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Quasiparticle Perspective on the Critical End Point and Lattice QCD Comparisons

This research explores the nuances between the Quasiparticle Model and Lattice QCD, particularly focusing on the Critical End Point (CEP) of QCD phase transitions. Key findings discuss improved calculations of the equation of state (EoS) and singular contributions relevant to cosmology. Moreover, the paper addresses hydrodynamic models under varying conditions at RHIC and LHC, and how fluctuations in baryon number influence the understanding of phase transitions and freeze-out dynamics. Central to the investigation is the relationship between theoretical models and empirical data.

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Quasiparticle Perspective on the Critical End Point and Lattice QCD Comparisons

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  1. Quasiparticle Perspective on CEP B. Kämpfer Research Center Rossendorf/Dresden Technical University Dresden • Quasiparticle Model vs. Lattice QCD • Including the CEP • - Somewhat Hydro with M. Bluhm, R. Schulze, D. Seipt, supported by BMBF, GSI, EU

  2. nothing NJL Perspective (Fodor et al.) NJL Model (Schaefer-Wambach) PNJL: Weise, Ratti,...

  3. Lattice QCD Results 1. Phase Boundary Improved calculs. 2. EoS = 0 Taylor expansion reweighting, overlapping, complex mu

  4. Quasiparticle Model lattice 1-loop selfenergies effective stat. + thermo.consist.

  5. Bielefeld 2001 E. Shuryak:

  6. Bielefeld-Swansea data Important for Cosmology: T(t) c0 phase transition Important for Cosmology: n(t) c2 c6 c4

  7. c2  QPM  susceptibility peak: crit. behavior

  8. Isentropic Expansion chemical freeze-out: T, muB  s/n Nf=2 QPM thermodynamics looks fine

  9. T ) kink in (T, (r,h) 2. div. of h r Including the CEP Gebhard, Krey 1. QPM Phenomenological Construction (holds only near CEP)

  10. 3. Singular Part of EoS: Parametric Form QCD: 3D Ising Model Guida+Zinn-Justin

  11. 0=const (r,h) (R, ) R=const h=const r=const

  12. Toy Model I: smooth reg. EoS 1. pQCD 2. critical curve additional information 170 MeV Allton et al. 2002 3. CEP: Fodor-Katz 333

  13. Finite Grid Effects

  14. CEP CEP: Attractor - Repulsor unphysical no focusing effect Wambach et al.

  15. A Funnel Effect due to Phase Transition? Barz, Kämpfer, Csernai, Lukacs PLB 1984 1D Hydro & relaxation time approx. focusing effect squeezing of chem. freeze-out points exp. not observed

  16. Toy Model II: 2-Phase Ansatz Nonaka, Asakawa (2004) critical curve: given by

  17. Toy Model III: QPM & CEP

  18. lattice change of effective carriers of baryon number fluctuations

  19. Need of Modifying lQCD by CEP? K. Paech et al. Hydro with CEP Conjecture: hydro evolution of v2, pT at top-RHIC & LHC does not feel CEP using P. Kolbs code + init.parameters Kolb-Rapp off-equilibrium hadron EoS with U. Heinz/Ohio

  20. 2+1 EoS ready? RHIC Init.conds. Karsch Bernard 0.2 Bernard 0.1 Aoki

  21. A Family of EoS‘s QPM + lin.interpol. + + fix * sound waves interpolation is better than extrapolation

  22. Strange Baryons data disfavor phase transition Huovinen 2005: opposite conclusion (inspection of small pT)

  23. D Mesons Meson non-hydro behavior of open charm? or K?

  24. Looking for Hydro Scaling

  25. To Do List 1. shape fluctuations K. Werner (core-corona) 2. shape & energy density fluctuations T. Kodama et al.

  26. Summary & Outlook -- Lattice QCD vs. Quasiparticle Model: perfect description of either p(T,0) or p(T,mu) extrapolation to larger mu consistency of chem.freeze-out and isentropes -- Toy models for including CEP: many free parameters, size of critical region = ? lattice QCD + CEP = small effects allowed -- v2 hydro: RHIC: EoS at Tc does not matter too much -- CERN-SPS – CBM-FAIR: very different

  27. back up slides

  28. hydro lQCD QCD QPM EoS

  29. Relativistic Hydro with U. Heinz/Ohio Init. Conds.: b dependent profiles from wounded nucleon & binary collisions s < 110 fm-3, nB < 0.4 fm-3: RHIC200 P. Kolb et al. Freeze-out: Cooper-Frye, T = 100 MeV Kolb-Rapp off-equilibrium EoS: p(e,nB), T(e,nB), muB(e,nB)

  30. Interpolation is Better than Extrapolation * lQCD lQCD/res.gas/KR V2: weak dependence on EoS

  31. w/o CEP

  32. The 10% Problem c2  c0 c0

  33. Weak Dependence of v2 on EoS

  34. Progress of lQCD: High-density part fixed High Density EoS x tiny baryon density effects QPM(2.0) : bag model QPM(1.0) Progress of lQCD: Low-density part fixed (=resonance gas: Redlich)

  35. with CEP

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