High Temperature/Density QCD

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1 High Temperature/Density QCD Frithjof Karsch, BNL and Bielefeld University Temperature ~17 MeV Early Universe Future LHC Experiments Crossover Current RHIC Experiments RHIC Energy Scan Critical Point 1 st order phase Hadron Gas The Phases of QCD Quark-Gluon Plasma Future FAIR Experiments transition Color Superconductor physics of the early universe hot: OUTLINE - Overview T 1 12 K - Equation of State, T c - Transport Coefficients - Quarkonium - Charge Fluctuations - Critical Point properties of compact stars MeV Vacuum Nuclear Matter MeV 9 MeV Neutron Stars Baryon Chemical Potential dense: n B 1n NM F. Karsch, LQCD review 29 p.1/25

2 The Phases of Nuclear Matter Key Questions (NP LRP 27) Temperature Early Universe Future LHC Experiments The Phases of QCD Current RHIC Experiments Quark-Gluon Plasma RHIC Energy Scan study properties of strongly interacting nuclear matter and elementary particles under extreme conditions ~17 MeV Crossover Critical Point 1 st order phase Hadron Gas Nuclear Vacuum Matter MeV MeV 9 MeV Future FAIR Experiments transition Color Superconductor Neutron Stars Baryon Chemical Potential strongly interacting QCD = Quantum Chromo Dynamics GOAL: learn about basic mechanisms that characterize QCD chiral symmetry breaking; confinement; asymptotic freedom; axial anomaly What are the phases of strongly interacting matter, and what role do they play in the cosmos? What does QCD predict for the properties of strongly interacting matter? What governs the transition of quarks and gluons into pions and nucleons? F. Karsch, LQCD review 29 p.2/25

3 Heavy Ion collisions and the QGP simple Bjorken model 1-d hydrodynamic expansion equation of motion: µ T µν = energy density: dǫ dτ + 1 τ (ǫ + p) 1 τ 2 «4 3 η + θ = ǫ(τ )δ(τ τ ) understanding the time evolution requires knowledge of the equation of state and transport coefficients (bulk (θ) and shear (η) viscosity) F. Karsch, LQCD review 29 p.3/25

4 most cited US-Thermo papers 28 1) M. Cheng et al (hotqcd Collaboration), The QCD equation of state with almost physical quark masses, Phys. Rev. D77, (28) [63 citations] 5) M. Cheng et al (RBC-Bielefeld Collaboration), The Transition temperature in QCD, Phys. Rev. D74, 5457 (26) [45 citations] 1) S. Datta et al (BNL-Bielefeld), Behavior of charmonium systems after deconfinement, Phys. Rev. D69, 9457 (24) [39 citations] 2) H. B. Meyer (MIT), A Calculation of the shear viscosity in SU(3) gluodynamics, Phys. Rev. D76, 1171 (27) [34 citations] 24) H. B. Meyer (MIT), A Calculation of the bulk viscosity in SU(3) gluodynamics, Phys. Rev. Lett. 1, 1621 (28) [34 citations] 33) O. Kaczmarek and F. Zantow (Bielefeld-BNL), Static quark anti-quark interactions in zero and finite temperature QCD. I. Heavy quark free energies, running coupling and quarkonium binding, Phys. Rev. D71, (25) [3 citations] F. Karsch, LQCD review 29 p.4/25

5 ...some statistics from SPIRES... 5 top cited papers in hep-lat during each year in year # Thermo # Thermo the top-cited the top-cited papers (WW) papers (US) Thermo (WW) Thermo (US) (finite-µ) 48 (Quarkonium) (finite-µ) 1 (Quarkonium) (MEM) 6 (Quarkonium) ((2+1)-f, T c ) 4 ((2+1)-f, T c ) ((2+1)-f, EoS) 1 ((2+1)-f, EoS) about 4% of the 5 top cited papers in hep-lat deal with QCD thermodynamics about 1/3 of these papers involve authors from the US (=USQCD). They gained increasing impact F. Karsch, LQCD review 29 p.5/25

6 Bulk thermodynamics Goal: QCD thermodynamics with realistic quark masses in (2+1)-f QCD and controlled extrapolation to the continuum limit; T c, EoS,.. for µ q N τ = 4, 6: bulk thermodynamics on a line of constant physics (LCP): RBC-Bielefeld collaboration (i) use m l =.1m s, corresponding to m π 22 MeV; (ii) tune m s to physical strange quark mass using m K, m ss at all values of the cut-off analyze EoS in a wide T -range: 14 MeV< T< 8 MeV PRD77, (28) extend analysis to N τ = 8; compare p4 and asqtad results: joint project of RBC, Bielefeld, MILC, LANL and LLNL hotqcd collaboration, arxiv: F. Karsch, LQCD review 29 p.6/25

7 Parametrization of LGT-EoS: Input to hydrodynamic models easy to use analytic parametrization of LGT-EoS for hydrodynamic model calculations: matches to hadron resonance gas model at low temperature ( ) ( ǫ 3p 1 d2 = 1 T 4 [1 + e (T c 1)/c 2) ] 2 T + d ) 4 2 T 4 (ε-3p)/t 4 p4 asqtad HRG Data d 2 [GeV] 2 d 4 [GeV] 4 p4-1 MeV.241(6).35(9) HRG+p4.24(2).54(17) asq-1 MeV.293(6). HRG+asqtad.312(5) T [MeV] A. Bazavov et al. (hotqcd Collaboration), arxiv: [hep-lat] Data c 1 [GeV] c 2 [GeV] p4-1 MeV.1938(6).1361(4) HRG+p4.273(6).172(3) asq-1 MeV.1943(6).167(4) HRG+asqtad.248(6).188(4) F. Karsch, LQCD review 29 p.7/25

8 EoS and velocity of sound p/ǫ velocity of sound: c 2 s = dp dǫ = ǫd(p/ǫ) dǫ + p ǫ s c V hotqcd c 2 s Tr p4 lqcd T-1 MeV HRG+lqcd HRG (T c =18 MeV) VH2 hydro asqtad T [MeV] hydro-expansion: p/ǫ < 1/3 slows down expansion; increases plasma lifetime e.g. 1 ǫ [GeV/fm 3 ] 1 τ 5.5 fm (ideal gas) τ 7 fm (LGT EoS) F. Karsch, LQCD review 29 p.8/25

9 Pressure, Energy and Entropy p/t 4 from integration over (ǫ 3p)/T 5 ; starting integration at T = MeV with p() = ; use hadron resonance gas at T = 1 MeV to estimate systematic error: [p(t )/T 4 ] HRG.265 high-t region is well under control; significant deviations from conformal limit ε/t 4 3p/T 4 Tr ε SB /T 4 p4 asqtad p4 asqtad T [MeV] AND AdS/CFT Tr s SB /T s/t 3 p4: N τ =8 6 asqtad: N τ =8 6 T [MeV] AdS/CFT band: 185 MeV T 195 MeV hotqcd: p4 vs. asqtad (arxiv: ) F. Karsch, LQCD review 29 p.9/25

10 Open Issues: Low and High-T asymptotics (ε-3p)/t 4 asqtad: N τ =8 6 p4: N τ =8 6 Tr T [MeV] LGT vs resonance gas approach to continuum limit N τ = 6, 8 O(5MeV ) shift of T-scale LGT below HRG for T< 18 MeV coarser lattice, larger cut-off effects but: Which HRG? M max =1.5 GeV, 2.5 GeV, (ε-3p)/t 4 p4: N τ =4 6 8 asqtad: N τ =6 8 T [MeV] Tr LGT vs. pert. theory approach to continuum limit N τ = 6, 8: no significant cut-off dependence for T> 3 MeV strong deviations from conformal limit: find (ǫ 3p)/T 4 a/t 2 + b/t 4 for 3MeV< T< 7MeV F. Karsch, LQCD review 29 p.1/25

11 Chiral symmetry restoration: χ-condensate and susceptibility sudden change in chiral condensate is, of course, related to peaks in the (singlet) chiral susceptibility ψψ l,t m l m s ψψ s,t ψψ l, m l m s ψψ s, χ tot /T 2 = 1 T 2 d ψψ l,t dm l = 2χ dis /T 2 + χ con /T l,s Tr N τ = χ tot /T 2 hotqcd preliminary.6.4 asqtad p4fat p4 and asqtad: hotqcd *p4fat3 asqtad T [MeV] F. Karsch, LQCD review 29 p.11/25

12 Transition temperature in 2- and (2+1)-flavor QCD T [MeV] use T= scale: r=.469fm Nf=2: V.G. Bornyakov et al, POS Lat25, 157 (26) (improved Wilson, Nt=8, 1; input: r=.5 fm) (added Nt=12, Lattice 7) (rescaled to r) Y. Maezawa et al., hep lat/725 (QM 26) (improved Wilson, Nt=4, 6; input: m rho) (no cont. exp. yet) Nf=2=1: C. Bernard et al., Phys.Rev. D71, 3454 (25) (improved staggered (asqtad), Nt=4,6,8, input r1) (rescaled to r) M. Cheng et al., Phys.Rev D74, 5457 (26) (improved staggered (p4), Nt=4,6; input r) Y. Aoki et al., Phys. Lett. B643, 46 (26), arxiv: (staggered (stout), Nt=4,6,8,1,12; input fk) (converted to r) chiral deconfinement chiral+deconfinement F. Karsch, LQCD review 29 p.12/25

13 Transition temperature in 2- and (2+1)-flavor QCD T [MeV] Nf=2: use T= scale: r=.469fm Known shortcomings: too few data: 3-parameter fit to 4 data points for T c determined at V.G. Bornyakov et al, POS Lat25, 157 (26) (improved Wilson, Nt=8, 1; input: r=.5 fm) m (added π > 55 MeV Nt=12, Lattice 7) (rescaled to r) no continuum extrapolation attempted yet; would like to see results in units of r Y. Maezawa et al., hep lat/725 (QM 26) (improved Wilson, Nt=4, 6; input: m rho) (no cont. exp. yet) Nf=2=1: C. Bernard et al., Phys.Rev. D71, 3454 (25) N τ = 4, 6, 8, but small spatial volume for larger N τ ; still large statistical errors on individual data points (improved staggered (asqtad), Nt=4,6,8, input r1) (rescaled to r) M. Cheng et al., Phys.Rev D74, 5457 (26) only N τ = 4 and 6 (improved staggered (p4), Nt=4,6; input r) only one quark mass; T c determination partly based on determination of inflection points (converted to r) Y. Aoki et al., Phys. Lett. B643, 46 (26) (staggered (stout), Nt=4,6,8,1; input fk) chiral deconfinement chiral+deconfinement F. Karsch, LQCD review 29 p.12/25

14 Future EoS calculations Extreme Scale Computing Workshop F. Karsch, LQCD review 29 p.13/25

15 Viscosity and elliptic flow at RHIC asymmetric interaction region asymmetric pressure gradients asymmetric flow velocities: elliptic flow hydrodynamic modeling of flow pattern requires small shear viscosity over entropy: η/s lattice calculations give small η/s: η/s.1 for T/T c ( ) spectral representation of energy-momentum correlator T 12 ()T 12 (t) = dω ρ(ω) cosh(ω(t 1/2T)) sinh(ω/2t) shear viscosity η = lim ω ρ(ω) ω ρ(ω) K(x =1/2T,ω)/T 4 T=1.65T c T=1.24T c ω/t H. Meyer, Phys. Rev. D76, 1171 (27) F. Karsch, LQCD review 29 p.14/25

16 Transport coefficients QGP: a perfect fluid? (??) η shear /s 1/4π η bulk large at T c ρ θ (ω)/(t 4 sinh(ω/2t)) T=1.24T c T=1.65T c G XX (τ, T) = X = P, ǫ, (ǫ 3P) dωρ X (ω) cosh(ω(τ 1/2T) sinh(ω/2t) -.5 ω/t ρ(ω) 9 π ζ(t)ω ω 2 ω 2 + ω 2, τ R 1/ω spectral analysis of SU(3) gauge theory bulk viscosity SU(2): 2 nd order transition: τ R ω G pp (τ, T) 9Tζ(T)ω (T) +... K. Hübner, FK, C. Pica, PR D78, 9451 H. Meyer, Phys. Rev. Lett. 1, 1621 (28). (28) the role of relaxation times (width of the sound peak) needs to get better controled F. Karsch, LQCD review 29 p.15/25

17 Heavy quark spectral functions and correlation functions spectral function from potential model using lattice free energy σ(ω)/ω 2 1.2T c 1.5T c 2.T c free lattice, 1.5T c ω [GeV] G/G rec τ [fm] A.Mocsy, P. Petreczky, PRD77, 1451 (28) reconstructed spectral functions using the Maximum Entropy Method σ/ω 2.75T c 1.12T c 1.5T c ω a S. Datta et al., PRD69, 9457 (24) G J/ψ (τ, T) = dωρ J/ψ (ω) cosh(ω(τ 1/2T) sinh(ω/2t) O.Kaczmarek, F. Zantow, PRD71, (25) 5 F 1 (r,t) [MeV] -5 T/T c r [fm] heavy quark free energy F. Karsch, LQCD review 29 p.16/25

18 Heavy quark spectral functions and correlation functions spectral function from potential model using lattice free energy σ(ω)/ω 2 1.2T c 1.5T c 2.T c free lattice, 1.5T c ω [GeV] G/G rec τ [fm] reconstructed spectral functions using the Maximum Entropy Method σ/ω 2.75T c 1.12T c 1.5T c ω a G J/ψ (τ, T) = dωρ J/ψ (ω) cosh(ω(τ 1/2T) sinh(ω/2t) O.Kaczmarek, F. Zantow, PRD71, (25) 5 need to get better control over ultra-violet cut-off effects (Wilson-doublers) F 1 (r,t) [MeV] use better fermion actions -5 T/T c overlap fermions domain wall fermions 3. r [fm] (truncated) perfect actions... heavy quark free energy F. Karsch, LQCD review 29 p.16/25

19 Future transport and quarkonium spectroscopy calculations Extreme Scale Computing Workshop F. Karsch, LQCD review 29 p.17/25

20 Extending the phase diagram to non-vanishing chemical potential non-zero baryon number density: µ > Z(V, T, µ) = DADψD ψ e S E(V,T,µ) = DAD det M(µ) e S E(V,T) three (partial) solutions for large T, small µ complex fermion determinant; long standing problem F. Karsch, LQCD review 29 p.18/25

21 Extending the phase diagram to non-vanishing chemical potential non-zero baryon number density: µ > Z(V, T, µ) = DADψD ψ e S E(V,T,µ) = DAD det M(µ) e S E(V,T) T/T RHIC, LHC F,K 24 F,K 22 T.2 c, Bielefeld-Swansea (N f =2) T c, Forcrand, Philipsen (N f =2) T c, Forcrand, Philipsen (N f =3) T c, Fodor, Katz (N f =2+1) µ B /T T f, J.Cleymans et. al low energy RHIC, FAIR T c (µ) T c () : 1.56(4)(µ B/T) 2 deforcrand, Philipsen (imag. µ) 1.78(38)(µ B /T) 2 Bielefeld-Swansea (O(µ 2 ) reweighting) search for critical point establish relation between freeze-out and critical behavior F. Karsch, LQCD review 29 p.18/25

22 Quark number susceptibility......and its susceptibility rapid change in quark/baryon/strangeness number susceptibility reflects change in mass of the carrier of these quantum numbers DECONFINEMENT quark number susceptibility feels nearby singular point just like the energy density scaling field: t = T T c T c «2 + A µq, µ crit = singular part: f s (T,µ q ) = b 1 f s (tb 1/(2 α) ) t 2 α T c Y. Hatta, T. Ikeda, PRD67 (23) 1428 c 2 χ q 2 2 ln Z µ 2 q ǫ ln Z T t 1 α, c 4 χ q 4 4 ln Z µ 4 q t α (µ = ) t 1 α, C V 2 ln Z T 2 t α (µ = ) 2 nd derivative w.r.t µ q looks like energy density 4 th derivative w.r.t µ q looks like specific heat F. Karsch, LQCD review 29 p.19/25

23 Quadratic fluctuations of baryon number, charge & strangeness vanishing chemical potentials: RBC-Bielefeld, Phys. Rev. D79, 7455 (29) B χ 2 Q χ 2 S χ T[MeV] SB full: N t =4 open: N t =6 χ Q 2 = 1 V T 3 Q2 χ B 2 = 1 V T 3 N2 B χ S 2 = 1 V T 3 N2 S rapid approach to SB limit smooth change of quadratic fluctuations across transition region chiral limit: χ B 2, χq 2 T T c 1 α + regular F. Karsch, LQCD review 29 p.2/25

24 Quartic fluctuations of baryon number, charge & strangeness vanishing chemical potentials: RBC-Bielefeld, Phys. Rev. D79, 7455 (29) χ 4 B χ 4 Q χ 4 S full: N τ =4 open: N τ =6 SB T [MeV] χ Q 4 = 1 V T 3 ( Q 4 3 Q 2 2) χ B 4 = 1 V T 3 ( N 4 B 3 N2 B 2) χ S 4 = 1 V T 3 ( N 4 S 3 N2 S 2) rapid approach to SB limit large light quark number & charge fluctuations across transition region chiral limit: χ B 4, χq 4 T T c α + regular F. Karsch, LQCD review 29 p.21/25

25 Estimating the location of the critical point: (T CEP, µ c ) i) T CEP : find the largest temperature for which all c n stay positive ii) µ c /T CEP : estimate lim ( ) µc r n = T CEP n r n n cn c n T / T c () Nt=4 Nt=6 Gavai,Gupta Fodor,Katz ρ 2 ρ 4 µ B / T c () r 2 r 4 O(a 2 ) improved action; slight quark mass dependence; weak cut-off dependence first non-trivial estimate of T CEP requires 8 th order for c n : r 6 already O(c 6 ) requires more statistics F. Karsch, LQCD review 29 p.22/25

26 Future finite density calculations Extreme Scale Computing Workshop F. Karsch, LQCD review 29 p.23/25

27 Conclusions bulk thermodynamics with almost physical quark masses seems to be well under control; exploitation of USQCD resources allowed a world-wide leading, unique study of bulk thermodynamics with improved staggered fermions; low temperature region requires finer lattices to control systematics and allow a comparison with hadron gas phenomenology; high-t regime requires calculations on larger lattices to establish contact to (resummed) perturbation theory calculations of transport coefficients in quenched QCD yield results consistent with interpretation of heavy ion experiments, but require more work to control systematics studies of finite density QCD do not yet give a conclusive answer on the existence or non-existence of a critical point in the QCD phase diagram F. Karsch, LQCD review 29 p.24/25

28 F. Karsch, LQCD review 29 p.25/25