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

▶
r r s
SMART_READER_LITE
LIVE PREVIEW

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

Mar 19, 2024 258 likes •444 views

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.

slide-1
SLIDE 1

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
slide-2
SLIDE 2

Conjectured phase diagram of QCD

T µ Tc Critical Endpoint? Vacuum

Hadrons

Hadron Resonance Gas

Quarkyonic matter Nuclear matter

Color superconductors Neutron stars

Asymptotic freedom

❤❡r❡ ❜❡ ❞r❛❣♦♥s❄

1

slide-3
SLIDE 3

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 Tc ≃ 154 MeV

1 2 3 4 5 200 400 600 800 1000 1200 T [MeV] p/T4 Nτ=6 Nτ=8 Nτ=10 Nτ=12 p4, Nτ=6 p4, Nτ=8 200 300 400 500

T[MeV]

1 2 3 4 5

p/T

4 HRG HTL NNLO lattice continuum limit SB

2

left: A.Bazavov et al, Phys.Rev. D97 (2018) no.1, 014510 right: S.Borsanyi et al, Phys.Lett. B730 (2014) 99-104

slide-4
SLIDE 4

An experiment: modifying the Dirac spectrum

Numerical studies of Hadron spectrum upon Dirac low-mode truncation

¯

qq = πρ(0) Qtop = n− − n+

Chiral spin SU(2)CS and SU(2nf) symmetries derived similarity due to suppression of low modes in high T QCD? 3

M.Denissenya,L.Glozman,C.B.Lang, Phys.Rev.D91, 034505

slide-5
SLIDE 5

High temperature lattice ensembles

  • nf = 2 Möbius DW fermions, Symanzik gauge action
  • Ns = 32 lattices, Tc = 175MeV
  • Ls is set between 10 − 24 for good chirality
  • spatial correlations in z-direction:

zT = (nza)/(Nta) = nz/Nt

  • Temperatures between 1.25Tc − 5.5Tc:

T [MeV] 323 × 12 323 × 8 323 × 6 323 × 4 β = 4.10 220 β = 4.18 260 β = 4.30 220 330 440 660 β = 4.37 380 β = 4.50 480 960 4

JLQCD collab. (G.Cossu et al), Phys.Rev. D93 (2016) no.3, 034507 A.Tomiya et al, Phys.Rev. D96 (2017) no.3, 034509

slide-6
SLIDE 6

Eigenvalue distribution at high T

Spectral density ρ(λ) for high T ensembles

40 eigenmodes / configuration ∼ 15 configurations

Strong suppression

  • f low modes!

350 700 1050 1400 |λ| [MeV] 0.00 0.02 0.04 0.06 0.08 0.10 ρ(λ)

32 × 8 β = 4.10 T = 220 MeV

350 700 1050 1400 |λ| [MeV] 0.00 0.05 0.10 0.15 0.20 0.25 ρ(λ)

32 × 4 β = 4.30 T = 660 MeV

mud = 0.001 mud = 0.005 mud = 0.01

5

slide-7
SLIDE 7

Operators and the Dirac algebra

Measure local isovectors OΓ(x) = ¯ q(x)Γq(x) Fix direction of propagation (z-direction): CΓ(nz) =

  • nx,ny,nt

OΓ(nx, ny, nz, nt)OΓ(0, 0, 0, 0)† Using ∂µjµ = ∂µjµ

5 = 0 the Gamma structures for the Vectors are:

V =   γ1 = Vx γ2 = Vy γ4 = Vt   A =   γ1γ5 = Ax γ2γ5 = Ay γ4γ5 = At   T =   γ1γ3 = Tx γ2γ3 = Ty γ4γ3 = Tt   X =   γ1γ3γ5 = γ2γ4 = Xx γ2γ3γ5 = γ4γ1 = Xy γ4γ3γ5 = γ1γ2 = Xt   γ3 & γ3γ5 no propagation due to current conservation! + Pion, Scalar 6

slide-8
SLIDE 8

What to expect from two-flavor LQCD and χS?

Symmetry of massless L:

SU(2)L × SU(2)R × U(1)A × U(1)V

PS

Pseudoscalar ¯ q( τ ⊗ γ5)q

S

Scalar ¯ q( τ ⊗ 1D)q

U(1)A

V

Vector ¯ q( τ ⊗ γk)q

A

Axial Vector ¯ q( τ ⊗ γ5γk)q

T

Tensor Vector ¯ q( τ ⊗ γ3γk)q

X

Axial Tensor V. ¯ q( τ ⊗ γ5γ3γk)q

SU(2)A U(1)A U(1)A broken by ¯ qq and axial anomaly SU(2)L × SU(2)R broken by ¯ qq 7

slide-9
SLIDE 9

Spatial correlations for T ≤ 2Tc

10

  • 7

10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 C(nz) / C(nz=1) PS S Vx Vt Ax At Tx Tt Xx Xt

220 MeV 260 MeV

0.5 1 1.5 2 zT 10

  • 7

10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 C(nz) / C(nz=1)

320 MeV

0.5 1 1.5 2 zT

380 MeV

E1 E2 E3

8

slide-10
SLIDE 10

Spatial correlations for T > 2Tc

10

  • 11

10

  • 10

10

  • 9

10

  • 8

10

  • 7

10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 C(nz) / C(nz=1) PS S Vx Vt Ax At Tx Tt Xx Xt

440 MeV 480 MeV

1 2 3 4 zT 10

  • 11

10

  • 10

10

  • 9

10

  • 8

10

  • 7

10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 C(nz) / C(nz=1)

660 MeV

1 2 3 4 zT

960 MeV

9

slide-11
SLIDE 11

E1 and E2 multiplets at 2Tc

0.5 1 1.5 2 zT 10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 C(nz) / C(nz=1) free PS free Vx free Tt dressed PS dressed S dressed Vx dressed Ax dressed Tt dressed Xt

dressed PS, S dressed Vx, Ax, Tt, Xt free Vx, Ax free Tt, Xt free PS, S

380 MeV

free (U(x)µ = 1), non-interacting quarks: chiral symmetry

U(1)A : S ↔ PS SU(2)A : Vx ↔ Ax U(1)A : Tt ↔ Xt

dressed meson correlators: larger symmetry 10

slide-12
SLIDE 12

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

1 2 3 4

zT

1.00 1.25 1.50 1.75

Vx/Ax

mud=0.001 mud=0.005 mud=0.01

SU(2)A

32x8 β=4.10

220 MeV

1 2 3 4

zT

1.00 1.25 1.50 1.75

PS/S U(1)A

32x8 β=4.18

260 MeV

11

*previous talk, JLQCD collab. (K.Suzuku et al), EPJ Web Conf. 175 (2018) 07025

slide-13
SLIDE 13

SU(2)CS chiral spin and SU(4) symmetries

Ψ

SU(2)CS

− − − − − → ei

Σ θ/2Ψ

  • Σ = {γk, −iγ5γk, γ5}

⋄ Physical interpretation:

    uL uR dL dR    

⋄ for spatial z−correlators generated by representations: R1 : {γ1, −iγ5γ1, γ5} R2 : {γ2, −iγ5γ2, γ5} ⇒ Ay ↔ Tt ↔ Xt Ax ↔ Tt ↔ Xt ⋄ Minimal group containing SU(2)CS and χS is SU(4): Vx ↔ Tt ↔ Xt ↔ Ax Vy ↔ Tt ↔ Xt ↔ Ay

  • E2

Vt ↔ Tx ↔ Xx ↔ At Vt ↔ Ty ↔ Xy ↔ At

  • E3

12 all components of fundamental vector mix!

L.Glozman, Eur.Phys.J. A51 (2015) no.3, 27 L.Glozman and M.Pak, Phys.Rev. D92 (2015) no.1, 016001

slide-14
SLIDE 14

Symmetries of the Lagrangian

Ψ

SU(2)CS

− − − − − → ei

Σ θ/2Ψ

  • Σ = {γk, −iγ5γk, γ5}

Free, massless Lagrangian: L = ¯ Ψi / ∂Ψ

breaks SU(2)CS

Covariant derivative: Dµ = ∂µ − igAµ Massless (fermionic) Lagrangian: L = ¯ Ψi / DΨ = ¯ Ψiγ0D0Ψ + ¯ ΨiγiDiΨ

0.5 1 1.5 2 zT 1.0 1.5 2.0

Ax/Tt SU(2)CS

SU(2)CS invariant

  • Kinetic term breaks SU(2)CS
  • ‘Magnetic’ term breaks SU(2)CS
  • ‘Electric’ term is SU(2)CS symmetric

Ax and Tt mix under SU(2)CS Use ratio to measure breaking! 13

slide-15
SLIDE 15

0.8 1.0 1.2 1.4 1.6 1.8

CAx(nz) / CAx(nz=1) ______________ CTt(nz) / CTt(nz=1)

T = 220 MeV, full QCD free quarks

full QCD propagator propagator with free quarks

32x12

T = 320 MeV, full QCD T = 380 MeV, full QCD T = 480 MeV, full QCD free quarks

full QCD propagators propagator with free quarks

32x8

0.0 1.0 2.0 3.0 4.0 zT 0.6 0.8 1.0 1.2 1.4 1.6 1.8

CAx(nz) / CAx(nz=1) ______________ CTt(nz) / CTt(nz=1)

T = 440 MeV, full QCD free quarks

full QCD propagator propagator with free quarks

32x6

0.0 1.0 2.0 3.0 4.0 zT

T = 660 MeV, full QCD T = 960 MeV, full QCD free quarks

full QCD propagators propagator with free quarks

32x4

Ax/Tt ratio measures SU(2)CS breaking 14

slide-16
SLIDE 16

The phase diagram & chemical potential

S = β

  • d3x ¯

Ψ[γµDµ + µγ4]Ψ 15

slide-17
SLIDE 17

Conclusions

spatial correlations at temperatures 1.25 − 5.5Tc chiral symmetry and effective U(1)A restoration above Tc 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