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. Vairo 1 and H.P. Schadler 5 1 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, 03/11/2016 main results to be published next week 1 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Overview & introduction Polyakov loop in 2+1 flavor QCD Static Q ¯ Q correlators at finite temperature Summary 2 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Introduction QCD phase diagram ☛ ✟ ✟ ✠ Plasma phase: ✡ ✠ ✎ ☞ Time evolution since Big Bang quark-gluon-plasma T > T c ≈ 160 MeV deconfinement, color screening, iso-vector chiral symmetry, . . . ✍ ✌ ☛ ✟ Hadronic phase: ✡ ✠ ✎ ☞ dilute hadron gas T c ≫ T ≈ 0 MeV ☛ ✡ confinement, hidden chiral symmetry, center symmetry (YM), . . . ✍ ✌ 3 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Introduction Lattice gauge theory at finite temperature QCD expectation values LGT on a Euclidean space-time grid 0 1 2 . . . N x N τ � i � dV d L [ φ ; α ] �O� QCD = D φ O [ φ ] e a fields φ QCD = { A µ , ψ, ¯ Q ψ } parameters α QCD = { g , m q , . . . } . . . observable O [ φ QCD ] 2 Lagrangian L QCD [ φ QCD , α QCD ] Q † Q 1 τ 0 Why non-perturbative approaches? periodic boundaries Non-Abelian group SU(3) x QCD scale Λ Q CD ∼ 200 MeV Interpret finite τ direction as Crossover transition at T ≈ T c inverse temperature aN τ = 1 / T 4 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Observables in lattice gauge theory at finite T Thermal observables in lattice gauge theory The archetype of thermal observables The Polyakov loop on the lattice 0 1 2 . . . N x Finite N τ direction: aN τ = 1 / T N τ Loops wrapping around the N τ direction directly sensitive to T Q Archetype: Polyakov loop L N τ . . � . W ( β, N τ , x ) = U 0 ( x 0 , x ) 2 x 0 = 1 L ( β, N τ ) = Tr W ( β, N τ , x ) 1 N c τ 0 periodic boundaries Interpretation x Free energy of a static quark related to the renormalized Polyakov loop � L r � = e − N τ aC Q � L b � = exp [ − F Q T ] 5 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Observables in lattice gauge theory at finite T Thermal observables in lattice gauge theory The archetype of thermal observables The Polyakov loop in pure YM theory Finite N τ direction: aN τ = 1 / T Loops wrapping around the N τ direction directly sensitive to T QUENCHED ! Archetype: Polyakov loop L N τ � W ( β, N τ , x ) = U 0 ( x 0 , x ) x 0 = 1 L ( β, N τ ) = Tr W ( β, N τ , x ) S. Gupta et. al., PRD 77, 034503 (2008) N c ✎ ☞ The renormalized Polyakov loop Interpretation is an order parameter of the Free energy of a static quark related transition in pure YM theory. ✍ ✌ to the renormalized Polyakov loop ✎ ☞ Due to Z(3) center symmetry � L r � = e − N τ aC Q � L b � = exp [ − F Q ✍ ✌ T ] 5 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD 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 as a ‘cartoon’ Im ρ ( L ) 1 0.5 0 Re -0.5 -1 -1 -0.5 0 0.5 1 Z(3) center symmetry for T < T c ✎ ☞ � L � = 0 ⇔ F Q = ∞ Confinement in pure gauge theory ✍ ✌ 6 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD 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 as a ‘cartoon’ Im ρ ( L ) 1 0.5 0 Re -0.5 -1 -1 -0.5 0 0.5 1 No center symmetry for T > T c ✎ ☞ � L � > 0 ⇔ F Q = finite Deconfinement in pure gauge theory ✍ ✌ 6 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD 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 as a ‘cartoon’ Im ρ ( L ) 1 0.5 0 Re -0.5 -1 -1 -0.5 0 0.5 1 Center symmetry is broken in QCD by sea quarks for T < T c ✎ ☞ � L � > 0 ⇔ F Q = finite due to string breaking F Q ≃ � i E i due to static hadrons with energies E i (cf. HRG models) ✍ ✌ 6 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Crossover temperature puzzle The crossover temperature puzzle in full QCD The many faces of T c Y. Aoki et. al., PL B643 46-54 (2006) 7 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary 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 85 054503 (2012) ml ml ms = 1 ms = 1 N τ 27 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) ∞ ✎ ☞ Y. Aoki et. al., PL B643 46-54 (2006) ∂χ q ∂ 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
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary 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 85 054503 (2012) ml ml ms = 1 ms = 1 N τ 27 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) ∞ ✎ ☞ Y. Aoki et. al., PL B643 46-54 (2006) ∂χ q ∂ 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 T c from L due to physi- cal reasons? Does L provide reliable informa- tion about T c in full QCD? ✍ ✌ 7 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Bare Polyakov loop Bare Polyakov loop and renormalization ✎ ☞ 9 bare f Q Free energy needs renormalization N τ 8 4 6 � L � = e − N τ aC Q � L b � 8 7 10 12 6 f Q = f bare ⇒ + N τ aC Q Q 5 4 What is the nature of C Q ? 3 ✍ ✌ 2 ✎ ☞ 1 β C Q ( β ) independent of N τ 6 6.4 6.8 7.2 7.6 8 8.4 8.8 9.2 9.6 ✎ ☞ C Q diverges as Bare free energy: C Q = 1 / a ( β ) c Q ( β ) = F bare f bare Q = − log � L b � Q c Q is related Z 3 T 31 – 43 lattice spacings for each N τ exp [ − c Q ] ∝ Z 3 ( g 2 ) ✍ ✌ T range from 0 . 72 T c up to 30 T c ✍ ✌ 8 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators 0 1 2 . . . N x N τ periodic boundaries . . . 2 1 τ 0 Q † Q r x ✎ ☞ Free energy of static Q ¯ pair: Q Q ( T , r ) = Tf Q ¯ Q ( T , r ) F Q ¯ Q ( T , r ) = − log � L ( T , 0 ) L † ( T , r ) � f Q ¯ Poylakov loop correlator C P ( T , r ) ✍ ✌ 9 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators ✎ ☞ 0 1 2 . . . N x r ≫ 1 / T : static Q ¯ Q decorrelate N τ periodic boundaries r →∞ C P ( T , r ) = � L ( T ) � 2 lim Apparent due to color screening ✍ ✌ . . . 2 1 τ 0 Q † Q r x ✎ ☞ Free energy of static Q ¯ pair: Q Q ( T , r ) = Tf Q ¯ Q ( T , r ) F Q ¯ Q ( T , r ) = − log � L ( T , 0 ) L † ( T , r ) � f Q ¯ Poylakov loop correlator C P ( T , r ) ✍ ✌ 9 / 25
Static Q ¯ Overview & introduction Polyakov loop in 2+1 flavor QCD Q correlators Summary Renormalization with QQ procedure Polyakov loop as asymptotic limit of static meson correlators ✎ ☞ 0 1 2 . . . N x r ≫ 1 / T : static Q ¯ Q decorrelate N τ periodic boundaries r →∞ C P ( T , r ) = � L ( T ) � 2 lim Apparent due to color screening ✍ ✌ . ✎ ☞ . . For any color configuration of Q ¯ 2 Q 1 r →∞ C S ( T , r ) = � L ( T ) � 2 lim τ 0 Q † Q r C S is defined in Coulomb gauge as x 3 ✎ ☞ C S ( T , r ) = 1 � W a ( T , 0 ) W † a ( T , r ) Free energy of static Q ¯ pair: Q 3 a = 1 Q ( T , r ) = Tf Q ¯ Q ( T , r ) F Q ¯ ✍ ✌ Q ( T , r ) = − log � L ( T , 0 ) L † ( T , r ) � f Q ¯ Poylakov loop correlator C P ( T , r ) ✍ ✌ 9 / 25
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