Deconfinement and Polyakov loop in 2+1 flavor QCD J. H. Weber 1 in - - PowerPoint PPT Presentation

▶
deconfinement and polyakov loop in 2 1 flavor qcd
SMART_READER_LITE
LIVE PREVIEW

Deconfinement and Polyakov loop in 2+1 flavor QCD J. H. Weber 1 in - - PowerPoint PPT Presentation

Feb 28, 2024 145 likes •556 views

Static Q Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Deconfinement and Polyakov loop in 2+1 flavor QCD J. H. Weber 1 in collaboration with A. Bazavov 2 , N. Brambilla 1 , H.T. Ding 3 , P. Petreczky 4 , A.

slide-1
SLIDE 1

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary

Deconfinement and Polyakov loop in 2+1 flavor QCD

  • J. H. Weber1 in collaboration with
  • A. Bazavov2, N. Brambilla1, H.T. Ding3, P. Petreczky4, A. Vairo1 and H.P.

Schadler5

1Physik Department, Technische Universität München, Garching, 2University of Iowa, 4Central China Normal University, Wuhan 4Brookhaven National Lab 5Universität Graz

Determination of the Fundamental Parameters in QCD MITP, 03/11/2016

main results to be published next week

1 / 25

slide-2
SLIDE 2

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators at finite temperature Summary

2 / 25

slide-3
SLIDE 3

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Introduction

QCD phase diagram

☛ ✡ ✟ ✠

Time evolution since Big Bang

☛ ✡ ✟ ✠

Hadronic phase:

✎ ✍ ☞ ✌

dilute hadron gas Tc ≫ T ≈ 0 MeV confinement, hidden chiral symmetry, center symmetry (YM), . . .

☛ ✡ ✟ ✠

Plasma phase:

✎ ✍ ☞ ✌

quark-gluon-plasma T > Tc ≈ 160 MeV deconfinement, color screening, iso-vector chiral symmetry, . . .

3 / 25

slide-4
SLIDE 4

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Introduction

Lattice gauge theory at finite temperature

QCD expectation values OQCD =

  • Dφ O[φ] e

i dVd L[φ;α]

fields φQCD = {Aµ, ψ, ¯ ψ} parameters αQCD = {g, mq, . . .}

  • bservable O[φQCD]

Lagrangian LQCD[φQCD, αQCD] Why non-perturbative approaches? Non-Abelian group SU(3) QCD scale ΛQCD ∼ 200 MeV Crossover transition at T ≈ Tc LGT on a Euclidean space-time grid

x τ a 1 2 . . . Nx 1 2 . . . Nτ Q Q† Q periodic boundaries

Interpret finite τ direction as inverse temperature aNτ = 1/T

4 / 25

slide-5
SLIDE 5

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Observables in lattice gauge theory at finite T

Thermal observables in lattice gauge theory

The archetype of thermal observables Finite Nτ direction: aNτ = 1/T Loops wrapping around the Nτ direction directly sensitive to T Archetype: Polyakov loop L W (β, Nτ, x) =

Nτ

  • x0=1

U0(x0, x) L(β, Nτ) = Tr W (β, Nτ, x) Nc Interpretation Free energy of a static quark related to the renormalized Polyakov loop Lr = e−Nτ aCQ Lb = exp [−FQ T ] The Polyakov loop on the lattice

x τ 1 2 . . . Nx 1 2 . . . Nτ Q periodic boundaries 5 / 25

slide-6
SLIDE 6

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Observables in lattice gauge theory at finite T

Thermal observables in lattice gauge theory

The archetype of thermal observables Finite Nτ direction: aNτ = 1/T Loops wrapping around the Nτ direction directly sensitive to T Archetype: Polyakov loop L W (β, Nτ, x) =

Nτ

  • x0=1

U0(x0, x) L(β, Nτ) = Tr W (β, Nτ, x) Nc Interpretation Free energy of a static quark related to the renormalized Polyakov loop Lr = e−Nτ aCQ Lb = exp [−FQ T ] The Polyakov loop in pure YM theory

  • S. Gupta et. al., PRD 77, 034503 (2008)

QUENCHED !

✎ ✍ ☞ ✌ The renormalized Polyakov loop is an order parameter of the transition in pure YM theory. ✎ ✍ ☞ ✌ Due to Z(3) center symmetry 5 / 25

slide-7
SLIDE 7

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Observables in lattice gauge theory at finite T

Z(3) center symmetry and Polyakov loop susceptibility

Center symmetry in pure YM theory

Re Im

ρ(L)

as a ‘cartoon’

  • 1 -0.5 0

0.5 1

  • 1
  • 0.5

0.5

1

Z(3) center symmetry for T < Tc

✎ ✍ ☞ ✌ L = 0 ⇔ FQ = ∞ Confinement in pure gauge theory 6 / 25

slide-8
SLIDE 8

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Observables in lattice gauge theory at finite T

Z(3) center symmetry and Polyakov loop susceptibility

Center symmetry in pure YM theory

Re Im

ρ(L)

as a ‘cartoon’

  • 1 -0.5 0

0.5 1

  • 1
  • 0.5

0.5

1

No center symmetry for T > Tc

✎ ✍ ☞ ✌ L > 0 ⇔ FQ = finite Deconfinement in pure gauge theory 6 / 25

slide-9
SLIDE 9

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Observables in lattice gauge theory at finite T

Z(3) center symmetry and Polyakov loop susceptibility

Center symmetry in pure YM theory

Re Im

ρ(L)

as a ‘cartoon’

  • 1 -0.5 0

0.5 1

  • 1
  • 0.5

0.5

1 Center symmetry is broken in QCD by sea quarks for T < Tc ✎ ✍ ☞ ✌

L > 0 ⇔ FQ = finite due to string breaking FQ ≃

i Ei due to static hadrons with energies Ei (cf. HRG models)

6 / 25

slide-10
SLIDE 10

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Crossover temperature puzzle

The crossover temperature puzzle in full QCD

The many faces of Tc

  • Y. Aoki et. al., PL B643 46-54 (2006)

7 / 25

slide-11
SLIDE 11

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Crossover temperature puzzle

The crossover temperature puzzle in full QCD

The many faces of Tc

  • Y. Aoki et. al., PL B643 46-54 (2006)

Newer results from HotQCD collaboration

  • A. Bazavov et. al., PRD 85 054503 (2012)

Nτ ml ms = 1 27 ml ms = 1 20 8 182(3) 185(3) 12 170(3) 174(3) ∞ 161(6) 165(6) 6 168(2) 171(2) 8 161(2) 164(2) 12 157(3) 161(2) ∞ 156(8) 160(6) ∞ 156(8) 160(6)

✎ ✍ ☞ ✌

∂χq ∂T , q = l, s dominated by regular part of free

energy; singular part is not easily accessible.

✎ ✍ ☞ ✌

L has no demonstrated relation to singular part of free energy with massive light quarks.

7 / 25

slide-12
SLIDE 12

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Crossover temperature puzzle

The crossover temperature puzzle in full QCD

The many faces of Tc

  • Y. Aoki et. al., PL B643 46-54 (2006)

Newer results from HotQCD collaboration

  • A. Bazavov et. al., PRD 85 054503 (2012)

Nτ ml ms = 1 27 ml ms = 1 20 8 182(3) 185(3) 12 170(3) 174(3) ∞ 161(6) 165(6) 6 168(2) 171(2) 8 161(2) 164(2) 12 157(3) 161(2) ∞ 156(8) 160(6) ∞ 156(8) 160(6)

✎ ✍ ☞ ✌

∂χq ∂T , q = l, s dominated by regular part of free

energy; singular part is not easily accessible.

✎ ✍ ☞ ✌

L has no demonstrated relation to singular part of free energy with massive light quarks.

✎ ✍ ☞ ✌

Is the higher value of Tc from L due to physi- cal reasons? Does L provide reliable informa- tion about Tc in full QCD?

7 / 25

slide-13
SLIDE 13

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Bare Polyakov loop

Bare Polyakov loop and renormalization

1 2 3 4 5 6 7 8 9 6 6.4 6.8 7.2 7.6 8 8.4 8.8 9.2 9.6 fQ

bare

β Nτ 12 10 8 6 4

✎ ✍ ☞ ✌

Bare free energy: f bare

Q

= F bare

Q

T = − log Lb 31 – 43 lattice spacings for each Nτ T range from 0.72Tc up to 30Tc

✎ ✍ ☞ ✌

Free energy needs renormalization L = e−Nτ aCQ Lb ⇒ fQ = f bare

Q

+ NτaCQ What is the nature of CQ?

✎ ✍ ☞ ✌

CQ(β) independent of Nτ CQ diverges as CQ = 1/a(β)cQ(β) cQ is related Z3 exp [−cQ] ∝ Z3(g2)

8 / 25

slide-14
SLIDE 14

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Polyakov loop as asymptotic limit of static meson correlators

x τ 1 2 . . . Nx 1 2 . . . Nτ Q Q† r periodic boundaries ✎ ✍ ☞ ✌

Free energy of static Q ¯ Q pair: FQ ¯

Q(T, r) = TfQ ¯ Q(T, r)

fQ ¯

Q(T, r) = − log L(T, 0)L†(T, r)

Poylakov loop correlator CP(T, r)

9 / 25

slide-15
SLIDE 15

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Polyakov loop as asymptotic limit of static meson correlators

x τ 1 2 . . . Nx 1 2 . . . Nτ Q Q† r periodic boundaries ✎ ✍ ☞ ✌

Free energy of static Q ¯ Q pair: FQ ¯

Q(T, r) = TfQ ¯ Q(T, r)

fQ ¯

Q(T, r) = − log L(T, 0)L†(T, r)

Poylakov loop correlator CP(T, r)

✎ ✍ ☞ ✌

r ≫ 1/T: static Q ¯ Q decorrelate lim

r→∞ CP(T, r) = L(T)2

Apparent due to color screening

9 / 25

slide-16
SLIDE 16

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Polyakov loop as asymptotic limit of static meson correlators

x τ 1 2 . . . Nx 1 2 . . . Nτ Q Q† r periodic boundaries ✎ ✍ ☞ ✌

Free energy of static Q ¯ Q pair: FQ ¯

Q(T, r) = TfQ ¯ Q(T, r)

fQ ¯

Q(T, r) = − log L(T, 0)L†(T, r)

Poylakov loop correlator CP(T, r)

✎ ✍ ☞ ✌

r ≫ 1/T: static Q ¯ Q decorrelate lim

r→∞ CP(T, r) = L(T)2

Apparent due to color screening

✎ ✍ ☞ ✌

For any color configuration of Q ¯ Q lim

r→∞ CS(T, r) = L(T)2

CS is defined in Coulomb gauge as CS(T, r) = 1 3

3

  • a=1

Wa(T, 0)W †

a (T, r)

9 / 25

slide-17
SLIDE 17

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Polyakov loop as asymptotic limit of static meson correlators

x τ 1 2 . . . Nx 1 2 . . . Nτ Q Q† r periodic boundaries ✎ ✍ ☞ ✌

Free energy of static Q ¯ Q pair: FQ ¯

Q(T, r) = TfQ ¯ Q(T, r)

fQ ¯

Q(T, r) = − log L(T, 0)L†(T, r)

Poylakov loop correlator CP(T, r)

✎ ✍ ☞ ✌

r ≫ 1/T: static Q ¯ Q decorrelate lim

r→∞ CP(T, r) = L(T)2

Apparent due to color screening

✎ ✍ ☞ ✌

For any color configuration of Q ¯ Q lim

r→∞ CS(T, r) = L(T)2

CS is defined in Coulomb gauge as CS(T, r) = 1 3

3

  • a=1

Wa(T, 0)W †

a (T, r)

✎ ✍ ☞ ✌

Cr

S

Cb

S =

Cr

P

Cb

P = Lr

Lb 2 = exp [−2NτcQ]

9 / 25

slide-18
SLIDE 18

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Static meson correlators at short distances r ≪ 1/T

x τ 1 2 . . . Nx 1 2 . . . Nτ Q Q† r periodic boundaries ✎ ✍ ☞ ✌

r ≪ 1/T: small thermal effects in FS(T, r) = −T log CS(T, r For r ≪ 1/T: vacuum-like due to asymptotic freedom

10 / 25

slide-19
SLIDE 19

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Static meson correlators at short distances r ≪ 1/T

x τ 1 2 . . . Nx 1 2 . . . Nτ Q Q† r periodic boundaries ✎ ✍ ☞ ✌

r ≪ 1/T: small thermal effects in FS(T, r) = −T log CS(T, r For r ≪ 1/T: vacuum-like due to asymptotic freedom

✎ ✍ ☞ ✌

r ≪ 1/T is a vacuum-like regime FS(T, r) = VQ ¯

Q(r) + O(rT)

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 FS [GeV] r [fm] T [MeV] 650 600 550 500 450 400 350 325 300 275 250 225 200 190

Preliminary!

✎ ✍ ☞ ✌

F r

S − F b S

a = V r

Q ¯ Q − V b Q ¯ Q

a = −2cQ

10 / 25

slide-20
SLIDE 20

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with QQ procedure

Renormalization constant cQ from Q ¯ Q procedure

✎ ✍ ☞ ✌

Q ¯ Q procedure: We fix the static energy (VQ ¯

Q ≡ V )

V r(β, r) = V b(β, r) + 2cQ(β) for each β (β omitted below) to V r(r) = Vi ri , r 2 ∂V (r) ∂r

  • r=ri

= Ci, with V0 = 0.954, V1 = 0.2065 and C0 = 1.65, C1 = 1.0 We take 2cQ from HotQCD,

  • A. Bazavov et. al., PRD 90 094503 (2014)

we interpolate in β and add NτcQ to f bare

Q

(T[β, Nτ]).

  • 0.42
  • 0.4
  • 0.38
  • 0.36
  • 0.34
  • 0.32

5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 cQ β final via r0 via r1

  • 0.2
  • 0.1

0.1 5.8 6.2 6.6 7 7.4 7.8 ∂βcQ β relaxed

  • ptimal

poly

✎ ✍ ☞ ✌

Drawbacks of T ≈ 0 lattices computationally expensive currently limited to β ≤ 7.825 Advantages of T ≈ 0 lattices unambiguous procedure

11 / 25

slide-21
SLIDE 21

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Deconfinement temperature

Renormalized Polyakov loop, free energy

0.01 0.1 120 140 160 180 200 220 240 L T [MeV] Nτ 12 10 8 6 160 200 240 280 320 360 400 440 480 520 120 140 160 180 200 220 240 FQ [MeV] T [MeV] 12 10 8 6

✎ ✍ ☞ ✌

Renormalized Polyakov loop and free energy: Cutoff effects are large for Nτ = 6 only in crossover region. Cutoff effects on par with errors for T > 200 MeV Errors due to NτcQ become dominant for high T

12 / 25

slide-22
SLIDE 22

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Deconfinement temperature

Renormalized Polyakov loop, free energy and temperature derivatives

0.0007 0.001 0.002 0.003 0.004 0.005 120 140 160 180 200 220 240 dL/dT T [MeV] 12 10 8 6 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 120 140 160 180 200 220 240 SQ T [MeV] 12 10 8 6

✎ ✍ ☞ ✌

Expose the ‘critical behavior’ in the Polyakov loop and in the free energy: Temperature derivative of L

dL dT peaks at T ≈ 190 MeV

Temperature derivative of FQ SQ = −

dFQ dT peaks at T ≈ 160 MeV

Is there any relation between the maxima and the deconfinement crossover?

12 / 25

slide-23
SLIDE 23

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Deconfinement temperature

Renormalized Polyakov loop, free energy and temperature derivatives

0.0007 0.001 0.002 0.003 0.004 0.005 120 140 160 180 200 220 240 dL/dT T [MeV] 12 10 8 6 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 120 140 160 180 200 220 240 SQ T [MeV] 12 10 8 6

✎ ✍ ☞ ✌

Different inflection points of L and FQ? In principle the entropy SQ(T) = −

dFQ(T) dT

is a measurable quantity. → The inflection point of FQ is renormalization scheme independent. The inflection point of L is scheme dependent with no physics implied.

12 / 25

slide-24
SLIDE 24

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Deconfinement temperature

Relation between entropy and pseudocritical temperature

1 1.5 2 2.5 3 3.5 4 4.5 5 140 160 180 200 220 240 260 280 300 T [MeV] SQ(T) Tc Nτ=6 local fit global 1/Nτ

4 fit

HRG 1 1.5 2 2.5 3 3.5 4 4.5 5 120 140 160 180 200 220 240 260 280 300 T [MeV] SQ(T) Tc Nτ=8 local fit global 1/Nτ

4 fit

global 1/Nτ

2 fit

HRG 1 1.5 2 2.5 3 3.5 4 4.5 5 120 140 160 180 200 220 240 260 280 300 T [MeV] SQ(T) Tc Nτ=10 local fit global 1/Nτ

4 fit

global 1/Nτ

2 fit

HRG 1 1.5 2 2.5 3 3.5 4 4.5 5 120 140 160 180 200 220 240 260 280 300 T [MeV] SQ(T) Tc Nτ=12 local fit global 1/Nτ

4 fit

global 1/Nτ

2 fit

HRG

Tc is from O(2) scaling fits to chiral susceptibilities

  • A. Bazavov et. al., PRD 85 054503 (2012)

13 / 25

slide-25
SLIDE 25

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Continuum results

Continuum limit of the free energy

100 200 300 400 500 600 120 140 160 180 200 220 240 T [MeV] FQ(T) [MeV] global fit local fit HISQ, 2013 stout HRG

  • S. Borsanyi et al.,

JHEP 09, 073 (2010)

  • A. Bazavov,P. Petreczky,

Phys.Rev. D87, 094505

✎ ✍ ☞ ✌

FQ lies for low T below and for high T above the older HISQ result. Hadron resonance gas agrees with our data up to T 135 MeV.

14 / 25

slide-26
SLIDE 26

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Continuum results

The entropy at the (almost) physical point

1 2 3 4 5 6 7 8 9 10 0.8 1 1.2 1.4 1.6 1.8 2 SQ(T) T/Tc Nf=2+1, mπ=161 MeV Nf=3, mπ=440 MeV Nf=2, mπ=800 MeV Nf=0

  • P. Petreczky, K. Petrov
  • Phys. Rev. D70, 054503 (2004)
  • O. Kaczmarek, F. Zantow,

hep-lat/0506019 (2005)

✎ ✍ ☞ ✌

The peak decreases for lower quark masses and for finer lattices. The entropy peaks at TS = 153+6.5

−5

MeV in the continuum limit.

15 / 25

slide-27
SLIDE 27

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with gradient flow

Alternative renormalization scheme with gradient flow

✎ ✍ ☞ ✌

Gradient flow approach

  • M. Lüscher, JHEP 08, 071(2010), . . .

Artificial fifth dimension t Diffusion-type field evolution ˙ Vµ =−g2

0 {∂µS[V ]}Vµ

Fields at finite flow time Vµ ≡Vµ(x, t), Vµ(x, 0)=Uµ(x) Fields are smeared out over length scale ft = √ 8t, no short distance singularities flow time t defines a specific renormalization scheme if a ≪ ft = √ 8t ≪ 1/T = aNτ adapt flow time for higher T

50 100 150 200 250 300 350 400 450 500 550 120 160 200 240 280 320 360 400 FQ [MeV] T [MeV] FQ(T), QQ _ pr. FQ(T,12), QQ _ pr. FQ(T,12), ft/ f0=1 Flow data from

  • P. Petreczky, H.-P. Schadler,

PRD 92, 094517 (2015)

✎ ✍ ☞ ✌

ft dependent cutoff effects are quite mild for T 400 MeV. Hence, results at flow time ft differ only by a constant and cross-check Q ¯ Q procedure.

16 / 25

slide-28
SLIDE 28

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with gradient flow

Polyakov loop susceptibility

P.M. Lo et. al., PRD 88, 074502 (2013)

QUENCHED !

✎ ✍ ☞ ✌

Polyakov loop susceptibility: χA = (VT)3 |L|2 − |L|2 Mixes representations: |L3|2 = |L6| − |L3| Casimir scaling violations prohibit application of Q ¯ Q procedure

17 / 25

slide-29
SLIDE 29

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with gradient flow

Polyakov loop susceptibility

Nτ = 12

✎ ✍ ☞ ✌

Polyakov loop susceptibility: χA = (VT)3 |L|2 − |L|2 2+1 flavor HISQ data, renormalized via gradient flow χA strongly flow time dependent, no indication for critical behavior

17 / 25

slide-30
SLIDE 30

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with gradient flow

Ratios of Polyakov loop susceptibilities

0.2 0.4 0.6 0.8 1 1.2 150 200 250 300 T[MeV] RA Nτ=6 Nτ=8 Nτ=10 Nτ=12

bare ratio

0.2 0.4 0.6 0.8 1 1.2 150 200 250 300 T[MeV] RA 0f0 1f0 2f0 3f0

Nτ = 8

✎ ✍ ☞ ✌

Longitudinal and transverse Polyakov loop susceptibilities: χL = (VT)3 Re L2 − Re L2 , χT = (VT)3 Im L2 RA = χA/χL: step function behavior cannot be related to crossover.

18 / 25

slide-31
SLIDE 31

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Renormalization with gradient flow

Ratios of Polyakov loop susceptibilities

0.2 0.4 0.6 0.8 1 1.2 1.4 150 200 250 300 T[MeV] RT Nτ=6 Nτ=8 Nτ=10 Nτ=12

flow time ft = 1f0

0.2 0.4 0.6 0.8 1 1.2 1.4 150 200 250 300 T[MeV] RT Nτ=6 Nτ=8 Nτ=10 Nτ=12

flow time ft = 3f0

✎ ✍ ☞ ✌

Longitudinal and transverse Polyakov loop susceptibilities: χL = (VT)3 Re L2 − Re L2 , χT = (VT)3 Im L2 RT = χT/χL: crossover pattern for ft ≥ f0, exposes critical behavior.

18 / 25

slide-32
SLIDE 32

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Singlet free energy

Singlet free energy

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 FS [GeV] r [fm] T [MeV] 650 600 550 500 450 400 350 325 300 275 250 225 200 190

Preliminary!

✎ ✍ ☞ ✌

Singlet free energy: CS(r, T) = 1

3 3

  • a=1

Wa(T, 0)W †

a (T, r) = e−FS(r,T)/T

Consistent with T = 0 static energy VQ ¯

Q(r) up to r ∼ 0.45/T

Deviation from VQ ¯

Q(r) is driven by the onset of color screening

19 / 25

slide-33
SLIDE 33

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Singlet free energy

Confining and screening regimes

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.03 0.06 0.1 0.2 0.3 0.6 1.0 αQQ

_(r,T)

r [fm]

T [MeV] 133 154 162 170 177 181 222 266 320 369 445 502 546 666 814

Preliminary!

✎ ✍ ☞ ✌

Effective coupling constant makes different regimes explicit αQ ¯

Q(r, T) = r 2

CF ∂E(r, T) ∂r , E = {FS(r, T), VQ ¯

Q(r)}

αQ ¯

Q(r, T) 0.5 for T 2Tc: QGP in HIC is strongly coupled

20 / 25

slide-34
SLIDE 34

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Singlet free energy

240 270 300 330 370 400 T [MeV] r [fm] VQ ¯

Q(r) − FS(T, r) [MeV]

0.3 0.2 0.1 0.06 0.03 15 10 5

  • 5
  • 10

Preliminary!

✎ ✍ ☞ ✌

Thermal modifications small for r → 0 → study VQ ¯

Q(r) − FS(r, T)

VQ ¯

Q(r) and FS(r, T) differ by up to 10 MeV for r 0.27/T

21 / 25

slide-35
SLIDE 35

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Singlet free energy

T=399 MeV T=409 MeV T=400 MeV T=407 MeV C.L. Nt = 4 Nt = 6 Nt = 8 Nt = 10 Nt = 12 r [fm] VQ ¯

Q(r) − FS(T, r) [MeV]

0.3 0.2 0.1 0.06 0.03 80 60 40 20

Preliminary!

✎ ✍ ☞ ✌

Thermal modifications small for r → 0 → study VQ ¯

Q(r) − FS(r, T)

VQ ¯

Q(r) and FS(r, T) differ by up to 10 MeV for r 0.27/T

Cutoff effects are rather large, finer lattices (larger Nτ) required

21 / 25

slide-36
SLIDE 36

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary Polyakov loop correlator

Static Q ¯ Q free energy

  • 2
  • 1.8
  • 1.6
  • 1.4
  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 FQQ

_ -T log 9 [GeV]

r [fm] T [MeV] 650 600 550 500 450 400 350 325 300 275 250 225 200 175

Preliminary!

✎ ✍ ☞ ✌

CP(r, T) = L(T, 0)L†(T, r) = e−

FQ ¯ Q (r,T) T

= 1 9e− FS (r,T)

T

+ 8 9e− FO (r,T)

T

Consistent with T = 0 static energy VQ ¯

Q(r) up to r ∼ 0.15/T

This deviation from VQ ¯

Q(r) is driven by the color-octet contribution

22 / 25

slide-37
SLIDE 37

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary

Summary (I)

We extract different deconfinement observables from the renormalized Polyakov loop. Our analysis is firmly based on the Q ¯ Q procedure. Renormalization scheme dependence leads to an inflection point of the Polyakov loop at higher temperatures T ≈ 200 MeV. We see crossover behavior at T ≈ Tc for the entropy SQ(T) = −

dFQ(T) d T

and for the ratio of Polyakov susceptibilities RT(T) = χT (T)

χL(T) .

We extract Tc = 153+6.5

−5

MeV from the entropy, in agreement with Tc = 160(6) MeV from chiral susceptibilities (O(2) scaling fits for ml/ms = 1/20). Nτ ∞ 12 10 8 6 Tc(SQ) 153+6.5

−5

157.5(6) 159(4.5) 162(4.5) 167.5(4.5) Tc(χm,l) 160(6) 161(2) [162(2)]∗ 164(2) 171(2)

23 / 25

slide-38
SLIDE 38

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary

Summary (II)

Static Q ¯ Q correlators show remnants of confinement at least up to 4Tc. Onset of thermal effects strongly depends on individual observables, is much faster if color octet states contribute. Singlet free energy (T > 0) and static energy (T = 0) differ by 10 MeV for short distances. Precision test of perturbation theory for static correlators at finite T is in preparation.

24 / 25

slide-39
SLIDE 39

Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators Summary

Thank You for listening!

25 / 25