Deconfinement and Polyakov loop in 2+1 flavor QCD

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1 Deconfinement and Polyakov loop in 2+ flavor QCD J. H. Weber in collaboration with A. Bazavov 2, N. Brambilla, H.T. Ding 3, P. Petreczky 4, A. Vairo and H.P. Schadler 5 Physik Department, Technische Universität München, Garching, 2 University of Iowa, 4 Central China Normal University, Wuhan 4 Brookhaven National Lab 5 Universität Graz Determination of the Fundamental Parameters in QCD MITP, 3//26 main results to be published next week / 25

2 Overview & introduction Polyakov loop in 2+ flavor QCD Static Q Q correlators at finite temperature Summary 2 / 25

3 Overview & introduction Polyakov loop in 2+ flavor QCD Static Q Q correlators Summary Introduction Time evolution since Big Bang QCD phase diagram Plasma phase: quark-gluon-plasma T > Tc 6 MeV deconfinement, color screening, iso-vector chiral symmetry,... Hadronic phase: dilute hadron gas Tc T MeV confinement, hidden chiral symmetry, center symmetry (YM),... 3 / 25

4 Introduction Lattice gauge theory at finite temperature QCD expectation values O QCD = Dφ O[φ] e i dv d L[φ;α] fields φ QCD = {A µ, ψ, ψ} parameters α QCD = {g, m q,...} observable O[φ QCD ] Lagrangian L QCD [φ QCD, α QCD ] Why non-perturbative approaches? Non-Abelian group SU(3) QCD scale Λ QCD 2 MeV Crossover transition at T T c LGT on a Euclidean space-time grid 2... N x N τ τ x a Q Q Q. 2 periodic boundaries Interpret finite τ direction as inverse temperature an τ = /T 4 / 25

5 Observables in lattice gauge theory at finite T Thermal observables in lattice gauge theory The archetype of thermal observables Finite N τ direction: an τ = /T Loops wrapping around the N τ direction directly sensitive to T Archetype: Polyakov loop L N τ W (β, N τ, x) = U (x, x) Interpretation L(β, N τ ) = x = Tr W (β, Nτ, x) N c Free energy of a static quark related to the renormalized Polyakov loop L r = e Nτ ac Q L b = exp [ F Q T ] The Polyakov loop on the lattice 2... N x N τ τ x Q. 2 periodic boundaries 5 / 25

6 Observables in lattice gauge theory at finite T Thermal observables in lattice gauge theory The archetype of thermal observables Finite N τ direction: an τ = /T Loops wrapping around the N τ direction directly sensitive to T Archetype: Polyakov loop L N τ W (β, N τ, x) = U (x, x) Interpretation L(β, N τ ) = x = Tr W (β, Nτ, x) N c Free energy of a static quark related to the renormalized Polyakov loop L r = e Nτ ac Q L b = exp [ F Q T ] The Polyakov loop in pure YM theory QUENCHED! S. Gupta et. al., PRD 77, 3453 (28) The renormalized Polyakov loop is an order parameter of the transition in pure YM theory. Due to Z(3) center symmetry 5 / 25

7 Observables in lattice gauge theory at finite T Z(3) center symmetry and Polyakov loop susceptibility Center symmetry in pure YM theory ρ(l) Im as a cartoon Re Z(3) center symmetry for T < T c L = F Q = Confinement in pure gauge theory 6 / 25

8 Observables in lattice gauge theory at finite T Z(3) center symmetry and Polyakov loop susceptibility Center symmetry in pure YM theory ρ(l) Im as a cartoon Re No center symmetry for T > T c L > F Q = finite Deconfinement in pure gauge theory 6 / 25

9 Observables in lattice gauge theory at finite T Z(3) center symmetry and Polyakov loop susceptibility Center symmetry in pure YM theory ρ(l) Im as a cartoon Re Center symmetry is broken in QCD by sea quarks for T < T c L > F Q = finite due to string breaking F Q Ei due to static hadrons with energies Ei (cf. HRG models) i 6 / 25

10 Crossover temperature puzzle The crossover temperature puzzle in full QCD The many faces of T c Y. Aoki et. al., PL B (26) 7 / 25

11 Crossover temperature puzzle The crossover temperature puzzle in full QCD The many faces of T c Newer results from HotQCD collaboration A. Bazavov et. al., PRD (22) Y. Aoki et. al., PL B (26) Nτ m l ms = 27 m l ms = (3) 85(3) 2 7(3) 74(3) 6(6) 65(6) 6 68(2) 7(2) 8 6(2) 64(2) 2 57(3) 6(2) 56(8) 6(6) 56(8) 6(6) χ q, q = l, s dominated by regular part of free T energy; singular part is not easily accessible. L has no demonstrated relation to singular part of free energy with massive light quarks. 7 / 25

12 Crossover temperature puzzle The crossover temperature puzzle in full QCD The many faces of T c Newer results from HotQCD collaboration A. Bazavov et. al., PRD (22) Y. Aoki et. al., PL B (26) Nτ m l ms = 27 m l ms = (3) 85(3) 2 7(3) 74(3) 6(6) 65(6) 6 68(2) 7(2) 8 6(2) 64(2) 2 57(3) 6(2) 56(8) 6(6) 56(8) 6(6) χ q, q = l, s dominated by regular part of free T 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 T c from L due to physical reasons? Does L provide reliable information about T c in full QCD? 7 / 25

13 Bare Polyakov loop Bare Polyakov loop and renormalization f Q bare N τ Free energy needs renormalization L = e Nτ ac Q L b f Q = f bare Q + N τ ac Q Bare free energy: f bare Q = F Q bare T = log Lb 3 43 lattice spacings for each N τ T range from.72t c up to 3T c β What is the nature of C Q? C Q (β) independent of N τ C Q diverges as C Q = /a(β)c Q (β) c Q is related Z 3 exp [ c Q ] Z 3(g 2 ) 8 / 25

14 Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators periodic boundaries 2... N x N τ. 2 τ Q r Q x Free energy of static Q Q pair: F Q Q(T, r) = Tf Q Q(T, r) f Q Q(T, r) = log L(T, )L (T, r) Poylakov loop correlator C P (T, r) 9 / 25

15 Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators periodic boundaries 2... N x N τ. 2 τ Q r Q x Free energy of static Q Q pair: F Q Q(T, r) = Tf Q Q(T, r) f Q Q(T, r) = log L(T, )L (T, r) r /T : static Q Q decorrelate lim C P(T, r) = L(T ) 2 r Apparent due to color screening Poylakov loop correlator C P (T, r) 9 / 25

16 Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators periodic boundaries 2... N x N τ. 2 τ Q r Q x Free energy of static Q Q pair: F Q Q(T, r) = Tf Q Q(T, r) f Q Q(T, r) = log L(T, )L (T, r) Poylakov loop correlator C P (T, r) r /T : static Q Q decorrelate lim C P(T, r) = L(T ) 2 r Apparent due to color screening For any color configuration of Q Q lim C S (T, r) = L(T ) 2 r C S is defined in Coulomb gauge as C S (T, r) = 3 W a(t, )W a (T, r) 3 a= 9 / 25

17 Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators periodic boundaries 2... N x N τ. 2 τ Q r Q x Free energy of static Q Q pair: F Q Q(T, r) = Tf Q Q(T, r) f Q Q(T, r) = log L(T, )L (T, r) Poylakov loop correlator C P (T, r) r /T : static Q Q decorrelate lim C P(T, r) = L(T ) 2 r Apparent due to color screening For any color configuration of Q Q lim C S (T, r) = L(T ) 2 r C S is defined in Coulomb gauge as C S (T, r) = 3 W a(t, )W a (T, r) 3 a= C r S C b S = Cr P C b P = Lr L b 2 = exp [ 2N τ c Q ] 9 / 25

18 Renormalization with QQ procedure Static meson correlators at short distances r /T periodic boundaries 2... N x N τ. 2 τ Q rq x r /T : small thermal effects in F S (T, r) = T log C S (T, r For r /T : vacuum-like due to asymptotic freedom / 25

19 Renormalization with QQ procedure Static meson correlators at short distances r /T periodic boundaries 2... N x N τ. 2 τ Q rq x r /T : small thermal effects in F S (T, r) = T log C S (T, r For r /T : vacuum-like due to asymptotic freedom r /T is a vacuum-like regime F S (T, r) = V Q Q(r) + O(rT ) F S [GeV] T [MeV] Preliminary! r [fm] FS r FS b a = V r Q Q V b Q Q a = 2c Q / 25

20 Renormalization with QQ procedure Renormalization constant c Q from Q Q procedure Q Q procedure: We fix the static energy (V Q Q V ) V r (β, r) = V b (β, r) + 2c Q (β) for each β (β omitted below) to V r (r) = Vi, r 2 V (r) = C i, r i r r=r i with V =.954, V =.265 and C =.65, C =. We take 2c Q from HotQCD, A. Bazavov et. al., PRD (24) we interpolate in β and add N τ c Q to f bare Q (T [β, N τ ]) c Q. β c Q poly optimal relaxed via r via r final Drawbacks of T lattices computationally expensive currently limited to β Advantages of T lattices unambiguous procedure β β / 25

21 Deconfinement temperature Renormalized Polyakov loop, free energy. L N τ T [MeV] Renormalized Polyakov loop and free energy: F Q [MeV] T [MeV] Cutoff effects are large for N τ = 6 only in crossover region. Cutoff effects on par with errors for T > 2 MeV Errors due to N τ c Q become dominant for high T 2 / 25

22 Deconfinement temperature Renormalized Polyakov loop, free energy and temperature derivatives dl/dt T [MeV] Expose the critical behavior in the Polyakov loop and in the free energy: S Q T [MeV] Temperature derivative of L Temperature derivative of F Q dl peaks at T 9 MeV S dt Q = df Q peaks at T 6 MeV dt Is there any relation between the maxima and the deconfinement crossover? 2 / 25

23 Deconfinement temperature Renormalized Polyakov loop, free energy and temperature derivatives dl/dt T [MeV] Different inflection points of L and F Q? S Q T [MeV] In principle the entropy S Q (T ) = df Q (T ) is a measurable quantity. dt The inflection point of F Q is renormalization scheme independent. The inflection point of L is scheme dependent with no physics implied. 2 / 25

24 Deconfinement temperature Relation between entropy and pseudocritical temperature S Q (T) local fit global /N τ 4 fit HRG S Q (T) local fit global /N τ 4 fit global /N τ 2 fit HRG 3 N τ =6 3 N τ = T c 2 T c.5.5 T [MeV] T [MeV] S Q (T) local fit global /N τ 4 fit global /N τ 2 fit HRG S Q (T) local fit global /N τ 4 fit global /N τ 2 fit HRG 3 N τ = 3 N τ = T c 2 T c.5.5 T [MeV] T c is from O(2) scaling fits to chiral susceptibilities A. Bazavov et. al., PRD (22) T [MeV] / 25

25 Continuum results Continuum limit of the free energy F Q (T) [MeV] global fit local fit HISQ, 23 stout HRG A. Bazavov,P. Petreczky, Phys.Rev. D87, 9455 S. Borsanyi et al., JHEP 9, 73 (2) 3 2 T [MeV] F Q lies for low T below and for high T above the older HISQ result. Hadron resonance gas agrees with our data up to T 35 MeV. 4 / 25

26 Continuum results The entropy at the (almost) physical point S Q (T) T/T c N f =2+, m π =6 MeV N f =3, m π =44 MeV N f =2, m π =8 MeV N f = The peak decreases for lower quark masses and for finer lattices. The entropy peaks at T S = MeV in the continuum limit. O. Kaczmarek, F. Zantow, hep-lat/569 (25) P. Petreczky, K. Petrov Phys. Rev. D7, 5453 (2 5 / 25

27 Renormalization with gradient flow Alternative renormalization scheme with gradient flow Gradient flow approach M. Lüscher, JHEP 8, 7(2),... Artificial fifth dimension t Diffusion-type field evolution V µ = g 2 { µs[v ]}V µ Fields at finite flow time V µ V µ(x, t), V µ(x, )=U µ(x) Fields are smeared out over length scale f t = 8t, no short distance singularities flow time t defines a specific renormalization scheme if a f t = 8t /T = an τ adapt flow time for higher T F Q [MeV] F Q (T,2), f t / F Q (T,2), QQ f = pr. F Q (T), QQ pr. 5 Flow data from P. Petreczky, H.-P. Schadler, 5 PRD 92, 9457 (25) T [MeV] f t dependent cutoff effects are quite mild for T 4 MeV. Hence, results at flow time f t differ only by a constant and cross-check Q Q procedure. 6 / 25

28 Renormalization with gradient flow Polyakov loop susceptibility QUENCHED! P.M. Lo et. al., PRD 88, 7452 (23) Polyakov loop susceptibility: χ A = (VT ) ( 3 L 2 L 2) Mixes representations: L 3 2 = L 6 L 3 Casimir scaling violations prohibit application of Q Q procedure 7 / 25

29 Renormalization with gradient flow Polyakov loop susceptibility N τ = 2 Polyakov loop susceptibility: χ A = (VT ) ( 3 L 2 L 2) 2+ flavor HISQ data, renormalized via gradient flow χ A strongly flow time dependent, no indication for critical behavior 7 / 25

30 Renormalization with gradient flow Ratios of Polyakov loop susceptibilities.2 R A bare ratio.2 R A N τ = N τ =6 N τ =8 N τ = N τ =2.8.6 f f 2f 3f T[MeV] T[MeV] Longitudinal and transverse Polyakov loop susceptibilities: χ L = (VT ) 3 ( Re L 2 Re L 2), χ T = (VT ) 3 ( Im L 2 ) R A = χ A /χ L : step function behavior cannot be related to crossover. 8 / 25

31 Renormalization with gradient flow Ratios of Polyakov loop susceptibilities.4.2 R T N τ =6 N τ =8 N τ = N τ =2.4.2 R T N τ =6 N τ =8 N τ = N τ =2.8 flow time f t = f.8 flow time f t = 3f T[MeV] T[MeV] Longitudinal and transverse Polyakov loop susceptibilities: χ L = (VT ) 3 ( Re L 2 Re L 2), χ T = (VT ) 3 ( Im L 2 ) R T = χ T /χ L : crossover pattern for f t f, exposes critical behavior. 8 / 25

32 Singlet free energy Singlet free energy F S [GeV] T [MeV] Preliminary! r [fm] Singlet free energy: C S (r, T ) = W 3 a(t, )W a (T, r) = e F S (r,t )/T Consistent with T = static energy V Q Q(r) up to r.45/t Deviation from V Q Q(r) is driven by the onset of color screening a= 9 / 25

33 Singlet free energy Confining and screening regimes α QQ _ (r,t) T [MeV] Preliminary! r [fm] Effective coupling constant makes different regimes explicit α Q Q(r, T ) = r 2 E(r, T ) C F r, E = {F S (r, T ), V Q Q(r)} α Q Q(r, T ).5 for T 2T c: QGP in HIC is strongly coupled 2 / 25

34 Singlet free energy 5 V Q Q(r) FS(T, r) [MeV] 5-5 T [MeV] Preliminary! r [fm] Thermal modifications small for r study V Q Q(r) F S (r, T ) V Q Q(r) and F S (r, T ) differ by up to MeV for r.27/t 2 / 25

35 Singlet free energy 8 V Q Q(r) FS(T, r) [MeV] N t = 4 N t = 6 N t = 8 N t = N t = 2 T=399 MeV T=49 MeV T=4 MeV T=47 MeV C.L. Preliminary! r [fm] Thermal modifications small for r study V Q Q(r) F S (r, T ) V Q Q(r) and F S (r, T ) differ by up to MeV for r.27/t Cutoff effects are rather large, finer lattices (larger N τ ) required 2 / 25

36 Polyakov loop correlator Static Q Q free energy F QQ _ -T log 9 [GeV] Preliminary! T [MeV] r [fm] C P (r, T ) = L(T, )L (T, r) = e F Q Q (r,t ) T = F S (r,t ) 9 e T + 8 F O (r,t ) 9 e T Consistent with T = static energy V Q Q(r) up to r.5/t This deviation from V Q Q(r) is driven by the color-octet contribution 22 / 25

37 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 2 MeV. We see crossover behavior at T T c for the entropy S Q (T ) = df Q (T ) d T and for the ratio of Polyakov susceptibilities R T (T ) = χ T (T ) χ L (T ). We extract T c = MeV from the entropy, in agreement with T c = 6(6) MeV from chiral susceptibilities (O(2) scaling fits for m l /m s = /2). N τ T c(s Q ) (6) 59(4.5) 62(4.5) 67.5(4.5) T c(χ m,l ) 6(6) 6(2) [62(2)] 64(2) 7(2) 23 / 25

38 Summary (II) Static Q Q correlators show remnants of confinement at least up to 4T c. Onset of thermal effects strongly depends on individual observables, is much faster if color octet states contribute. Singlet free energy (T > ) and static energy (T = ) differ by MeV for short distances. Precision test of perturbation theory for static correlators at finite T is in preparation. 24 / 25

39 Thank You for listening! 25 / 25