The phase diagram of two flavour QCD

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1 The phase diagram of two flavour QCD Jan M. Pawlowski Universität Heidelberg & ExtreMe Matter Institute Quarks, Gluons and the Phase Diagram of QCD St. Goar, September 2nd 2009

2 Outline Phase diagram of two flavour QCD Quark confinement & chiral symmetry breaking Chiral phase structure at finite density Summary and outlook

3 Phase diagram of QCD

4 Phase diagram of QCD Strongly correlated quark-gluon-plasma RHIC serves the perfect fluid massless quarks (chiral symmetry) deconfinement quarkyonic: confinement & chiral symmetry hadronic phase FAIR, confinement & chiral symmetry breaking

5 Phase diagram of two flavour QCD Continuum methods RG-flows in QCD f π (T)/f π (0) Dual density Polyakov Loop PNJL & PQM model Braun, Haas, Marhauser,JMP 09 cf. talks by J. Braun & L. Haas (chiral limit) χ L,dual T [MeV] cf. talks by K. Fujushima W. Weise B.-J. Schaefer T [MeV] (chiral limit) 0 π/3 2π/3 π 4π/3 2πθ T conf T χ Schaefer, JMP, Wambach 07

6 Phase diagram of two flavour QCD Continuum methods RG-flows in QCD f π (T)/f π (0) Dual density Polyakov Loop PNJL & PQM model Braun, Haas, Marhauser,JMP 09 T [MeV] cf. talks by J. Braun & L. Haas (chiral limit) χ L,dual T [MeV] Full dynamical QCD cf. talks by K. Fujushima W. Weise B.-J. Schaefer 50 0 (chiral limit) 0 π/3 2π/3 π 4π/3 2πθ T conf T χ Schaefer, JMP, Wambach 07

7 Quark confinement & chiral symmetry breaking

8 Confinement Continuum methods (Functional RG-flows) RG-scale k: t = ln k Braun, Gies, JMP 07 V [A 0 ]= 1 2 Tr log AA [A 0]+O( t AA ) Tr log C C [A 0 ]+O( t C C )+O(V [A 0 ]) p 0 2πTn ga 0 p 2 AA (p 2 ) p 2 C C (p 2 ) p [GeV] Fischer, Maas, JMP 08 JMP, in preparation

9 Confinement Continuum methods Braun, Gies, JMP 07 V [A 0 ]= 1 2 Tr log AA [A 0]+O( t AA ) Tr log C C [A 0 ]+O( t C C )+O(V [A 0 ]) Polyakov loop potential p 2 AA (p 2 ) p 2 C C (p 2 ) subleading for T c,conf p [GeV] Fischer, Maas, JMP 08 JMP, in preparation

10 Confinement Continuum methods k k 1 = k k 1 =

11 Confinement Continuum methods Φ[A c 0]= 1 3 (1 + 2 cos 1 2 βac 0) Φ[ 8 3 π] = 0 Braun, Gies, JMP 07

12 Confinement Continuum methods for SU(N), G(2), Sp(2) cf. talk by Jens Braun Braun, Gies, JMP 07

13 Universal properties & gauge independence Continuum methods JMP, Marhauser 08

14 Imaginary chemical potential Lattice & Continuum QCD Roberge-Weiss symmetry ψ θ (t + β, x) = e 2πiθ ψ θ (t, x) with µ I =2πT θ Z θ = Z θ+1/3 deconfining confining

15 Dual order parameter Lattice & Continuum QCD O θ = O[e 2πiθt/β ψ] with ψ θ (t + β, x) = e 2πiθ ψ θ (t, x) imaginary chemical potential µ =2πiθ/β for ψ θ = e 2πiθt/β ψ 1 z = e 2πiθ z Õ = 0 dθ O θ e 2πiθ order parameter for confinement Dual order parameter Lattice Continuum Gattringer 06 Synatschke, Wipf, Wozar 08 Bruckmann, Hagen, Bilgici, Gattringer 08 Fischer, 09; Fischer, Mueller 09 Braun, Haas, Marhauser, JMP 09 imaginary chemical potential cf. talks by J. Braun, C. Fischer, L. Haas, A. Wipf

16 Dual order parameter Lattice & Continuum QCD Õ = 1 0 dθ O θ e 2πiθ no imaginary chemical potential (lattice studies): DSE: 4 loop and more Õ FRG: 3 loop and more imaginary chemical potential I: evaluated at equations of motion Õ[ A 0 θ ] 0 Roberge-Weiss imaginary chemical potential II: evaluated at a fixed background standard FRG & DSE Õ[ A 0 θ ] 0 breaking of Roberge-Weiss

17 Dual order parameter Lattice & Continuum QCD Õ = 1 0 dθ O θ e 2πiθ no imaginary chemical potential (lattice studies): DSE: 4 loop and more Õ FRG: 3 loop and more imaginary chemical potential I: evaluated at equations of motion Õ[ A 0 θ ] 0 Roberge-Weiss imaginary chemical potential II: evaluated at a fixed background standard FRG & DSE Õ[ A 0 θ ] 0 breaking of Roberge-Weiss

18 Dual order parameter Continuum methods Oθ =!O[e2πiθt/β ψ]" with (Functional RG-flows) ψθ (t + β, #x) = e2πiθ ψθ (t, x) imaginary chemical potential µ = 2πiθ/β for ψθ = e2πiθt/β ψ! z=e 2πiθz 0 1 dθ Oθ e 2πiθ order parameter for confinement fπ (T, θ) fermionic pressure difference p(t, θ)! P (T, θ) P (T, 0) θ θ p T fπ T fixed A0 : no Roberge-Weiss periodicity Braun, Haas, Marhauser, JMP 09

19 Full dynamical QCD: N_f = 2 & chiral limit Continuum methods (Functional RG-flows) RG-flow of Effective Action (Effective Potential) mesonic quantum fluctuations t Γ k [φ] = flow of gluon propagator quark quantum fluctuations pure gauge theory flow cf. talk by L. Haas

20 Full dynamical QCD: N_f = 2 & chiral limit Continuum methods f π (T)/f π (0) Dual density Polyakov Loop χ L,dual T [MeV] cf. talks by J. Braun & L. Haas T χ = T conf 180MeV Braun, Haas, Marhauser, JMP 09

21 Full dynamical QCD: N_f = 2 & chiral limit Continuum methods ñ Φ 1% 0.8% Δ n ~ /L 0.6% 0.4% 0.2% 0% T [MeV] ñ = ñ[ A 0 ] ñ[0] Φ[ A 0 ]: Deviation of dual density from Polyakov loop Braun, Haas, Marhauser, JMP 09

22 Full dynamical QCD: N_f = 2 & chiral limit Continuum methods & lattice compatible with Karsch et al f π (T)/f π (0) Dual density Polyakov Loop χ L,dual T [MeV] T χ = T conf 180MeV compatible with Fodor et al 08? 175MeV T c,conf >T c,χ 150MeV N f = N f =2 N f = Braun, Haas, Marhauser, JMP 09

23 Full dynamical QCD: N_f = 2 & chiral limit Continuum methods T [MeV] π/3 2π/3 π 4π/3 2πθ T conf T χ chemical potential : µ = 2πi T θ Braun, Haas, Marhauser, JMP 09

24 Full dynamical QCD: N_f = 2 & chiral limit Continuum methods & lattice agreement lattice results Kratochvila et al 06 & Wu et al T [MeV] adjust 8-fermi interaction π/3 2π/3 π 4π/3 2πθ T conf T χ Polyakov-NJL model Sakai et al 09 Braun, Haas, Marhauser, JMP 09 T conf T χ

25 Chiral phase structure at finite density

26 Phase diagram of QCD Polyakov - Quark-Meson model quarkyonic phase? washed out by quantum fluctuations? N f =2 Schaefer, JMP, Wambach 07

27 Summary & Outlook

28 Summary & outlook Phase diagram of QCD Confinement & chiral symmetry breaking at finite temperature f π (T)/f π (0) Dual density Polyakov Loop χ L,dual T [MeV]

29 Summary & outlook Phase diagram of QCD Confinement & chiral symmetry breaking at finite temperature f π (T)/f π (0) Dual density Polyakov Loop 0.6 Dynamical hadronisation χ L,dual T [MeV] QCD flows dynamically into hadronic effective theories Next steps: real chemical potential & 2+1 flavours work in progress

30 Summary & outlook Phase diagram of QCD Confinement & chiral symmetry breaking at finite temperature Dynamical hadronisation critical point and phase lines in effective theories

31 Summary & outlook Phase diagram of QCD Confinement & chiral symmetry breaking at finite temperature Dynamical hadronisation critical point and phase lines in effective theories Hadronic properties e.g. Next step Top-down meets bottom-up Refine effective hadronic theories

32 Summary & outlook Phase diagram of QCD Confinement & chiral symmetry breaking at finite temperature Dynamical hadronisation critical point and phase lines in effective theories Hadronic properties non-equilibrium physics