleg Mogilevsky

  11. EoS in QCD with 2+1 quarks Lattice data from M. Cheng et al. Phys.Rev.D 2008 See details inour paper: Int. J. Mod. Phys. E (2011) Oleg Mogilevsky

  12. Summary: • A linear in T pressure term is admitted by the thermodynamic relation between and • We find that the A-BM with negative bag constantBleads to the best agreement with the lattice results. • The A-BM gives a simple analyticalparameterization of the QGP EoS. This opens new possibilities for its applications. Oleg Mogilevsky

  13. Why B < 0 ? No answer yet  It is allowed for T>Tc  Oleg Mogilevsky

  14. Pressure over energy density,velocity of sound We did not fit or , however, the correspon- dence to data is good. Oleg Mogilevsky

  15. How to change ? Oleg Mogilevsky

  16. Mass of Quasi-particles Gorenstein, Yang Phys.Rev.D 1995 Brau, Buisseret, Phys.Rev.D 2009 m ~ aT for T > 1.2 Tc Oleg Mogilevsky

  17. SU(Nc) gluodynamics Panero PRL 2009 All thermodynamic quantities follow essentially the same curves for different NC. Thus, our SU(3) fit of the A-BMcan be extrapolated forSU(NC) with and Oleg Mogilevsky

  18. Applications Dilepton production by dynamical quasiparticles in the strongly interacting quarkgluonplasma. arXiv:1004.2591 O. Linnyk. Oleg Mogilevsky

  19. Oleg Mogilevsky

  20. Summary: • The good fits of lead to awrong behavior of This happens because of a linear in Tterm admitted by the thermodynamic relation between and • We find that the A-BM with negative bag constantBleads to the best agreement with the lattice results. • The A-BM gives a simple analyticalparameterization of the QGP EoS. This opens new possibilities for its applications. Oleg Mogilevsky

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