The phase diagram of two flavour QCD Jan M. Pawlowski Universitt - PowerPoint PPT Presentation

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

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

Phase diagram of QCD

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

Phase diagram of two flavour QCD Continuum methods 1 f π (T)/f π (0) Dual density RG-flows in QCD PNJL & PQM model Polyakov Loop 0.8 0.6 Braun, Haas, Marhauser,JMP ’09 χ L,dual 0.4 cf. talks by K. Fujushima cf. talks by J. Braun & L. Haas W. Weise 0.2 B.-J. Schaefer (chiral limit) 160 180 200 0 150 160 170 180 190 200 210 220 230 T [MeV] 300 250 200 T [MeV] 150 100 T conf 50 T χ Schaefer, JMP , Wambach ‘07 (chiral limit) 0 0 π /3 2 π /3 4 π /3 π 2 πθ

Phase diagram of two flavour QCD Continuum methods 1 f π (T)/f π (0) Dual density RG-flows in QCD PNJL & PQM model Polyakov Loop 0.8 0.6 Full dynamical QCD Braun, Haas, Marhauser,JMP ’09 χ L,dual 0.4 cf. talks by K. Fujushima cf. talks by J. Braun & L. Haas W. Weise 0.2 B.-J. Schaefer (chiral limit) 160 180 200 0 150 160 170 180 190 200 210 220 230 T [MeV] 300 250 200 T [MeV] 150 100 T conf 50 T χ Schaefer, JMP , Wambach ‘07 (chiral limit) 0 0 π /3 2 π /3 4 π /3 π 2 πθ

Quark confinement & chiral symmetry breaking

Confinement Continuum methods (Functional RG-flows) Braun, Gies, JMP ‘07 RG-scale k: t = ln k V [ A 0 ] = − 1 2Tr log � AA � [ A 0 ] + O ( ∂ t � AA � ) − Tr log � C ¯ C � [ A 0 ] + O ( ∂ t � C ¯ C � ) + O ( V ′′ [ A 0 ]) p 0 → 2 π Tn − gA 0 p 2 � C ¯ p 2 � A A � ( p 2 ) C � ( p 2 ) p [GeV] Fischer, Maas, JMP ’08 JMP , in preparation

Confinement Continuum methods Braun, Gies, JMP ‘07 V [ A 0 ] = − 1 2Tr log � AA � [ A 0 ] + O ( ∂ t � AA � ) − Tr log � C ¯ C � [ A 0 ] + O ( ∂ t � C ¯ C � ) + O ( V ′′ [ A 0 ]) ‘Polyakov loop potential’ subleading for T c, conf p 2 � C ¯ p 2 � A A � ( p 2 ) C � ( p 2 ) p [GeV] Fischer, Maas, JMP ’08 JMP , in preparation

Confinement Continuum methods ⊗ k ∂ k − 1 = − − ⊗ ⊗ + 1 + 1 2 2 ⊗ ⊗ ⊗ − 1 + 2 ⊗ k ∂ k − 1 = + ⊗ ⊗ ⊗ − 1 + 2

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

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

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

Imaginary chemical potential Lattice & Continuum QCD x ) = − e 2 π i θ ψ θ ( t, x ) ψ θ ( t + β , � with µ I = 2 π T θ • Roberge-Weiss symmetry Z θ = Z θ +1 / 3 deconfining confining

Dual order parameter Lattice & Continuum QCD O θ = � O [ e 2 π i θ t/ β ψ ] � x ) = − e 2 π i θ ψ θ ( t, x ) with ψ θ ( t + β , � imaginary chemical potential µ = 2 π i θ / β for ψ θ = e 2 π i θ t/ β ψ � 1 z = e 2 π i θ z ˜ d θ O θ e − 2 π i θ order parameter for confinement O = 0 Dual order parameter • Lattice Gattringer ‘06 Synatschke, Wipf, Wozar ‘08 Bruckmann, Hagen, Bilgici, Gattringer ‘08 • Continuum Fischer, ’09; Fischer, Mueller ‘09 imaginary chemical potential Braun, Haas, Marhauser, JMP ‘09 cf. talks by J. Braun, C. Fischer, L. Haas, A. Wipf

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

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

Dual order parameter Continuum methods (Functional RG-flows) O θ = � O [ e 2 π i θ t/ β ψ ] � x ) = − e 2 π i θ ψ θ ( t, x ) with ψ θ ( t + β , � imaginary chemical potential µ = 2 π i θ / β for ψ θ = e 2 π i θ t/ β ψ � 1 z = e 2 π i θ z d θ O θ e − 2 π i θ order parameter for confinement 0 f π ( T, θ ) ’fermionic pressure di ff erence’ p ( T, θ ) ≃ P ( T, θ ) − P ( T, 0) θ θ f π p T T fixed A 0 : no Roberge-Weiss periodicity Braun, Haas, Marhauser, JMP ‘09

Full dynamical QCD: N_f = 2 & chiral limit Continuum methods (Functional RG-flows) mesonic quantum • RG-flow of Effective Action (Effective Potential) fluctuations ∂ t Γ k [ φ ] = 1 + 1 − − 2 2 quark quantum fluctuations • flow of gluon propagator ... pure gauge theory flow + + cf. talk by L. Haas

Full dynamical QCD: N_f = 2 & chiral limit Continuum methods f π (T)/f π (0) 1 Dual density Polyakov Loop 0.8 0.6 χ L,dual 0.4 0.2 160 180 200 0 150 160 170 180 190 200 210 220 230 T [MeV] cf. talks by J. Braun & L. Haas T χ = T conf ≃ 180MeV Braun, Haas, Marhauser, JMP ‘09

Full dynamical QCD: N_f = 2 & chiral limit Continuum methods 1% ∆ ˜ n Φ 0.8% 0.6% Δ n /L ~ 0.4% 0.2% 0% 140 160 180 200 220 240 T [MeV] n = ˜ n [ � A 0 � ] Deviation of dual density from Polyakov loop ∆ ˜ − Φ [ � A 0 � ] : n [0] ˜ Braun, Haas, Marhauser, JMP ‘09

Full dynamical QCD: N_f = 2 & chiral limit Continuum methods & lattice compatible with Karsch et al ’08 f π (T)/f π (0) 1 N f = 2 + 1 Dual density Polyakov Loop 0.8 0.6 T χ = T conf ≃ 180MeV χ L,dual N f = 2 0.4 0.2 160 180 200 compatible with Fodor et al ’08? 0 150 160 170 180 190 200 210 220 230 175MeV ≃ T c, conf > T c, χ ≃ 150MeV T [MeV] N f = 2 + 1 Braun, Haas, Marhauser, JMP ‘09

Full dynamical QCD: N_f = 2 & chiral limit Continuum methods 300 250 200 T [MeV] 150 100 T conf 50 T χ 0 0 π /3 2 π /3 4 π /3 π 2 πθ chemical potential : µ = 2 π i T θ Braun, Haas, Marhauser, JMP ‘09

Full dynamical QCD: N_f = 2 & chiral limit Continuum methods & lattice agreement lattice results 300 Kratochvila et al ‘06 & Wu et al ‘06 250 200 T [MeV] adjust 8-fermi interaction 150 100 T conf 50 T χ Polyakov-NJL model 0 Sakai et al ‘09 0 π /3 2 π /3 π 4 π /3 2 πθ Braun, Haas, Marhauser, JMP ‘09 T χ T conf

Chiral phase structure at finite density

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

Summary & Outlook

Summary & outlook • Phase diagram of QCD • Confinement & chiral symmetry breaking at finite temperature f π (T)/f π (0) 1 Dual density Polyakov Loop 0.8 0.6 χ L,dual 0.4 0.2 160 180 200 0 150 160 170 180 190 200 210 220 230 T [MeV]

Summary & outlook • Phase diagram of QCD • Confinement & chiral symmetry breaking at finite temperature f π (T)/f π (0) 1 Dual density Polyakov Loop 0.8 0.6 χ L,dual 0.4 0.2 160 180 200 0 150 160 170 180 190 200 210 220 230 T [MeV] • Dynamical hadronisation QCD flows dynamically into hadronic effective theories • Next steps: real chemical potential & 2+1 flavours work in progress

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

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

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