Hot QCD matter in magnetic fields: phase transition and permeability - PowerPoint PPT Presentation

Hot QCD matter in magnetic fields: phase transition and permeability Gergely Endr˝ odi University of Bielefeld Theoretical Physics Colloquium 24. June 2016

Preface: QCD phases and equation of state

The phases of QCD ◮ phases of QCD characterized by approx. order parameters ◮ quark condensate ¯ ψψ (chiral symmetry breaking) ◮ Polyakov loop P (deconfinement) 1 / 29

The phases of QCD ◮ phases of QCD characterized by approx. order parameters ◮ quark condensate ¯ ψψ (chiral symmetry breaking) ◮ Polyakov loop P (deconfinement) Bors´ anyi et al. ’10 1.0 1.0 Renormalized Polyakov loop Continuum � � � � Continuum � � � N t � 16 � 0.8 �� 0.8 � � N t � 16 � � N t � 12 � � � � N t � 12 � �� � �� � N t � 10 � N t � 10 � 0.6 �� 0.6 � � �� N t � 8 � N t � 8 � � � � l , s � � � � � � � ����� � �� 0.4 0.4 � ��� �� � � � � � ��� �� � � � � ��� 0.2 � � ����� � � � � � 0.2 �� �� � � � � � � � ������ � � � � � � � � � �� � ��� � � � � � � � � � � � � ��� � � � � 0.0 � �� �� � � 100 120 140 160 180 200 220 100 150 200 250 300 350 T � MeV � T � MeV � 1 / 29

The phases of QCD ◮ phases of QCD characterized by approx. order parameters ◮ quark condensate ¯ ψψ (chiral symmetry breaking) ◮ Polyakov loop P (deconfinement) Bors´ anyi et al. ’10 1.0 1.0 Renormalized Polyakov loop Continuum � � � � Continuum � � � N t � 16 � 0.8 �� 0.8 � � N t � 16 � � N t � 12 � � � � N t � 12 � �� � �� � N t � 10 � N t � 10 � 0.6 �� 0.6 � � �� N t � 8 � N t � 8 � � � � l , s � � � � � � � ����� � �� 0.4 0.4 � ��� �� � � � � � ��� �� � � � � ��� 0.2 � � ����� � � � � � 0.2 �� �� � � � � � � � ������ � � � � � � � � � �� � ��� � � � � � � � � � � � � ��� � � � � 0.0 � �� �� � � 100 120 140 160 180 200 220 100 150 200 250 300 350 T � MeV � T � MeV � ◮ crossover Aoki et al. ’06 Bhattacharya et al. ’14 1 / 29

The phases of QCD ◮ phases of QCD characterized by approx. order parameters ◮ quark condensate ¯ ψψ (chiral symmetry breaking) ◮ Polyakov loop P (deconfinement) Bors´ anyi et al. ’10 1.0 1.0 Renormalized Polyakov loop Continuum � � � � Continuum � � � N t � 16 � 0.8 �� 0.8 � � N t � 16 � � N t � 12 � � � � N t � 12 � �� � �� � N t � 10 � N t � 10 � 0.6 �� 0.6 � � �� N t � 8 � N t � 8 � � � � l , s � � � � � � � ����� � �� 0.4 0.4 � ��� �� � � � � � ��� �� � � � � ��� 0.2 � � ����� � � � � � 0.2 �� �� � � � � � � � ������ � � � � � � � � � �� � ��� � � � � � � � � � � � � ��� � � � � 0.0 � �� �� � � 100 120 140 160 180 200 220 100 150 200 250 300 350 T � MeV � T � MeV � ◮ crossover Aoki et al. ’06 Bhattacharya et al. ’14 ◮ T c ↔ inflection point Bazavov et al. ’18 1 / 29

Equation of state of QCD ◮ equilibrium description ǫ ( p ) of QCD matter ◮ encoded in, for example, p ( T ) 4 3 2 stout HISQ ( ε -3p)/T 4 p/T 4 1 s/4T 4 T [MeV] 0 130 170 210 250 290 330 370 Bazavov et al. ’14 Bors´ anyi et al. ’13 2 / 29

Phase diagram ◮ approaches: effective theories, low-energy models, lattice simulations, perturbation theory 3 / 29

Phase diagram ◮ approaches: effective theories, low-energy models, lattice simulations, perturbation theory ◮ tuning necessary for low-energy models 3 / 29

Permeability ◮ deviation to unity gives O ( B 2 ) contribution to EoS 4 / 29

Outline ◮ applications ◮ phase diagram ◮ magnetic catalysis and inverse catalysis ◮ new developments about the mass-dependence ◮ large B limit ◮ PNJL model and improvement ◮ permeability ◮ magnetic flux quantization ◮ current-current correlators ◮ connection to HRG and perturbation theory ◮ summary 5 / 29

Applications

Magnetic fields ◮ off-central heavy-ion collisions Kharzeev, McLerran, Warringa ’07 impact: chiral magnetic effect, anisotropies, elliptic flow . . . Fukushima ’12 Kharzeev, Landsteiner, Schmitt, Yee ’14 6 / 29

Magnetic fields ◮ off-central heavy-ion collisions Kharzeev, McLerran, Warringa ’07 impact: chiral magnetic effect, anisotropies, elliptic flow . . . Fukushima ’12 Kharzeev, Landsteiner, Schmitt, Yee ’14 ◮ magnetars Duncan, Thompson ’92 impact: equation of state, mass-radius relation Ferrer et al ’10 gravitational collapse/merger Anderson et al ’08 6 / 29

Magnetic fields ◮ off-central heavy-ion collisions Kharzeev, McLerran, Warringa ’07 impact: chiral magnetic effect, anisotropies, elliptic flow . . . Fukushima ’12 Kharzeev, Landsteiner, Schmitt, Yee ’14 ◮ magnetars Duncan, Thompson ’92 impact: equation of state, mass-radius relation Ferrer et al ’10 gravitational collapse/merger Anderson et al ’08 ◮ in the early universe, generated through phase transition in electroweak epoch Vachaspati ’91 Enqvist, Olesen ’93 6 / 29

Magnetic fields ◮ off-central heavy-ion collisions Kharzeev, McLerran, Warringa ’07 impact: chiral magnetic effect, anisotropies, elliptic flow . . . Fukushima ’12 Kharzeev, Landsteiner, Schmitt, Yee ’14 ◮ magnetars Duncan, Thompson ’92 impact: equation of state, mass-radius relation Ferrer et al ’10 gravitational collapse/merger Anderson et al ’08 ◮ in the early universe, generated through phase transition in electroweak epoch Vachaspati ’91 Enqvist, Olesen ’93 ◮ strength: B ≈ 10 15 T ≈ 10 20 B earth ≈ 5 m 2 π � competition between strong force and electromagnetism 6 / 29

Phase diagram – pedagogical review

Magnetic catalysis, free quarks ◮ chiral condensate ↔ spectral density around 0 Banks,Casher ’80 D + m ) − 1 m → 0 ¯ ψψ ∼ tr ( / − − − → ρ (0) ◮ for free quarks, ρ is determined by Landau levels: ◮ lowest Landau level has vanishing eigenvalue ◮ Landau levels have degeneracy ∝ B 7 / 29

Magnetic catalysis, free quarks ◮ chiral condensate ↔ spectral density around 0 Banks,Casher ’80 D + m ) − 1 m → 0 ¯ ψψ ∼ tr ( / − − − → ρ (0) ◮ for free quarks, ρ is determined by Landau levels: ◮ lowest Landau level has vanishing eigenvalue ◮ Landau levels have degeneracy ∝ B ◮ ρ (0) is enhanced by B 7 / 29

Magnetic catalysis, free quarks ◮ chiral condensate ↔ spectral density around 0 Banks,Casher ’80 D + m ) − 1 m → 0 ¯ ψψ ∼ tr ( / − − − → ρ (0) ◮ for free quarks, ρ is determined by Landau levels: ◮ lowest Landau level has vanishing eigenvalue ◮ Landau levels have degeneracy ∝ B ◮ ρ (0) is enhanced by B ◮ magnetic catalysis: ¯ ψψ is enhanced by B Gusynin, Miransky, Shovkovy ’96 Shovkovy ’13 7 / 29

Magnetic catalysis, full QCD ◮ in full QCD, gluons also affect ρ 8 / 29

Magnetic catalysis, full QCD ◮ in full QCD, gluons also affect ρ ◮ emergence of a gap that pushes low modes towards zero Bruckmann, Endr˝ odi, Giordano et al. ’17 8 / 29

Magnetic catalysis, full QCD ◮ in full QCD, gluons also affect ρ ◮ emergence of a gap that pushes low modes towards zero Bruckmann, Endr˝ odi, Giordano et al. ’17 ⇒ ρ (0) is enhanced by B 8 / 29

Magnetic catalysis, full QCD ◮ in full QCD, gluons also affect ρ ◮ emergence of a gap that pushes low modes towards zero Bruckmann, Endr˝ odi, Giordano et al. ’17 ⇒ ρ (0) is enhanced by B ◮ side remark: free case solution on the lattice ↔ Hofstadter’s butterfly (solid state physics model) Hofstadter ’76 8 / 29

Sea quarks in a magnetic field ◮ effect of B in full QCD Bruckmann, Endr˝ odi, Kov´ acs ’13 ◮ direct (valence) effect B ↔ q f ◮ indirect (sea) effect B ↔ q f ↔ g � ¯ � � � D ( B , A ) + m ) − 1 � D A µ e − S g det( / ( / ψψ ( B ) ∝ D ( B , A ) + m ) Tr � �� � � �� � sea valence 9 / 29

Sea quarks in a magnetic field ◮ effect of B in full QCD Bruckmann, Endr˝ odi, Kov´ acs ’13 ◮ direct (valence) effect B ↔ q f ◮ indirect (sea) effect B ↔ q f ↔ g � ¯ � � � D ( B , A ) + m ) − 1 � D A µ e − S g det( / ( / ψψ ( B ) ∝ D ( B , A ) + m ) Tr � �� � � �� � sea valence ◮ most important feature of gauge configurations: Polyakov loop 9 / 29