Chemical Freeze-out II Volume Dependence

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LGT results in 2+1 flavour QCD MILC Coll., hep-lat/0405029, hep-lat/0309118, hep-lat/0209079, Chiral condensate and susceptibility smooth change of the condensate with tempearture => crossoverNo change with => crossover ??? But:

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No change with => crossover ??Not necessary: e.g. SU(2) pure gauge theory SU(2) gauge theory exhibits 2-end order phase transition However, no change of with if There is scaling of physical observables near critical region J. Engels, F. Karsch & K.R.

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QCD at non-vanishing chemical potential Bielefeld-Swansea approachTaylor expansion of : , complex fermion determinant C.R. Allton, et al..

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Change of T_c with chemical potentialFrom dependence of chiral susceptibilities

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Chiral critical point in 3-flavour QCD Ch. Schmitd et al. Strong dependence of the position of second order endpoint on the quark mass! N_f=3, m=0.1 N_f=3, m=0.005T [MeV]miu [GeV]2-en ord.1-st ordercrossover transitionPure Gauge0.30.250.20.150.10.05 00.20.40.60.81.01.20Strong dependence of the slope on the quark massp4 improved action

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The endpoint of QCD in T-miu_B plane Fodor & Katz 01, 04 Multiparameter reweighting: Lee-Yang zeroes: renormalized physical operatorFinite volume V: If and: phase transition crossover transition

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Chemical freezeout curve from heavy ion data coincides with freezeout T at RHIC and SPC

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space-time evolution -- thermalization Initial conditions, momentum distribution L. McLerran & R. Venugopalan model Thermalization: pQCD+kinetics R. Baier, A.H. Mueller, D.Schiff, D.T.Son At LHC and RHIC: thermalization occurs relatively fast due to emission of gluons also from Parton Cascade Model B. Müller, D.K.Srivastava Large elliptic flow at RHIC fast 1fm thermalization of partonic medium

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Only 2-parameters needed to fix all particle yield ratios + approximate by experimentally known mass spectrum Statistical operator and mass spectrumresonance dominance (R. Hagedorn)Breit-Wigner res. particle yield thermal density BR thermal density of resonances

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Chemical freezeout curve from heavy ion data coincides with freezeout T at RHIC and SPC Cleymans & RedlichM. Bleicher et al..

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Particle Ratios along freezout curve Nu Xu & K.R 2000SPS

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From Meson to Baryon dominance baryon density along freezeout curve P. Braun-Munzinger, et al.., F. Antinoriexplicit dependence cancelled

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Heavy Ion Phenomenology through QCD Thermodynamics of confined phaseLattice Gauge Theory at finite and ?Based on common work with Bielefeld-Swansea LGT Coll. C.R. Allton, M. Doring, S. Ejiri, S.J. Hands, O. Kaczmarek, F. Karsch, E. Laermann, K.R. & Shinji Ejiri, Frithjof Karsch

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Taylor expansion of resonance pressure Factorization of the baryonic pressure Compare with LGT results: Consequences: For fixed any ratio of these observables is T-independent the ratio of the O(2) and O(4) coefficients: baryon mass spectrum

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factorization on the Lattice

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QCD partition function from LGT and Phenomenologycheck T-dependence c(T) Taylor coefficients of cosh(x)requires:

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Isovector and electric charge fluctuations related with space-like screening limit of the retarded photon self-energy =0 for In LGT: obtained from ,however requires independent Monte-Carlo calculations ;

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Charge Fluctuations Near DeconfinementS.N Jeon & V. Koch E. Shuryak & M. Stephanov U. Heinz & B. Muller …. Mass and quantum number gap between confined and deconfined phase

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Isovector susceptibility in LGT and resonances gas on the lattice: expanding cosh(x) one expects: LGT result supports decomposition of meson baryon contribution in confined phase

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quark condensate at finite density Baryon contribution:Net baryon pressureIn 2-flavour LGT calculations:

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From LGT to HRG Phenomenology: quantitative analysis of T-dependence of thermodynamics In HRG the pressure can be appr. obtained from the Taylor coefficients of LGT results from Integral method provides good T-dependence of LGT pressureuse c’s from LGT check P?

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Hadron Mass Spectrum versus quark mass chiral limit quenched limit extrapolate: from LGT or model

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Hadron Mass Spectrum – LGT and Bag model resultsLGT results for pion mass dependence of and their parity partners2QCDSF Coll., M. Göckeler, et al..F. Karsch, A. Tawfik, K.R.

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Bag Model and Hadron Masses -------------------- -------------------- --------------------- ------- --- ---------------------- ----------B----------- :surface boundary conditions Hadron Masses from: for and : q qggq

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Hadron resonance gas model and LGT Thermodynamics phenomenological partition function of hadron resonance gas with LGT mass spectrum provides good description of lattice results below deconf.

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Hadron resonance gas model and LGT thermodynamics

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Last Updated: 8th March 2018

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