QCD Global symmetries m m symmetry Chiral symmetry

QCD : Global symmetries m m symmetry Chiral symmetry QGP HG Quark Potential Debye screened confined Deconfinement and Chiral Symmetry restoration expected within QCD Chiral Condensate 1

QCD thermodynamics at finite baryon density K. Redlich in LGT and Heavy Ion Collisions QCD Thermodynamics in LGT critical parameters and EQS LGT at finite baryon density Fluctuations of conserved Q From LGT to heavy ion collisions critical freezeout conditions conservation laws and particle excitation functions strangeness production and energy dependence in-medium hadronic spectral functions T ? quark-gluon plasma --symmetry restored hadron gas -symmetry broken color superconductor 2

QCD on the Lattice PQCD not applicable near deconfinement QCD thermodynamics requires 3 LGT calculations

Lattice QCD – the Wilson action n Take limits: => and => 4

Effective theory for the Wilson line n Z(N)- invariance: Choose a gauge such as is independent and is a diagonal matrix => with 5

Wilson line and deconfinemnet { h –acts as an external field Consider fluctuations: to determine the position of the phase transition: < L(T, h)> h 0 h=0 6

Order parameter of chiral symmetry restoration effective quark mass shift Measures dynamically generated „constituent” quark mass: T=0 quarks „dress” with gluons in hot medium dressing „melts” { Consider chiral susceptibility: to determine the position of the chiral phase transition: How are chiral symmetry restoration and deconfinement T related in QCD? 7

Deconfinement and chiral symmetry restoration in N_f=2 flavour LGT (Bielefeld results) n n LGT predicts one thermal transition from hadronic matter to QGP where deconfinement sets in chiral symmetry is restored 8

Thermodynamical observable Deconfinement sudden increase in energy density 9

Critical Temperature in the chiral limit Fodor and Katz Karsch et al. . 2000 JHEP 0404 (2004) 050 MILC Coll. 2004 10

Deconfinement is density driven - (percolation) LGT result shows: dependence of on and , however for and for all Hadron resonance gas partition function provides a good description of m and depen. of deconfinement temperature A. Peikert, et al. . condition for deconfinement hadrons H. Satz percolation deconfinement hadrons + glubols lines of constant energy density in HG 11

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 => crossover No change with => crossover ? ? ? 12

No change with => crossover ? ? Not necessary: e. g. SU(2) pure gauge theory J. Engels, F. Karsch & K. R. 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 13

QCD at non-vanishing chemical potential Bielefeld-Swansea approach complex fermion determinant Taylor expansion of C. R. Allton, et al. . : , 14

Change of T_c with chemical potential From dependence of chiral susceptibilities 15

Chiral critical point in 3 -flavour QCD F. Karsch et al. Strong dependence of the position of second order endpoint on the quark mass! 0. 3 T [Me. V] Pure Gauge 0. 25 crossover transition 0. 2 1 -st order 2 -en ord. 0. 15 0. 1 N_f=3, m=0. 005 0. 05 Strong dependence of the slope on the quark mass miu [Ge. V] 0 0 0. 2 0. 4 0. 6 0. 8 p 4 improved action 1. 0 1. 2 16

The endpoint of QCD in T-miu_B plane Fodor & Katz 01, 04 • Multiparameter reweighting: renormalized physical operator Lee-Yang zeroes: Finite volume V: If and: phase transition crossover transition 17

Chemical freezeout curve from heavy ion data coincides with freezeout T at RHIC and SPC 18

space-time evolution -- thermalization Initial conditions, momentum distribution L. Mc. Lerran & R. Venugopalan model Thermalization: p. QCD+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 K. Geiger, J. Kapusta, B. Müller, D. K. Srivastava Large elliptic flow at RHIC thermalization of partonic medium fast < 1 fm 19

Heavy Ion collisions n n Chemical freeze-out: particle abundances are frozen in Thermal freeze-out: particle spectra are frozen in Test of equilibration requires to specify: level of observation: multiplicities, spectra, correlations Statistical operator ? ? include conservation laws: strangeness, isospin, baryon number 20

Statistical operator and mass spectrum resonance dominance (R. Hagedorn) + approximate by experimentally known mass spectrum Breit-Wigner res. particle yield thermal density BR thermal density of resonances Only 2 -parameters needed to fix all particle yield ratios 21

Particle multiplicity ratios Hagedorn resonance gas and particle multiplicity ratios at RHIC MODEL DATA P. Braun Munzinger, D. Magestro, J. Stachel & K. R Only 2 -parameters needed to fix all particle yields ratios obtained at SIS through AGS, SPS up to RHIC energy 22

Chemical freezeout curve from heavy ion data coincides with freezeout T at RHIC and SPC AGS, SPS, RHIC F. Becattini, et al. P. Braun-Munzinger, et al. J. Cleymans, et al. M. Kaneta & Nu Xu J. Stachel, et al. Cleymans & Redlich SIS R. Averbeck, R. Holzmann, V. Metag, R. S. Simon H. Oeschler, et al. . Thermal Freezeout see recent results of CERES Collaboration 23 & Broniowski, Florkowski

Particle Ratios along freezout curve Nu Xu & K. R SPS 24

From Meson to Baryon dominance baryon density along freezeout curve F. Antinori explicit P. Braun-Munzinger, et al. . , dependence cancelled 25

Kinetics of abelian charges Wang, K. R Consider: C. M. Ko, V. Koch, Z. Lin, M. Stephanov, Xin-Nian T, V Rate equation : Size of fluctuations Equilibrium limit 26

conservation on the average A A S exact conservation Consider thermal system with S=0 A A S=-1 S=0 S suppression factor 1 suppression increases with S and with decreassing collision energy 27

Correlated strangeness production H. Oeschler, et al. Kao. S (GSI-SIS) 28

Strangeness enhancement: energy and strangeness content dependence Tounsi & K. R decrease of enhancements from SPS to RHIC predicted ( A. Tounsi) Predicted order of magnitude of enhancements at RHIC close at 40 AGe. V too large Centrality dependence not correct when assuming , however (i) V do not need to scale linearly!! (ii) eq. S-S is not Pb-Pb with 60 Ideal test of C=>GC: changing by atomic number in central A—A collisions and not impact parameter in Pb—Pb !! 29

Statistical Model and Energy dependence of strangeness enhancement A. Mishke, A. Tounsi & K. R Strangeness enhancement larger for lower energy 30

Strange particle yields energy and centrality dependence STAR p+p =200 Ge. V Au+Au STAR preliminary 31

Thermal Model in pp and p. A collisions U. Heinz & F. Becattini good description of stable particle yields with the value of temperature similar as expected in A-A collision: however, Observed deviations of short lived resonances by a few sigma: J. Cleymans, S. Wheaton & K. R The ratios measured by NA 49 in p-Pb and Pb-Pb consistent with thermal model 32

Chemical equilibration: strangeness? Andronic, Braun-Munzinger &K. R. SPS RHIC H. Oeschler, et al. . , 33

Scaling relations of production However, since thus and 34

Chemical freezeout curve from heavy ion data coincides with freezeout T at RHIC and SPC 35

QCD Thermodynamics of confined phase Heavy Ion Phenomenology through ? Lattice 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 36

Taylor expansion of resonance pressure baryon mass spectrum 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: 37

factorization on the Lattice 38

QCD partition function from LGT and Phenomenology Taylor coefficients of cosh(x) check T-dependence c(T) requires: 39

Isovector and electric charge fluctuations ; =0 for related with space-like screening limit of the retarded photon self-energy In LGT: obtained from , however requires independent Monte-Carlo calculations 40

Charge Fluctuations Near Deconfinement Mass and quantum number gap between confined and deconfined phase S. N Jeon & V. Koch E. Shuryak & M. Stephanov U. Heinz & B. Muller …. 41

and Isovector susceptibility in LGT resonances gas on the lattice: expanding cosh(x) one expects: LGT result supports decomposition of meson baryon contribution in confined phase 42

density quark condensate at finite Baryon contribution: Net baryon pressure In 2 -flavour LGT calculations: 43

From LGT to HRG Phenomenology: quantitative analysis of T-dependence of thermodynamics In HRG the pressure LGT results from Integral method can be appr. obtained from the Taylor coefficients of use c’s from LGT check P? provides good T-dependence of LGT pressure 44

Hadron Mass Spectrum versus quark mass chiral limit quenched limit extrapolate: from LGT or model 45

Bag Model and Hadron Masses -------------------q ----------g q -------q g -----------------B------ : surface boundary conditions Hadron Masses from: for and : 46

Hadron Mass Spectrum – LGT and Bag model results F. Karsch, A. Tawfik, K. R. LGT results for pion mass dependence of and their parity partners 2 QCDSF Coll. , M. Göckeler, et al. . 47

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. 48

Hadron resonance gas model and LGT thermodynamics 49

Hadron resonance gas model and LGT thermodynamics ? ? n Critical structure due to QCD End-Point How large the singular contribution could be in the actual LGT calculations ? 50

Charge Fluctuations near QCD critical end-point The appearance of the critical and-point results in a long-range correlations induce Consequently: observables that are coupled to the sigma field should exhibit a critical behavior and expected to be divergent at the critical end-point, thus: Consider only isodublet sector through What could be the contribution of point appears at contribution, then describes statistical fluctuaitons in a thermal system if indeed the critical end? 51

Singular contribution to the quark number susceptibility Hatta & Stephanov, Ejiri, Karsch & K. R n n Consider effective Langrangian Calculate Free energy + take get: + • From the NJL model (G. E. Brown et al. ) • Take parameters from actual LGT calculations at and get: The quark mass on the lattice is still too large to possibly see the contribution of the singular part in the net quark number susceptibility 52 Rather no connection between NA 49 HORN and LGT

Isovector and baryon number susceptibilities Modelling isovector fluctuations: At only ~10% contribution is due to pion Including interactions e. g. actually reduces fluctuations strong Debye mass Modelling fluctuations within models that account for interactions between only a very few low lying particles is not sufficient. 53

Phase boundary of fixed energy density versus chemical freezeout LGT SPS 40 AGe. V Spliting of chemical freezeout and phase boundary surface most likely appearswhen the densities of mesons and baryons are comparable For E<30 AGe. V strong collective effects in hadronic medium are to be expected J. Cleymans et al. . Mesons Baryons 54

Conclusions • There is most likely no phase transition but rapid crossover in full QCD, However, improvement of flavor symmetry in the staggered fermion formulation may have an impact on the phase transition • There is a substantial progress at finite baryon density in LGT but we are far from final results: one needs to be closer to the continuum and chiral limit. No results for EQS at small quark mass • Lattice data provide evidence for Hagedorn type transition in full QCD (a density driven deconfinement transition). Good description of LGT thermodynamics and particle produciton yields by phenomenological statistical operator of hadron resonance gas • The splitting of chemical freezeout and critical line appears when meson/baryon ratio is of the order of unity (E<40 AGe. V) 55

and freezout curve ratios along the NA 49 data J. Cleymans, H. Oeschler & K. R. Include. F. Becattini, M. Gazdzicki, A. Keranen, J. Manninen & R. Stock very sensitive to contributions from weak decays ( A. Andronic J. Stachel). 56

Particle Ratios along freezout curve H. Oeschler, J. Cleymans & K. R Nu Xu & K. R SPS 57

N( )/K- independent of centrality P. Steinberg et al. . STAR Should be centrality dependent as 58

Thermal calculations Do not reproduce ratios of short-lived resonances (P. Fachini for STAR Coll. ) f 0 π- Λ(1520) pp 27 Ge. V Λ SPS model pp Na 49 NA 49 Pb. Pb ρ0 π- pp 27 Ge. V K*0 K- J. Rafelski 59

mesons Collision broadening – vector N N pion cloud modification M. Post, S. Leupold, U. Mosel; M. F. M. Lutz, G. Wolf, direct interactions with hadrons B. Friman; B. Friman M. Urban, M. Buballa, J. & H. Pierner Wambach R. Rapp, et al. . ; W. Weise, et al. . ; T. Hatsuda, S. H. Lee; 60 Ch. Gale, et al. . ; G. Chanfray et al. . ; G. E. Brown, et al. . ; . . .

Vector meson spectral function effective Lagrangian approach R. Rapp et al. . M. Post, S. Leupold, U. Mosel low M => significant contribution from couplings of: to the and to the states 61

Chiral Symmetry Restoration needs in-medium spectral function Boyd et al Weinberg sum rules: (Kapusta &Schuryak) in vacuum: spontaneous chir. sym. breaking in medium (phase tran. ): chir. sym. restored critical region very narrow 62

In medium effects and dilepton yield 1 -loop M. Post, S. Leupold, U. Mosel enhancement increases with decreasing / Baryon ratio vacuum 63

Isospin multiplets contribution to QCD thermodynamics Largest deviations in mesonic channel Diferent Isospin states contribution to thermodynamic pressure: Connected with LGT coefficient in the Taylor expansion of susceptibilities: 64

Quark mass dependence of the QCD thermodynamics below deconfinement Linear dependence of quark mass in LGT on the 65

Higher moments are important to search for deconfinement transition 66

Mixed susceptibilities 67

Strangeness enhancement: energy and strangeness content dependence Tounsi & K. R 68

Yields/Participant in A-A/p-p collisions { enhancement decreases In SM by A. Tounsi et al. . as energy increases Obtained with predicted thermal parameters: In Ur. QMD by M. Bleicher et al. . the opposite behaviour Compare with recent values from the fit to NA 49 data (F. Becattini et al. . ): 69

Antikaon nuclear Bound state in heavy ion collisions Y. Akaishi & T. Yamazaki A. Andronic, P. Braun-Munzinger & K. R strongly attractive -potential results in formation of deeply bound -- nuclear states M. Iwasaki et al nuclear state seen in KEK experiment reaction 70