Nuclear Matter between Heaven and Earth: The QCD Phase Diagram

Transcription

1 Antrittsvorlesung Frankfurt, October 2010 Nuclear Matter between Heaven and Earth: The QCD Phase Diagram Owe Philipsen Introduction to QCD and lattice simulations Phase diagram: the many faces of QCD Computational difficulties: we are still at the very beginning supported by

2 QCD according to Google... Was ist QCD...? Application: QCD Category: Audio brings the user a huge arsenal of quality features, and uses simplicity as its decoy. QCD is truly the most unique player available. The EOS 20D has a rear QCD (Quick Control Dial) which can be used to set exposure compensation, flash compensation, shutter speed or aperture

3 Quantum Chromodynamics, theory of strong interactions photons e,p gauge group U(1) gluons quarks gauge group SU(3) gluon self-interaction!

4 Running coupling + asymptotic freedom Coupling strength changes with energy scale: Gross, Politzer, Wilczek Nobel 2004 non-perturbative, nuclear physics 0.5! s (Q) 0.4 Bethke, July 2009 Deep Inelastic Scattering e + e Annihilation Heavy Quarkonia QCD! s(" Z) = ± Q [GeV] perturbative (QED-like), verified in high energy scattering! energy scale of physical process

5 Lattice gauge theory + Monte Carlo method QCD partition fcn: Z = DU f det M(µ f,m f ; U) e S gauge(β;u) links=gauge fields det M e S gauge lattice spacing a<< hadron << L! typically > dim. integral 4d : N 3 s N t Monte Carlo, importance sampling U Euclidean time: T = 1 an t Continuum limit: N t,a 0 Phase diagram: N t =4, 6 a 0.3, 0.2 fm Light fermions expensive, Simulate with different quark masses, extrapolate to physical point

6 Lattice gauge theory + Monte Carlo method QCD partition fcn: Z = DU f det M(µ f,m f ; U) e S gauge(β;u) links=gauge fields det M e S gauge lattice spacing a<< hadron << L! typically > dim. integral 4d : N 3 s N t Monte Carlo, importance sampling SUPERCOMPUTING! U Euclidean time: T = 1 an t soon Continuum limit: N t,a 0 Phase diagram: N t =4, 6 LOEWE - CSC a 0.3, 0.2 fm Light fermions expensive, at Goethe-Uni Simulate with different quark masses, extrapolate to physical point

7 Nuclear matter as we know it: light hadron spectrum from the lattice BMW collaboration (Budapest, Marseille, Wuppertal) M[MeV] r K * N L S X D S* X* O mesons= quark anti-quark states p K experiment width input QCD QCD is correct theory for strong interactions also at low energy!

8 QCD at high temperature/density: change of dynamics Phase transitions? Chiral symmetry: broken (nearly) restored chiral condensate, Cooper pairs

9 The QCD phase diagram established by experiment: Nuclear liquid gas transition with critical end point B

10 QCD phase diagram: theorist s view (science fiction) ~170 MeV T early universe T c! heavy ion collisions QGP confined compact stars? Color superconductor µ B ~1 GeV? Until 2001: no finite density lattice calculations, sign problem! Expectation based on simplifying models (NJL, linear sigma model, random matrix models,...) Check this from first principles QCD!

11 Zero and nearly zero baryon density QGP T c! T confined Color superconductor µ

12 QCD in the early universe QCD phase transition QGP + other particles

13 Expansion: pressure of photons + matter particles

14 The QCD equation of state: deconfinement Continuum extrapolation with physical quarks in progress

15 SM degrees of freedom with lattice QCD-EoS Hindmarsh, O.P. 05 Full line: free particles Dashed line: corrected for QCD interactions

16 Important for relic densities of WIMPS Weakly Interacting Massive Particles: dark matter candidates! Energy density of WIMPs depends on g eff,h eff of Standard Model increase of WIMPs by ~2-3% from QCD corrections Hindmarsh, O.P. 05 Planck satellite promises to constrain relic densities to better than 1%!

17 The calculable region of the phase diagram µ<t QGP T c! T confined Color superconductor µ Upper region: equation of state, screening masses, quark number susceptibilities etc. under control Here: phase diagram itself, most difficult!

18 Thermal QCD in experiment heavy ion collision experiments at RHIC, LHC, GSI... have finite baryon density!

19 Deconfinement on Earth:

20 Phase boundary from hadron freeze-out??

21 Theory: how to calculate p.t., critical temperature = crit. exponent

22 The order of the p.t., arbitrary quark masses µ =0 deconfinement p.t.: breaking of global Z(3) symmetry deconfinement critical line chiral p.t. restoration of global symmetry in flavour space SU(2) L SU(2) R U(1) A anomalous chiral critical line

23 Order of p.t., arbitrary quark masses µ =0 chiral p.t. m s m s! tric 0 0 2nd order O(4)? N = 2 f N = 3 f phys. crossover point 1st 2nd order Z(2) m, m u 2nd order Z(2) d 1st Pure Gauge! deconf. p.t. N = 1 f chiral critical line am s Nf=2+1 physical point tric m s - C 2/5 mud am u,d chiral critical line on N t =4,a 0.3 fm de Forcrand, O.P. 07 consistent with tri-critical point at m u,d =0,m tric s 2.8T But: chiral O(4) vs. 1st still open Di Giacomo et al 05, Kogut, Sinclair 07 N f anomaly! =2 Chandrasekharan, Mehta 07 U A (1)

24 The nature of the transition for phys. masses Aoki et al. 06 The nature of the phase transition at the physical point Fodor et al in the staggered approximation...in the continuum...is a crossover!

25 How to The identify sign the problem critical is surface: a phase Binder problemcumulant How to identify the order of the phase transition Z = B 4 ( ψψ) (δ ψψ) 4 DU [det M(µ)] f e S g[u] (δ ψψ) 2 2 V d Ising 1 first order 3positive crossover weights importance sampling requires µ = 0 : B 4 (m, L) = bl 1/ν (m m c 0), ν = 0.63 Dirac operator: D/ (µ) = γ 5 D/ ( µ )γ 5 det(m) complex for SU(3), µ 0 real positive for SU(2), µ = iµ i V 1 V > V 1 V 3 > V 2 > V 1 V=$$" 1.8 Crossover 3 N.B.: all expectation values real, imaginary parts 1.7 cancel, B 4 real positive for but importance sampling config. by config. impossible! 1.6 µ u = µ d First order 0 Same -1 problem -0.5 in many 0 condensed 0.5 matter 1 systems! x x c parameter along phase boundary, T = T c (x) 1.5 L=8 1.4 L=12 L= Ising am

26 1dim. illustration

27 Finite density: methods to evade the sign problem Reweighting: Z = ~exp(v) statistics needed, overlap problem DU det M(0) use for MC det M(µ) det M(0) e S g calculate integrand S µ=0 finite µ U Taylor expansion: O (µ) = O (0) + k=1 c k ( µ πt ) 2k coeffs. one by one, convergence? Imaginary µ = iµ i : no sign problem, fit by polynomial, then analytically continue O (µ i )= N k=0 c k ( µi πt ) 2k, µi iµ requires convergence for anal. continuation All require µ/t < 1!

28 Comparing The good news: approaches: comparing the critical T c (µ) line de Forcrand, Kratochvila 05 de Forcrand, Kratochvila LAT 05 N t = 4, N f = 4 ; same actions (unimproved staggered), same mass! imaginary µ 2 param. imag. µ dble reweighting, LY zeros Same, susceptibilities canonical confined <sign> ~ 0.85(1) D Elia, Lombardo 16 3 Azcoiti et al., 8 3 Fodor, Katz, 6 3 Our reweighting, 6 3 deforcrand, Kratochvila, 6 3 a µ <sign> ~ 0.45(5) µ/t QGP Agreement for µ/t 1 <sign> ~ 0.1(1) PdF & Kratochvila T/T c uni

29 Comparison with freeze-out curve so far lattice curve freeze-out curve (But not yet extrapolated to continuum; in progress)

30 Much harder: is there a QCD critical point?

31 Much harder: is there a QCD critical point? 1

32 Much harder: is there a QCD critical point? 2 1

33 Approach 1: CEP from reweighting Critical point from reweighting Fodor,Katz 04 JHEP 04 N t = 4, N f = physical quark masses, unimproved staggered fermions Lee-Yang zero: abrupt change: physics or problem of the method? Splittorff 05; Han, Stephanov 08 (entire curve generated from one point!)

34 Approach 2: follow chiral critical line surface chiral p.t. chiral p.t. m c (µ) m c (0) = 1 + ( µ c k πt k=1 ) 2k hard/easy de Forcrand, O.P. 08,09

35 Finite density: chiral critical line critical surface! 2nd order O(4)? N f = 2 2nd order Z(2) 1st Pure Gauge! Real world Heavy quarks! Real world Heavy quarks m tric s m s 0 0 phys. point 1st 2nd order Z(2) m, m u N f = 3 crossover d! N f = 1 0 m u,d * QCD critical point X crossover 1rst m s! 0 m u,d QCD critical point DISAPPEARED X crossover 1rst m s! m c (µ) m c (0) = 1 + ( µ c k πt k=1 ) 2k transition strengthens m > > m c (0) transition weakens m > m c (0) QGP QGP T T c! T T c confined Color superconductor confined Color superconductor! µ

36 Curvature of the chiral critical surface de Forcrand, O.P. 08,09

37 On coarse lattice exotic scenario: no chiral critical point at small density Weakening of p.t. with chemical potential also for: -Heavy quarks de Forcrand, Kim, Takaishi 05 -Light quarks with finite isospin density Kogut, Sinclair 07 -Electroweak phase transition with finite lepton density Gynther 03

38 Towards the continuum: N t =6,a 0.2 fm! 2nd order O(4)? N = 2 f 2nd order Z(2) 1st Pure Gauge m tric s N = 3 f phys. crossover point N = 1 f m s 0 0 1st Nt=6 Nt=4 2nd order Z(2) m, m u d! de Forcrand, Kim, O.P. 07 Endrodi et al 07 Physical point deeper in crossover region as a 0 Cut-off effects stronger than finite density effects! Preliminary: curvature of chiral crit. surface remains negative de Forcrand, O.P. 10

39 Un-discovering a critical point feels like...

40 Un-discovering a critical point feels like...

41 Recent model studies with similar results Fukushima 08, Bowman, Kapusta 09 Quark Chemical Potential [MeV] Light Quark Mass [MeV] G V = 0.8G S Strange Quark Mass [MeV] NJL-Polyakov loop model with vector-vector interaction, quark meson model Qualitative behaviour similar to exotic lattice scenario Critical end point at higher density!

42 Others with more (and non-chiral) critical points... NJL with vector interactions, Zhang, Kunihiro, Fukushima 09 Ginzburg-Landau approach Baym et al. 06 for quark condensates, beyond mean field methods... Ferroni, Koch, Pinto 10...

43 Outlook: what about high density physics? QGP T c! T confined? Color superconductor µ Required input for physics of compact stars, phase diagram + EoS needed Sign problem strong, methods for µ<t fail

44 Back to heaven: what are compact stars made of? Radius ~ km Mass ~ x Solar Mass ρ 0 : nuclear density

45 at small coupling (infinite density) What happens at realistic densities/couplings??

46 Effective theories! Split problem in perturbative (analytical) and non-perturbative (numerical) part µ Large densities: perturbative; eff. theories for exist, improve to NLO, discretise Intermediate densities: lattice, strong coupling expansion in α s eff. theory for infinite coupling exists, can be evaluated numerically nd order at =! 2 / N " 1 #$$% & 0 TCP #$$% = 1st orde Liquid-gas transition at infinite coupling, m=0 de Forcrand, Fromm 09 Deconfinement transition for heavy quarks Langelage, Lottini, O.P a µ Perturbative refinement to large but finite couplings possible!

47 Conclusions QCD is verified fundamental theory of nuclear matter Hot/dense QCD important: nuclear, astro- and particle physics, heavy ion collisions Phase diagram: on coarse lattices no chiral critical point for Still at the beginning: large discretisation and quark mass dependence, high densities need new methods Uncharted territory: do QCD critical points exist? µ<t