r rs Critical Endpoint? T c Hadron Resonance Gas Quarkyonic - PowerPoint PPT Presentation

SU ( 2 ) CS and SU ( 4 ) symmetries of high temperature QCD Christian Rohrhofer (Osaka Univ.) FLQCD @ YITP Kyoto University April 18th, 2019 PRD 96 (2017) no.9, 094501 1902.03191 in collaboration with: Y. Aoki, G. Cossu, H. Fukaya, C. Gattringer, L. Ya. Glozman, S. Hashimoto, C.B. Lang, S. Prelovsek

Conjectured phase diagram of QCD T Asymptotic freedom ❤❡r❡ ❜❡ ❞r❛❣♦♥s❄ Critical Endpoint? T c Hadron Resonance Gas Quarkyonic matter Hadrons Nuclear matter Color superconductors Vacuum Neutron stars µ 1

The high temperature phase of QCD • Experimental access by Heavy Ion Collisions (LHC, RHIC, FAIR, NICA) • Theoretical access through Lattice QCD: • High T thermodynamics turn to precision measurements • Sign problem for finite chemical potential • Critical temperature T c ≃ 154 MeV p/T 4 5 SB lattice continuum limit 5 4 4 N τ =6 3 N τ =8 4 N τ =10 p/T 3 N τ =12 p4, N τ =6 2 p4, N τ =8 2 HTL NNLO 1 1 HRG T [MeV] T[MeV] 0 0 200 400 600 800 1000 1200 200 300 400 500 left : A.Bazavov et al , Phys.Rev. D97 (2018) no.1, 014510 right : S.Borsanyi et al , Phys.Lett. B730 (2014) 99-104 2

An experiment: modifying the Dirac spectrum Numerical studies of Hadron spectrum upon Dirac low-mode truncation � ¯ qq � = πρ ( 0 ) Q top = n − − n + Chiral spin SU ( 2 ) CS and SU ( 2 n f ) symmetries derived similarity due to suppression of low modes in high T QCD? M.Denissenya,L.Glozman,C.B.Lang, Phys.Rev.D91, 034505 3

High temperature lattice ensembles • n f = 2 Möbius DW fermions, Symanzik gauge action • N s = 32 lattices, T c = 175MeV • L s is set between 10 − 24 for good chirality • spatial correlations in z -direction: zT = ( n z a ) / ( N t a ) = n z / N t • Temperatures between 1 . 25 T c − 5 . 5 T c : 32 3 × 12 32 3 × 8 32 3 × 6 32 3 × 4 T [MeV] β = 4 . 10 220 β = 4 . 18 260 β = 4 . 30 220 330 440 660 β = 4 . 37 380 β = 4 . 50 480 960 JLQCD collab. (G.Cossu et al ), Phys.Rev. D93 (2016) no.3, 034507 A.Tomiya et al , Phys.Rev. D96 (2017) no.3, 034509 4

Eigenvalue distribution at high T 0.10 0.08 32 × 8 0.06 ρ ( λ ) Spectral density ρ ( λ ) β = 4.10 0.04 T = 220 MeV for high T ensembles 0.02 0.00 0 350 700 1050 1400 40 eigenmodes / configuration | λ | [MeV] 0.25 ∼ 15 configurations m ud = 0.001 m ud = 0.005 0.20 m ud = 0.01 0.15 32 × 4 ρ ( λ ) Strong suppression β = 4.30 0.10 T = 660 MeV of low modes! 0.05 0.00 0 350 700 1050 1400 | λ | [MeV] 5

Operators and the Dirac algebra Measure local isovectors O Γ ( x ) = ¯ q ( x )Γ q ( x ) Fix direction of propagation ( z-direction ): � �O Γ ( n x , n y , n z , n t ) O Γ ( 0 , 0 , 0 , 0 ) † � C Γ ( n z ) = n x , n y , n t Using ∂ µ j µ = ∂ µ j µ 5 = 0 the Gamma structures for the Vectors are:     γ 1 = Vx γ 1 γ 5 = Ax V = γ 2 = Vy A = γ 2 γ 5 = Ay     γ 4 = Vt γ 4 γ 5 = At     γ 1 γ 3 = Tx γ 1 γ 3 γ 5 = γ 2 γ 4 = Xx T = γ 2 γ 3 = Ty X = γ 2 γ 3 γ 5 = γ 4 γ 1 = Xy     γ 4 γ 3 = Tt γ 4 γ 3 γ 5 = γ 1 γ 2 = Xt γ 3 & γ 3 γ 5 no propagation due to current conservation! + Pion, Scalar 6

What to expect from two-flavor L QCD and χ S? Symmetry of massless L : SU ( 2 ) L × SU ( 2 ) R × U ( 1 ) A × U ( 1 ) V Pseudoscalar Scalar U ( 1 ) A PS S ¯ ¯ q ( � τ ⊗ γ 5 ) q q ( � τ ⊗ 1 D ) q Vector Axial Vector SU ( 2 ) A V A ¯ ¯ q ( � τ ⊗ γ k ) q q ( � τ ⊗ γ 5 γ k ) q Tensor Vector Axial Tensor V. U ( 1 ) A T X ¯ ¯ q ( � τ ⊗ γ 3 γ k ) q q ( � τ ⊗ γ 5 γ 3 γ k ) q U ( 1 ) A broken by � ¯ qq � and axial anomaly SU ( 2 ) L × SU ( 2 ) R broken by � ¯ qq � 7

Spatial correlations for T ≤ 2 T c 0 10 220 MeV 260 MeV -1 10 -2 10 C(n z ) / C(n z =1) -3 10 PS S -4 10 Vx Vt -5 Ax 10 At Tx -6 10 Tt Xx -7 Xt 10 0 10 320 MeV 380 MeV -1 10 -2 10 C(n z ) / C(n z =1) -3 10 E 1 -4 E 2 10 -5 10 E 3 -6 10 -7 10 0 0.5 1 1.5 2 0 0.5 1 1.5 2 zT zT 8

Spatial correlations for T > 2 T c 0 10 -1 440 MeV 480 MeV 10 -2 10 -3 10 -4 C(n z ) / C(n z =1) 10 -5 10 PS S -6 10 Vx -7 Vt 10 Ax -8 10 At Tx -9 10 Tt -10 Xx 10 Xt -11 10 0 10 -1 660 MeV 960 MeV 10 -2 10 -3 10 -4 C(n z ) / C(n z =1) 10 -5 10 -6 10 -7 10 -8 10 -9 10 -10 10 -11 10 0 1 2 3 4 0 1 2 3 4 zT zT 9

E 1 and E 2 multiplets at 2 T c 0 10 free PS free Vx 380 MeV free Tt free ( U ( x ) µ = 1 ), -1 10 dressed PS non-interacting quarks: dressed S chiral symmetry dressed Vx -2 dressed Ax 10 dressed Tt C(n z ) / C(n z =1) dressed Xt U ( 1 ) A : S ↔ PS -3 10 SU ( 2 ) A : V x ↔ A x free PS, S dressed PS, S U ( 1 ) A : T t ↔ X t free Vx, Ax -4 10 free Tt, Xt -5 10 dressed meson dressed Vx, Ax, Tt, Xt correlators: larger symmetry -6 10 0 0.5 1 1.5 2 zT 10

SU ( 2 ) L × SU ( 2 ) R and U ( 1 ) A symmetries • � ¯ qq � and topological susceptibility* suggest ‘good’ symmetries • Use ratio of ‘connected’ operators as measure 260 MeV 1.75 SU(2) A 220 MeV 1.75 U(1) A 1.50 1.50 Vx/Ax m ud =0.001 PS/S m ud =0.005 m ud =0.01 1.25 1.25 1.00 32x8 1.00 32x8 β =4.10 β =4.18 0 1 2 3 4 0 1 2 3 4 zT zT *previous talk, JLQCD collab. (K.Suzuku et al ), EPJ Web Conf. 175 (2018) 07025 11

SU ( 2 ) CS chiral spin and SU ( 4 ) symmetries SU ( 2 ) CS → e i � Σ � � θ/ 2 Ψ Ψ − − − − − Σ = { γ k , − i γ 5 γ k , γ 5 }   u L u R all components of   ⋄ Physical interpretation:   d L fundamental vector mix!   d R ⋄ for spatial z − correlators generated by representations: R 1 : { γ 1 , − i γ 5 γ 1 , γ 5 } A y ↔ T t ↔ X t ⇒ R 2 : { γ 2 , − i γ 5 γ 2 , γ 5 } A x ↔ T t ↔ X t ⋄ Minimal group containing SU ( 2 ) CS and χ S is SU ( 4 ) : � V x ↔ T t ↔ X t ↔ A x E 2 V y ↔ T t ↔ X t ↔ A y � V t ↔ T x ↔ X x ↔ A t E 3 V t ↔ T y ↔ X y ↔ A t L.Glozman, Eur.Phys.J. A51 (2015) no.3, 27 L.Glozman and M.Pak, Phys.Rev. D92 (2015) no.1, 016001 12

Symmetries of the Lagrangian SU ( 2 ) CS → e i � Σ � � θ/ 2 Ψ Ψ − − − − − Σ = { γ k , − i γ 5 γ k , γ 5 } L = ¯ Ψ i / ∂ Ψ Free, massless Lagrangian: breaks SU ( 2 ) CS Covariant derivative: D µ = ∂ µ − igA µ L = ¯ D Ψ = ¯ Ψ i γ 0 D 0 Ψ + ¯ Ψ i / Ψ i γ i D i Ψ Massless (fermionic) Lagrangian: 2.0 SU ( 2 ) CS invariant SU(2) CS • Kinetic term breaks SU ( 2 ) CS 1.5 Ax/Tt • ‘Magnetic’ term breaks SU ( 2 ) CS • ‘Electric’ term is SU ( 2 ) CS symmetric 1.0 A x and T t mix under SU ( 2 ) CS Use ratio to measure breaking! 0 0.5 1 1.5 2 zT 13

1.8 T = 220 MeV, full QCD T = 320 MeV, full QCD 32x12 32x8 free quarks T = 380 MeV, full QCD 1.6 T = 480 MeV, full QCD free quarks full QCD propagator C Ax (n z ) / C Ax (n z =1) ______________ C Tt (n z ) / C Tt (n z =1) 1.4 full QCD propagators 1.2 1.0 propagator with 0.8 propagator with free quarks free quarks 1.8 T = 440 MeV, full QCD T = 660 MeV, full QCD 32x6 32x4 free quarks T = 960 MeV, full QCD 1.6 free quarks C Ax (n z ) / C Ax (n z =1) ______________ C Tt (n z ) / C Tt (n z =1) 1.4 1.2 full QCD propagator full QCD propagators 1.0 0.8 propagator with propagator with free quarks free quarks 0.6 0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0 zT zT A x / T t ratio measures SU ( 2 ) CS breaking 14

The phase diagram & chemical potential � β � d 3 x ¯ S = Ψ[ γ µ D µ + µγ 4 ]Ψ 0 15

Conclusions � spatial correlations at temperatures 1 . 25 − 5 . 5 T c � chiral symmetry and effective U ( 1 ) A restoration above T c � approximate SU ( 2 ) CS symmetric region → SU ( 4 ) ⇒ SU ( 2 ) CS a tool to distinguish color-electric and color-magnetic contributions chiral quarks connected by color-electric field as elementary objects at high T (strings?) Thank you for listening! 16