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Non-Perturbative Effects in Quark-Gluon Plasma: Equations & State

Explore non-perturbative effects in quark-gluon plasma with the equation of state. Analysis of lattice results, quasi-particle approach, modified Stefan-Boltzmann constant, bag models, and more by Oleg Mogilevsky. Discover possible physical origins, applications, and implications for QCD.

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Non-Perturbative Effects in Quark-Gluon Plasma: Equations & 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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