QCD from quark, gluon, and meson correlators

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1 QCD from quark, gluon, and meson correlators Mario Mitter Brookhaven National Laboratory Frankfurt, October 7 M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

2 fqcd collaboration - QCD (phase diagram) with FRG: J. Braun, L. Corell, A. K. Cyrol, W. J. Fu, M. Leonhardt, MM, J. M. Pawlowski, M. Pospiech, F. Rennecke, N. Strodthoff, N. Wink,... Temperature early universe LHC quark gluon plasma RHIC SPS <ψψ> crossover FAIR/NICA <ψψ> = / vacuum hadronic fluid n B= n B> AGS SIS nuclear matter µ quark matter crossover superfluid/superconducting SC phases? <ψψ> = / CFL neutron star cores [Schaefer, Wagner, 8] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

3 fqcd collaboration - QCD (phase diagram) with FRG: J. Braun, L. Corell, A. K. Cyrol, W. J. Fu, M. Leonhardt, MM, J. M. Pawlowski, M. Pospiech, F. Rennecke, N. Strodthoff, N. Wink,... Temperature early universe LHC quark gluon plasma RHIC SPS <ψψ> crossover FAIR/NICA <ψψ> = / vacuum hadronic fluid n B= n B> AGS SIS nuclear matter µ quark matter crossover superfluid/superconducting SC phases? <ψψ> = / CFL neutron star cores [Schaefer, Wagner, 8] large part of this effort: vacuum QCD and YM-theory M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

4 fqcd collaboration - QCD (phase diagram) with FRG: J. Braun, L. Corell, A. K. Cyrol, W. J. Fu, M. Leonhardt, MM, J. M. Pawlowski, M. Pospiech, F. Rennecke, N. Strodthoff, N. Wink,... Temperature early universe LHC quark gluon plasma RHIC SPS <ψψ> crossover FAIR/NICA <ψψ> = / vacuum hadronic fluid n B= n B> AGS SIS nuclear matter µ quark matter crossover superfluid/superconducting SC phases? <ψψ> = / CFL neutron star cores [Schaefer, Wagner, 8] large part of this effort: vacuum QCD and YM-theory why? M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

5 QCD from the effective action (gauge fixing necessary). Γ[Φ] = n {p i } Γ(n) Φ Φ n (p,..., p n )Φ (p ) Φ n ( p p n ) M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 3 /

6 QCD from the effective action (gauge fixing necessary). Γ[Φ] = n {p i } Γ(n) Φ Φ n (p,..., p n )Φ (p ) Φ n ( p p n ) full information about QFT encoded in Γ[Φ]/correlators: M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 3 /

7 QCD from the effective action (gauge fixing necessary). Γ[Φ] = n {p i } Γ(n) Φ Φ n (p,..., p n )Φ (p ) Φ n ( p p n ) full information about QFT encoded in Γ[Φ]/correlators: bound state spectrum: pole structure of the Γ (n) e.g. [Roberts, Williams, 94], [Alkofer, Smekal, ], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, 6] form factors: photon-particle correlators e.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, 8], [Sanchis-Alepuz, Williams, Alkofer, 3] decay constants e.g. [Maris, Roberts, Tandy, 97], [MM, Pawlowski, Strodthoff, in prep.] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 3 /

8 QCD from the effective action (gauge fixing necessary). Γ[Φ] = n {p i } Γ(n) Φ Φ n (p,..., p n )Φ (p ) Φ n ( p p n ) full information about QFT encoded in Γ[Φ]/correlators: bound state spectrum: pole structure of the Γ (n) e.g. [Roberts, Williams, 94], [Alkofer, Smekal, ], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, 6] form factors: photon-particle correlators e.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, 8], [Sanchis-Alepuz, Williams, Alkofer, 3] decay constants e.g. [Maris, Roberts, Tandy, 97], [MM, Pawlowski, Strodthoff, in prep.] thermodynamic quantities: Γ[Φ] grand potential equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, 3] fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, 6] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 3 /

9 QCD from the effective action (gauge fixing necessary). Γ[Φ] = n {p i } Γ(n) Φ Φ n (p,..., p n )Φ (p ) Φ n ( p p n ) full information about QFT encoded in Γ[Φ]/correlators: bound state spectrum: pole structure of the Γ (n) e.g. [Roberts, Williams, 94], [Alkofer, Smekal, ], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, 6] form factors: photon-particle correlators e.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, 8], [Sanchis-Alepuz, Williams, Alkofer, 3] decay constants e.g. [Maris, Roberts, Tandy, 97], [MM, Pawlowski, Strodthoff, in prep.] thermodynamic quantities: Γ[Φ] grand potential equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, 3] fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, 6] further quantities: Γ[Φ] eff. potential, propagators, t Hooft determinant chiral condensate(s)/ σ (dressed) Polyakov loop e.g. [Schaefer, Wambach 4], [Fischer, Luecker, Mueller ], [MM, Schaefer, 3] e.g. [Fischer, 9], [Braun, Haas, Marhauser, Pawlowski, 9], [MM, et al., 7] axial anomaly e.g.[grahl, Rischke, 3], [MM, Schaefer, 3], [Fejos, 5], [Heller, MM, 5] spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, 4] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 3 /

10 e.g. Debye mass in SU(3) YM theory [Cyrol, MM, Pawlowski, Strodthoff, 7] correlators from Functional Renormalisation Group (FRG) screening mass: fit to exponential decay of chromo-electric gluon propagator m S/T FRG first order HTL second order HTL, cp = second order HTL, cp = T [GeV] ms [GeV] T [GeV] excellent agreement with nd -order HTL perturbation theory for T.6 GeV smooth transition to nonperturbative regime M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 4 /

11 e.g. Center symmetry order parameters [MM, Hopfer, Schaefer, Alkofer, 7] quenched (scalar) Quantum Chromodynamics correlators from Dyson-Schwinger equation (DSE) lattice gluon input and vertex models Σ(T)/Σ(T=77 MeV) m=.5 GeV, d =.53 m=. GeV, d =.53 m=.5 GeV, d = T [MeV] q π from scalar propagator: dϕt n D ϕ( p =, ω n(ϕ)) from quark propagator: π dϕt n [ 4 tr D S(, ω n(ϕ)) ] cf. e.g. [Fischer 9], [Braun, Haas, Marhauser, Pawlowski, 9],... M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 5 /

12 e.g. EOS and axial anomaly in QCD-enhanced models equation of state N f = + PQM model with FRG unquenched Polyakov-loop potential from [Braun, Haas, Marhauser, Pawlowski, ] η -meson screening mass N f = PQM model, extended MF running t Hooft determinant from [MM, Pawlowski, Strodthoff, 4] (ε - 3P)/T Wuppertal-Budapest, HotQCD N t =8, HotQCD N t =, PQM FRG PQM emf PQM MF t m/[mev] m η m ηpqm m σpqm m πpqm T/[MeV] [Herbst, MM, Pawlowski, Schaefer, Stiele, 3] [Haas, Stiele, Braun, Pawlowski, Schaffner-Bielich, 3] [Heller, MM, 5]. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 6 /

13 e.g. EOS and axial anomaly in QCD-enhanced models equation of state N f = + PQM model with FRG unquenched Polyakov-loop potential from [Braun, Haas, Marhauser, Pawlowski, ] η -meson screening mass N f = PQM model, extended MF running t Hooft determinant from [MM, Pawlowski, Strodthoff, 4] (ε - 3P)/T Wuppertal-Budapest, HotQCD N t =8, HotQCD N t =, PQM FRG PQM emf PQM MF t m/[mev] m η m ηpqm m σpqm m πpqm T/[MeV] [Herbst, MM, Pawlowski, Schaefer, Stiele, 3] [Haas, Stiele, Braun, Pawlowski, Schaffner-Bielich, 3] [Heller, MM, 5]. phase diagrams e.g. [Schaefer, Wambach 4], [Fischer, Luecker, Mueller ], [MM, Schaefer, 3] spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, 4] fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, 6] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 6 /

14 Nonperturbative QCD two crucial phenomena: SχSB and confinement very sensitive to small quantitative errors similar scales - hard to disentangle M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 7 /

15 Nonperturbative QCD two crucial phenomena: SχSB and confinement very sensitive to small quantitative errors similar scales - hard to disentangle crawling towards QCD at finite density: quenched matter part [MM, Strodthoff, Pawlowski, 4] pure SU(N) YM-theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, 6] N f = QCD [Cyrol, MM, Strodthoff, Pawlowski, 7] YM-theory at finite temperature T > [Cyrol, MM, Strodthoff, Pawlowski, 7] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 7 /

16 Nonperturbative QCD two crucial phenomena: SχSB and confinement very sensitive to small quantitative errors similar scales - hard to disentangle crawling towards QCD at finite density: quenched matter part [MM, Strodthoff, Pawlowski, 4] pure SU(N) YM-theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, 6] N f = QCD [Cyrol, MM, Strodthoff, Pawlowski, 7] YM-theory at finite temperature T > [Cyrol, MM, Strodthoff, Pawlowski, 7] use results from lattice gauge theory to check truncation: what do we need from the lattice? M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 7 /

17 (Euclidean) Correlation functions with the FRG S[Φ] = Γ Λ [Φ]: use only perturbative QCD input αs (Λ = O() GeV) mq (Λ = O() GeV) M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 8 /

18 (Euclidean) Correlation functions with the FRG S[Φ] = Γ Λ [Φ]: use only perturbative QCD input αs (Λ = O() GeV) mq (Λ = O() GeV) integration of momentum shells: k Γ k [A, c, c, q, q] = M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 8 /

19 (Euclidean) Correlation functions with the FRG S[Φ] = Γ Λ [Φ]: use only perturbative QCD input αs (Λ = O() GeV) mq (Λ = O() GeV) integration of momentum shells: k Γ k [A, c, c, q, q] = full non-perturbative quantum effective action M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 8 /

20 (Euclidean) Correlation functions with the FRG S[Φ] = Γ Λ [Φ]: use only perturbative QCD input αs (Λ = O() GeV) mq (Λ = O() GeV) integration of momentum shells: k Γ k [A, c, c, q, q] = full non-perturbative quantum effective action gauge-fixed approach (Landau gauge): ghosts appear M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 8 /

21 (Euclidean) Correlation functions with the FRG S[Φ] = Γ Λ [Φ]: use only perturbative QCD input αs (Λ = O() GeV) mq (Λ = O() GeV) integration of momentum shells: k Γ k [A, c, c, q, q] = full non-perturbative quantum effective action gauge-fixed approach (Landau gauge): ghosts appear functional derivatives equations for correlators aim for apparent convergence of Γ[Φ] = lim k Γ k [Φ] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 8 /

22 Mesons via dynamical hadronization [Gies, Wetterich, ] change of variables: particular 4-Fermi channels meson exchange efficient inclusion of pole structure no spurious singularities low-energy effective model parameters from QCD - range of validity k Γ k = + M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 9 /

23 Mesons via dynamical hadronization [Gies, Wetterich, ] change of variables: particular 4-Fermi channels meson exchange efficient inclusion of pole structure no spurious singularities low-energy effective model parameters from QCD - range of validity k Γ k = + (bosonized) 4-fermi-interaction h π /( m π ) λ π. RG-scale k [GeV] Yukawa interaction h π RG-scale k [GeV] [MM, Strodthoff, Pawlowski, 4] [Braun, Fister, Haas, Pawlowski, Rennecke, 4] [MM, Strodthoff, Pawlowski, 4] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 9 /

24 N f = Landau-gauge QCD [Cyrol, MM, Pawlowski, Strodthoff, 7] Truncation: systematics of improving the truncation? M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

25 N f = Landau-gauge QCD [Cyrol, MM, Pawlowski, Strodthoff, 7] Truncation: systematics of improving the truncation? BRST-invariant operators, e.g. ψ /D n ψ M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

26 Some representative equations (numerics-heavy) [MM, Strodthoff, Pawlowski, 4], [Cyrol, Fister, MM, Strodthoff, Pawlowski, 6] cf. FormTracer [Cyrol, MM, Strodthoff, 6] t = t = + + perm. t = + perm. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

27 Some representative equations (numerics-heavy) [MM, Strodthoff, Pawlowski, 4], [Cyrol, Fister, MM, Strodthoff, Pawlowski, 6] t = + cf. FormTracer [Cyrol, MM, Strodthoff, 6] t = + t = t = + perm. t = t = + + perm. + + perm. t = + + perm. t = + perm. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

28 Some representative equations (numerics-heavy) [MM, Strodthoff, Pawlowski, 4], [Cyrol, Fister, MM, Strodthoff, Pawlowski, 6] t = + cf. FormTracer [Cyrol, MM, Strodthoff, 6] t = + t = t = + perm. t = t = + + perm. + + perm. t = + + perm. t = t = perm. t = + + perm. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

29 Chiral symmetry breaking χsb resonance in 4-Fermi interaction λ (pion pole): M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

30 Chiral symmetry breaking χsb resonance in 4-Fermi interaction λ (pion pole): β-function of momentum independent 4-Fermi interaction: t λ = λ + a λ + b λ α + c α, b >, a, c t = +... t λ g = g =, T > g = g cr λ g > g cr [Braun, ] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

31 (transverse) running couplings [Cyrol, MM, Pawlowski, Strodthoff, 7].5 m π =47 MeV. A 3 A 4 -. running couplings.5 α c - ca α A 3 α A 4 α q - qa α cr.5. p [GeV] agreement in perturbative regime required by Slavnov-Taylor identities non-degenerate in nonperturbative regime: reflects gluon mass gap α qaq > α cr : necessary for chiral symmetry breaking area above α cr very sensitive to errors use STI in perturbative regime M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 3 /

32 Quark propagator [Cyrol, MM, Pawlowski, Strodthoff, 7] Γ qq (p) = Z q (p) ( /p + M(p) ) quark propagator dressings error estimate m π =4 MeV m π =6 MeV m π =85 MeV lattice, β=5., m π =8 MeV lattice, β=5.9, m π =95 MeV. p [GeV] SχSB: M q() M q(p Λ QCD ) FRG vs. lattice: bare mass, scale setting, lattice Z q? very sensitive to qqa-interaction, relative scales lattice data: O. Oliveira, A. Kzlersu, P. J. Silva, J.-I. Skullerud, A. Sternbeck, A. G. Williams, arxiv: [hep-lat]. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 4 /

33 Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 7] quark-gluon interaction most crucial for chiral symmetry breaking transverse tensor basis (8 tensors), e.g. γ µ, i ( /p + /q ) γ µ [, p, / /q ] γ µ λ (i) (p, q) λ (i) (p, q, p q) M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 5 /

34 Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 7] quark-gluon interaction most crucial for chiral symmetry breaking transverse tensor basis (8 tensors), e.g. γ µ, i ( /p + /q ) γ µ [, p, / /q ] γ µ λ (i) (p, q) λ (i) (p, q, p q) quark-gluon vertex dressings lattice, λ () q -, β=5.9, m qα π =95 MeV lattice, λ () q -, β=5., m qα π =8 MeV λ (4) q -, m qα π =85 3 λ (7) q - qα, m π =85 λ () q - qα, m π =85 error estimate leading tensors: classical tensor: constrained by STI at large momenta chirally symmetric break chiral symmetry - m π =4 MeV systematic lattice error?. p [GeV] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 5 /

35 Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 7] quark-gluon interaction most crucial for chiral symmetry breaking transverse tensor basis (8 tensors), e.g. γ µ, i ( /p + /q ) γ µ [, p, / /q ] γ µ λ (i) (p, q) λ (i) (p, q, p q) quark-gluon vertex dressings lattice, λ () q -, β=5.9, m qα π =95 MeV lattice, λ () q -, β=5., m qα π =8 MeV λ (4) q -, m qα π =85 3 λ (7) q - qα, m π =85 λ () q - qα, m π =85 error estimate leading tensors: classical tensor: constrained by STI at large momenta chirally symmetric break chiral symmetry - m π =4 MeV systematic lattice error?. p [GeV] chirally symmetric tensors from operator q /D 3 q worsen result counteracted by tensor structures in Γ (4) AA qq and Γ(5) A 3 qq from q /D 3 q M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 5 /

36 Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 7] quark-gluon interaction most crucial for chiral symmetry breaking transverse tensor basis (8 tensors), e.g. γ µ, i ( /p + /q ) γ µ [, p, / /q ] γ µ λ (i) (p, q) λ (i) (p, q, p q) quark-gluon vertex dressings lattice, λ () q -, β=5.9, m qα π =95 MeV lattice, λ () q -, β=5., m qα π =8 MeV λ (4) q -, m qα π =85 3 λ (7) q - qα, m π =85 λ () q - qα, m π =85 error estimate leading tensors: classical tensor: constrained by STI at large momenta chirally symmetric break chiral symmetry - m π =4 MeV systematic lattice error?. p [GeV] chirally symmetric tensors from operator q /D 3 q worsen result counteracted by tensor structures in Γ (4) AA qq and Γ(5) A 3 qq from q /D 3 q expansion in BRST-invariant operators improves convergence? lattice data: O. Oliveira, A. Kzlersu, P. J. Silva, J.-I. Skullerud, A. Sternbeck, A. G. Williams, arxiv: [hep-lat]. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 5 /

37 Gluon propagator [Cyrol, MM, Pawlowski, Strodthoff, 7] Γ AA (p) = Z A (p) p ( δ µν p µ p ν /p ) 3 gluon propagator dressing /Z A.5.5 error estimate m π =4 MeV m π =6 MeV.5 m π =85 MeV lattice, β=5.9, m π =5 MeV. p [GeV] infrared suppression confinement smooth transition to pert. theory insensitive to pion mass scaling solution: lattice comparison? lattice data: A. Sternbeck, K. Maltman, M. Müller-Preussker, L. von Smekal, PoS LATTICE () 43. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 6 /

38 More correlators [Cyrol, MM, Pawlowski, Strodthoff, 7] antiquark momentum p [GeV] λ () four-fermi vertex dressings p λ (V-A) q - q - qq p λ (S+P) - adj q - q - qq p λ (η ) q - q - qq p λ (S-P) - q - q - qq p λ (V-A)adj q - q - qq p λ (V+A) q - q - qq p λ (S+P) + adj q - q - qq p λ (S+P) + q - q - qq p λ (S-P) - adj q - q - qq m π =4 MeV gluon momentum k [GeV] p [GeV] Yukawa interaction dressings h () q - qπ p*h () q - qπ p*h (3) q - qπ p h (4) q - qπ m π =4 MeV -quark--gluon vertex dressings p λ () q - qα p λ () q - qα p λ (3) q - qα p λ (4) q - qα m π =4 MeV p λ (5) q - qα p λ (6) q - qα.. p [GeV] p [GeV] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 7 /

39 Pure SU(N) YM-theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, 6] [Cyrol, MM, Pawlowski, Strodthoff, 7] Truncation (blue: magnetic (transverse) leg, red: electric (longitudinal) leg): /Z c ( p) λ M cca ( p) λm A 3 ( p) λ M A 4 ( p) /Z M A ( p) /Z E A ( p) λe A 3 ( p) λ E A 4 ( p) M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 8 /

40 Vacuum [Cyrol, Fister, MM, Pawlowski, Strodthoff, 6] truncation: momentum dependent dressing functions for all classical tensors hardest part of solution: fulfilling the modified STI ( scaling solution) M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 9 /

41 Vacuum [Cyrol, Fister, MM, Pawlowski, Strodthoff, 6] truncation: momentum dependent dressing functions for all classical tensors hardest part of solution: fulfilling the modified STI ( scaling solution) Γ () AA (p) Z A(p) p ( δ µν p µ p ν /p ) IR-suppression confinement smooth transition to perturbation theory running couplings degeneracy at large p due to STI test of truncation gluon propagator dressing 3 FRG, scaling FRG, decoupling Sternbeck et al. running couplings α Acc α A 3 α A 4. p [GeV]. p [GeV] lattice data: A. Sternbeck, E. M. Ilgenfritz, M. Muller-Preussker, A. Schiller, and I. L. Bogolubsky, PoS LAT6, 76. M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 9 /

42 Propagators at T 6= [Cyrol, MM, Pawlowski, Strodthoff, 7] Zeroth mode correlation functions T= T =.45 T =.93 T =.98 T =. T =. T =.8 magnetic gluon propagator dressing magnetic gluon propagator dressing T= T =.45 T =.98 T =. T =.7 T =.36 T =.8..5 p [GeV] p [GeV] SU() SU(3) M. Mitter (BNL) Correlators of QCD 5 Frankfurt, October 7 /

43 Propagators at T 6= [Cyrol, MM, Pawlowski, Strodthoff, 7] Zeroth mode correlation functions 5 T= T =.45 T =.93 T =.98 T =. T =. T = magnetic gluon propagator dressing magnetic gluon propagator dressing p [GeV] SU() SU(3) 5 T= T =.45 T =.93 T =.98 T =. T =. T = electric gluon propagator dressing electric gluon propagator dressing 3 p [GeV] 4. T= T =.45 T =.98 T =. T =.7 T =.36 T = p [GeV] 4. 5 T= T =.45 T =.98 T =. T =.7 T =.36 T = p [GeV] lattice data: A. Maas, J. M. Pawlowski, L. von Smekal, D. Spielmann, Phys.Rev. D85 () (SU()) P. J. Silva, O. Oliveira, P. Bicudo, and N. Cardoso, Phys. Rev. D89, 7453 (4). (SU(3)) M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

44 Backgrounds, ghost and zero crossing [Cyrol, MM, Pawlowski, Strodthoff, 7] Ā important near T c, cf. [Herbst et al., 5] Kaczmarek et al. Huebner 6 L[ϕ] <L> ren+mult T [GeV] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

45 Backgrounds, ghost and zero crossing [Cyrol, MM, Pawlowski, Strodthoff, 7] Ā important near T c, cf. [Herbst et al., 5] magnetic zero crossing in 3g-vertex Kaczmarek et al. Huebner 6 L[ϕ] p [GeV].35.3 <L> ren+mult T [GeV] T [GeV] 3.. ghost propagator dressing.5..5 T = T =.45 T =.93 T =.98 T =. T =. T =.8 magnetic three-gluon vertex dressing T = T =.75 GeV T =.5 GeV T =. GeV T =.4 GeV T =.8 GeV..5 5 p [GeV] p [GeV] M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

46 Status and Outlook vacuum QCD QCD from α S (Λ = O() GeV) and m q (Λ = O() GeV) good agreement with lattice correlators more checks on convergence of vertex expansion M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

47 Status and Outlook vacuum QCD QCD from α S (Λ = O() GeV) and m q (Λ = O() GeV) good agreement with lattice correlators more checks on convergence of vertex expansion finite temperature YM-theory: good agreement with magnetic lattice correlators electric correlators: argued for importance of backgrounds near T c Debye mass consistent with HTL perturbation theory at T.6 GeV M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

48 Status and Outlook vacuum QCD QCD from α S (Λ = O() GeV) and m q (Λ = O() GeV) good agreement with lattice correlators more checks on convergence of vertex expansion finite temperature YM-theory: good agreement with magnetic lattice correlators electric correlators: argued for importance of backgrounds near T c Debye mass consistent with HTL perturbation theory at T.6 GeV next stop: T, µ > equation of state fluctuations of conserved charges order parameters M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

49 Status and Outlook vacuum QCD QCD from α S (Λ = O() GeV) and m q (Λ = O() GeV) good agreement with lattice correlators more checks on convergence of vertex expansion finite temperature YM-theory: good agreement with magnetic lattice correlators electric correlators: argued for importance of backgrounds near T c Debye mass consistent with HTL perturbation theory at T.6 GeV next stop: T, µ > equation of state fluctuations of conserved charges order parameters further applications: input for QCD-enhanced models other strongly-interacting theories M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 /

Chiral symmetry breaking in continuum QCD

Chiral symmetry breaking in continuum QCD Mario Mitter Ruprecht-Karls-Universität Heidelberg Trieste, September 206 M. Mitter (U Heidelberg) χsb in continuum QCD Trieste, September 206 / 20 fqcd collaboration