Chiral symmetry breaking in continuum QCD
|
|
|
- Blaise Alexander Ellis
- 5 years ago
- Views:
Transcription
1 Chiral symmetry breaking in continuum QCD Mario Mitter Ruprecht-Karls-Universität Heidelberg Graz, April 19, 2016 M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
2 fqcd collaboration - QCD (phase diagram) with FRG: J. Braun, A. K. Cyrol, L. Fister, W. J. Fu, T. K. Herbst, MM N. Müller, J. M. Pawlowski, S. Rechenberger, F. Rennecke, N. Strodthoff Temperature early universe LHC quark gluon plasma RHIC SPS <ψψ> 0 crossover FAIR/NICA <ψψ> = / 0 vacuum hadronic fluid n B= 0 n B> 0 AGS SIS nuclear matter µ quark matter crossover superfluid/superconducting 2SC phases? <ψψ> = / 0 CFL neutron star cores M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
3 Outline 1 Motivation 2 YM correlation functions 3 Matter part of Quenched Landau gauge QCD 4 A glimpse at unquenching 5 Phenomenological Application: η -meson mass at chiral crossover 6 Conclusion M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
4 QCD phase diagram with functional methods works well at µ = 0: agreement with lattice (ε - 3P)/T Wuppertal-Budapest, 2010 HotQCD N t =8, 2012 HotQCD N t =12, 2012 PQM FRG PQM emf PQM MF t [Herbst, MM, Pawlowski, Schaefer, Stiele, 13] Lattice set A set B l,s (T) / l,s (T=0) T [MeV] [Luecker, Fischer, Welzbacher, 2014] [Luecker, Fischer, Fister, Pawlowski, 13] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
5 QCD phase diagram with functional methods works well at µ = 0: agreement with lattice different results at large µ (possibly already at small µ) T [MeV] µb T =2 χ crossover σ(t=0)/2 Φ crossover Φ crossover χ 1st order CEP µb T = µ [MeV] m π =138 MeV [Herbst, Pawlowski, Schaefer, 2013] [Braun, Haas, Pawlowski, unpublished] µ B /T=2 µ B /T=3 T [MeV] Lattice: curvature range κ= DSE: chiral crossover DSE: critical end point DSE: deconfinement crossover µ q [MeV] [Luecker, Fischer, Fister, Pawlowski, 13] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
6 QCD phase diagram with functional methods works well at µ = 0: agreement with lattice different results at large µ (possibly already at small µ) calculations need model input: Polyakov-quark-meson model with FRG: inital values at Λ O(Λ QCD ) input for Polyakov loop potential quark propagator DSE: IR quark-gluon vertex T [MeV] µb T =2 χ crossover σ(t=0)/2 Φ crossover Φ crossover χ 1st order CEP µb T = µ [MeV] m π =138 MeV [Herbst, Pawlowski, Schaefer, 2013] [Braun, Haas, Pawlowski, unpublished] T [MeV] Lattice: curvature range κ= DSE: chiral crossover DSE: critical end point µ B /T=2 DSE: deconfinement crossover µ B /T= µ q [MeV] [Luecker, Fischer, Fister, Pawlowski, 13] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
7 QCD phase diagram with functional methods works well at µ = 0: agreement with lattice different results at large µ (possibly already at small µ) calculations need model input: Polyakov-quark-meson model with FRG: inital values at Λ O(Λ QCD ) input for Polyakov loop potential quark propagator DSE: IR quark-gluon vertex possible explanation for disagreement: µ 0: relative importance of diagrams changes summed contributions vs. individual contributions T [MeV] µb T =2 χ crossover σ(t=0)/2 Φ crossover Φ crossover χ 1st order CEP µb T = µ [MeV] m π =138 MeV [Herbst, Pawlowski, Schaefer, 2013] [Braun, Haas, Pawlowski, unpublished] T [MeV] Lattice: curvature range κ= DSE: chiral crossover DSE: critical end point µ B /T=2 DSE: deconfinement crossover µ B /T= µ q [MeV] [Luecker, Fischer, Fister, Pawlowski, 13] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
8 Back to QCD in the vacuum (Wetterich equation) use only perturbative QCD input: α S (Λ = O(10) GeV) (and m q (Λ)) M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
9 Back to QCD in the vacuum (Wetterich equation) use only perturbative QCD input: α S (Λ = O(10) GeV) (and m q (Λ)) Wetterich equation with initial condition S[Φ] = Γ Λ [Φ] k Γ k [A, c, c, q, q] = 1 2 effective action Γ[Φ] = lim k 0 Γ k [Φ] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
10 Back to QCD in the vacuum (Wetterich equation) use only perturbative QCD input: α S (Λ = O(10) GeV) (and m q (Λ)) Wetterich equation with initial condition S[Φ] = Γ Λ [Φ] k Γ k [A, c, c, q, q] = 1 2 effective action Γ[Φ] = lim k 0 Γ k [Φ] k : integration of momentum shells controlled by regulator full field-dependent equation with (Γ (2) k [Φ]) 1 on rhs M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
11 Back to QCD in the vacuum (Wetterich equation) use only perturbative QCD input: α S (Λ = O(10) GeV) (and m q (Λ)) Wetterich equation with initial condition S[Φ] = Γ Λ [Φ] k Γ k [A, c, c, q, q] = 1 2 effective action Γ[Φ] = lim k 0 Γ k [Φ] k : integration of momentum shells controlled by regulator full field-dependent equation with (Γ (2) k [Φ]) 1 on rhs gauge-fixed approach (Landau gauge): ghosts appear gauge invariance: Γ (k) fulfills (modified) Slavnov-Taylor identities M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
12 Vertex Expansion approximation necessary - vertex expansion Γ[Φ] = n p 1,...,p n 1 Γ (n) Φ 1 Φ n (p 1,..., p n 1 )Φ 1 (p 1 ) Φ n ( p 1 p n 1 ) M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
13 Vertex Expansion approximation necessary - vertex expansion Γ[Φ] = n p 1,...,p n 1 Γ (n) Φ 1 Φ n (p 1,..., p n 1 )Φ 1 (p 1 ) Φ n ( p 1 p n 1 ) functional derivatives with respect to Φ i = A, c, c, q, q: equations for 1PI n-point functions, e.g. gluon propagator: t 1 = M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
14 Vertex Expansion approximation necessary - vertex expansion Γ[Φ] = n p 1,...,p n 1 Γ (n) Φ 1 Φ n (p 1,..., p n 1 )Φ 1 (p 1 ) Φ n ( p 1 p n 1 ) functional derivatives with respect to Φ i = A, c, c, q, q: equations for 1PI n-point functions, e.g. gluon propagator: t 1 = want apparent convergence of Γ[Φ] = lim k 0 Γ k [Φ] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
15 Quenched Landau gauge QCD two crucial phenomena: SχSB and confinement similar scales - hard to disentangle see e.g. [Williams, Fischer, Heupel, 2015] quenched QCD: allows separate investigation: M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
16 Quenched Landau gauge QCD two crucial phenomena: SχSB and confinement similar scales - hard to disentangle see e.g. [Williams, Fischer, Heupel, 2015] quenched QCD: allows separate investigation: recent results in pure YM theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] matter part [MM, Strodthoff, Pawlowski, 2014] (with FRG-YM propagators from [Fischer, Maas, Pawlowski, 2009], [Fister, Pawlowski, unpublished]) M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
17 Vertex Expansion in YM theory [Cyrol, Fister, MM, Strodthoff, Pawlowski, to be published] full. mom. dep. full. mom. dep. sym. point and tadpole config. M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
18 Derivation of equations VertEXpand Mathematica package for the derivation of vertices from a given action using FORM (Denz,Held,Rodigast; unpub.) Vertices/ Vertices/ Feynman Feynman Rules Rules DoFun VertEXpand Action ERGE DoFun DoFun Mathematica package for the derivation of functional equations (Braun,Huber; Comput.Phys. Commun. 183 (2012) ) Symbolic Symbolic Flow Flow Equations Equations FORMTracer Algebraic Algebraic Flow Flow Equations Equations high-performance, easy-to-use Mathematica tracing tool using FORM (Cyrol,Mitter,Pawlowski,Strodthoff; in prep.) Compilable Compilable Kernels Kernels CreateKernels Mathematica package for the automatic generation of compilable C++ kernels for use in connection with the frgsolver (Cyrol,Mitter,Pawlowski,Strodthoff; unpub.) Numerical Numerical solution solution frgsolver Flexible, high-performance, parallelized C++ OOP framework for the numerical solution of functional equations (Cyrol,Mitter,Pawlowski,Strodthoff; unpub.) [Cyrol, MM, Pawlowski, Strodthoff, ] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
19 (Truncated) equations in YM theory [Cyrol, Fister, MM, Strodthoff, Pawlowski, to be published] t 1 = + t 1= t = + perm. t = perm. t = perm. M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
20 Results I [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] Γ (2) AA (p) Z A(p) p 2 ( δ µν p µ p ν /p 2) Γ (2) cc (p) Zc(p) p2 3 gluon propagator dressing 2 1 Sternbeck et al. ghost propagator dressing 10 1 Sternbeck et al p [GeV] p [GeV] band: family of decoupling solutions bounded by scaling solution M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
21 Results II [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] comparison to Maas, unpublished Huber, von Smekal 12 (black lines) running couplings α gh-gl α 3g α 4g ghost-gluon vertex dressing FRG, scaling FRG, decoupling DSE, scaling DSE, decoupling p [GeV] p [GeV] band: family of decoupling solutions bounded by scaling solution M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
22 Results III [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] comparison to Maas unpublished comparison to Maas unpublished Blum, Huber, MM, von Smekal 14 (black lines) Cyrol, Huber, von Smekal 14 (black lines) three-gluon vertex dressing FRG, scaling FRG, decoupling DSE, scaling DSE, decoupling four-gluon vertex dressing 10 1 FRG, scaling FRG, decoupling DSE, scaling DSE, decoupling p [GeV] p [GeV] band: family of decoupling solutions bounded by scaling solution M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
23 Apparent Convergence [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] gluon propagator dressing RG scale dep. 1D mom. dep. 3D mom. dep p [GeV] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
24 Gluon mass gap [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] confinement in linearly covariant gauges gluon mass gap [Braun, Gies, Pawlowski, 2010] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
25 Gluon mass gap [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] confinement in linearly covariant gauges gluon mass gap Γ (2) AA (p) Π T (p) Z A (p) p 2 + Π L (p) Z A,L (p) p 2 Π T (p) = ( δ µν p µ p ν /p 2), Π L (p) = p µ p ν /p 2 [Braun, Gies, Pawlowski, 2010] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
26 Gluon mass gap [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] confinement in linearly covariant gauges gluon mass gap Γ (2) AA (p) Π T (p) Z A (p) p 2 + Π L (p) Z A,L (p) p 2 Π T (p) = ( δ µν p µ p ν /p 2), Π L (p) = p µ p ν /p 2 [Braun, Gies, Pawlowski, 2010] Slavnov-Taylor id. (lin. cov. gauge): no quantum corrections to Z A,L M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
27 Gluon mass gap [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] confinement in linearly covariant gauges gluon mass gap Γ (2) AA (p) Π T (p) Z A (p) p 2 + Π L (p) Z A,L (p) p 2 Π T (p) = ( δ µν p µ p ν /p 2), Π L (p) = p µ p ν /p 2 [Braun, Gies, Pawlowski, 2010] Slavnov-Taylor id. (lin. cov. gauge): no quantum corrections to Z A,L infrared regular 1PI correlators: quantum corrections: lim qu Z A (p) p 2 = lim qu Z A,L (p) p 2 p 0 p 0 M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
28 Gluon mass gap [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] confinement in linearly covariant gauges gluon mass gap Γ (2) AA (p) Π T (p) Z A (p) p 2 + Π L (p) Z A,L (p) p 2 Π T (p) = ( δ µν p µ p ν /p 2), Π L (p) = p µ p ν /p 2 [Braun, Gies, Pawlowski, 2010] Slavnov-Taylor id. (lin. cov. gauge): no quantum corrections to Z A,L infrared regular 1PI correlators: quantum corrections: lim qu Z A (p) p 2 = lim qu Z A,L (p) p 2 p 0 p 0 no mass gap without infrared irregularities M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
29 Gluon mass gap [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] confinement in linearly covariant gauges gluon mass gap Γ (2) AA (p) Π T (p) Z A (p) p 2 + Π L (p) Z A,L (p) p 2 Π T (p) = ( δ µν p µ p ν /p 2), Π L (p) = p µ p ν /p 2 [Braun, Gies, Pawlowski, 2010] Slavnov-Taylor id. (lin. cov. gauge): no quantum corrections to Z A,L infrared regular 1PI correlators: quantum corrections: lim qu Z A (p) p 2 = lim qu Z A,L (p) p 2 p 0 p 0 no mass gap without infrared irregularities follows also from three-gluon vertex STI M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
30 Infrared irregularities [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] scaling solution: scaling singularity is sufficient! M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
31 Infrared irregularities [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] scaling solution: scaling singularity is sufficient! decoupling solution: irregularities cannot be diagrammatic (ghost is not enough) possibilities (longitudinal) massless modes: [Schwinger, 62], [Cornwall, 82], [Aguilar et. al, 11] Savvidy-Vacuum (gluon background): [Savvidy, 77], [Eichhorn, Gies, Pawlowski, 11] both at the same time... M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
32 Infrared irregularities [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] scaling solution: scaling singularity is sufficient! decoupling solution: irregularities cannot be diagrammatic (ghost is not enough) possibilities (longitudinal) massless modes: [Schwinger, 62], [Cornwall, 82], [Aguilar et. al, 11] Savvidy-Vacuum (gluon background): [Savvidy, 77], [Eichhorn, Gies, Pawlowski, 11] both at the same time... numerical finding: no transversal irregularities information from long. system necessary M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
33 Quadratic divergence and solution types [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] [ ] msti Γ (2) µν AA,k (p) = m 2 (k) δ µν m 2 (Λ UV ) α(λ UV ) Λ 2 UV quadratic divergence physical mass gap vs. quadratic divergence? M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
34 Quadratic divergence and solution types [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] [ ] msti Γ (2) µν AA,k (p) = m 2 (k) δ µν m 2 (Λ UV ) α(λ UV ) Λ 2 UV quadratic divergence physical mass gap vs. quadratic divergence? scaling solution determines m 2 (Λ UV ) uniquely M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
35 Quadratic divergence and solution types [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] [ ] msti Γ (2) µν AA,k (p) = m 2 (k) δ µν m 2 (Λ UV ) α(λ UV ) Λ 2 UV quadratic divergence physical mass gap vs. quadratic divergence? scaling solution determines m 2 (Λ UV ) uniquely variation of m 2 (Λ UV ) decoupling solutions STI-compatible? confining solutions? M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
36 Different solutions [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] 8 gluon propagator [GeV -2 ] confined phase Higgs phase ghost propagator dressing 10 1 confined phase Higgs phase p [GeV] p [GeV] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
37 confinement criteria [Cyrol, Fister, MM, Pawlowski, Strodthoff, to be published] gluon mass gap location of gluon propator maximum m 2 [GeV 2 ] 1 confined phase Higgs phase m 2 min m 2 Λ - m2 Λ,scaling [GeV2 ] position of gluon prop. max. [GeV] confined Higgs fit points fit m 2 c m 2 Λ - m2 Λ,scaling [GeV2 ] (m 2 Λ -m2 c )/m2 c M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
38 Chiral symmetry breaking χsb resonance in 4-Fermi interaction λ (pion pole): M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
39 Chiral symmetry breaking χsb resonance in 4-Fermi interaction λ (pion pole): resonance singularity without momentum dependency t λ = a λ 2 + b λ α + c α 2, b > 0, a, c 0 t = t λ g = 0 g = 0, T > 0 g = g cr λ g > g cr [Braun, 2011] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
40 Effective running couplings [MM, Pawlowski, Strodthoff, 2014] running couplings α s p [GeV] α crit α c - Ac α q - Aq α A 3 agreement in perturbative regime required by gauge symmetry 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 M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
41 4-Fermi vertex via dynamical hadronization [Gies, Wetterich, 2002] change of variables: particular 4-Fermi channels meson exchange efficient inclusion of momentum dependence no singularities identifies relevant effective low-energy dofs from QCD k Γ k = (bosonized) 4-fermi-interaction h 2 π /(2 m2 π ) λ π RG-scale k [GeV] Yukawa interaction h π RG-scale k [GeV] [MM, Strodthoff, Pawlowski, 2014] [Braun, Fister, Haas, Pawlowski, Rennecke, 2014] [MM, Strodthoff, Pawlowski, 2014] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
42 Vertex Expansion in the matter system -1 FRG Yang-Mills results -1 mom. dep. classical tensor structure mom. dep. classical tensor structure -1 full mom. dep. all tensor structures mom. dep. full mom. dep. STI-consistent dressing Fierz-complete basis at p = 0 and mom. dep. -1 mom. dep. full effective... potential mom. dep. M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
43 Equations in the matter system [MM, Strodthoff, Pawlowski, 2014] 1 t = t = perm. t = 2 + perm. M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
44 Equations in the matter system [MM, Strodthoff, Pawlowski, 2014] t = perm. 1 t = t = + perm. + + t = perm. t = 2 + perm. M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
45 Equations in the matter system [MM, Strodthoff, Pawlowski, 2014] t = perm. 1 t = t = + perm. + + t = perm. t = 2 + perm. 1 t = t = perm. M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
46 Gluon FRG input Γ (2) AA (p) Z A(p) p 2 ( δ µν p µ p ν /p 2) [Fischer, Maas, Pawlowski, 2009], [Fister, Pawlowski, unpublished] gluon propagator dressing 1/Z A Bowman et al., 04 Sternbeck et al., p [GeV] FRG FRG result self-consistent calculation within FRG approach sets the scale in comparison to lattice QCD M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
47 Quark propagator [MM, Pawlowski, Strodthoff, 2014] Γ (2) qq (p) Z q(p) ( /p + M(p) ) quark propagator dressings Bowman et al., 05 1/Z q M q p [GeV] FRG vs. lattice: bare mass, quenched, scale M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
48 Quark propagator [MM, Pawlowski, Strodthoff, 2014] Γ (2) qq (p) Z q(p) ( /p + M(p) ) quark propagator dressings Bowman et al., 05 1/Z q M q p [GeV] FRG vs. lattice: bare mass, quenched, scale agreement not sufficient: need apparent convergence at µ 0 M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
49 other 4-Fermi channels (mesons) [MM, Pawlowski, Strodthoff, 2014] (bosonized) 4-fermi-interactions RG-scale k [GeV] h 2 π /(2 m2 π ) λ η λ (S+P)- adj λ V-A λ V+A λ (V-A) adj λ (S-P)- λ(s-p)- adj λ (S+P)+ λ(s+p)+ adj bosonized only σ-π-channel sufficient diquark momentum configuration more important other channels: quantitatively not important in loops M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
50 Quark-gluon interactions I [MM, Pawlowski, Strodthoff, 2014] quark-gluon interaction most crucial for chiral symmetry breaking full tensor basis sufficient chiral symmetry breaking strength? M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
51 Quark-gluon interactions I [MM, Pawlowski, Strodthoff, 2014] quark-gluon interaction most crucial for chiral symmetry breaking full tensor basis sufficient chiral symmetry breaking strength? 2 (1) z q - Aq (4) z q - Aq quark-gluon couplings (7) z q - Aq (5) z q - Aq (6) z q - Aq (2) z q - Aq (3) z q - Aq (8) z q - Aq vertex strength: reflects gluon gap 8 tensors (transversally projected): classical tensor chirally symmetric break chiral symmetry p [GeV] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
52 Quark-gluon interactions I [MM, Pawlowski, Strodthoff, 2014] quark-gluon interaction most crucial for chiral symmetry breaking full tensor basis sufficient chiral symmetry breaking strength? 2 (1) z q - Aq (4) z q - Aq quark-gluon couplings (7) z q - Aq (5) z q - Aq (6) z q - Aq (2) z q - Aq (3) z q - Aq (8) z q - Aq vertex strength: reflects gluon gap 8 tensors (transversally projected): classical tensor chirally symmetric break chiral symmetry p [GeV] important non-classical tensors: c.f., [Hopfer et al., 2012], [Williams, 2014], [Aguilar et al., 2014] qγ 5 γ µɛ µνρσ{f νρ, D σ}q ( 1 2 T (5) qaq + T (7) qaq ): increases Zq/decreases Mq considerably anom. chromomagn. momentum (T (4) qaq ) increases Mq moderately M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
53 Quark-gluon interactions I [MM, Pawlowski, Strodthoff, 2014] quark-gluon interaction most crucial for chiral symmetry breaking full tensor basis sufficient chiral symmetry breaking strength? 2 (1) z q - Aq (4) z q - Aq quark-gluon couplings (7) z q - Aq (5) z q - Aq (6) z q - Aq (2) z q - Aq (3) z q - Aq (8) z q - Aq vertex strength: reflects gluon gap 8 tensors (transversally projected): classical tensor chirally symmetric break chiral symmetry p [GeV] important non-classical tensors: c.f., [Hopfer et al., 2012], [Williams, 2014], [Aguilar et al., 2014] qγ 5 γ µɛ µνρσ{f νρ, D σ}q ( 1 2 T (5) qaq + T (7) qaq ): increases Zq/decreases Mq considerably anom. chromomagn. momentum (T (4) qaq ) increases Mq moderately considerably less chiral symmetry breaking with full tensor basis M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
54 Quark-gluon interactions I [MM, Pawlowski, Strodthoff, 2014] quark-gluon interaction most crucial for chiral symmetry breaking full tensor basis sufficient chiral symmetry breaking strength? 2 (1) z q - Aq (4) z q - Aq quark-gluon couplings (7) z q - Aq (5) z q - Aq (6) z q - Aq (2) z q - Aq (3) z q - Aq (8) z q - Aq vertex strength: reflects gluon gap 8 tensors (transversally projected): classical tensor chirally symmetric break chiral symmetry p [GeV] important non-classical tensors: c.f., [Hopfer et al., 2012], [Williams, 2014], [Aguilar et al., 2014] qγ 5 γ µɛ µνρσ{f νρ, D σ}q ( 1 2 T (5) qaq + T (7) qaq ): increases Zq/decreases Mq considerably anom. chromomagn. momentum (T (4) qaq ) increases Mq moderately considerably less chiral symmetry breaking with full tensor basis also important ingredient for bound-state equations M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
55 Quark-gluon interactions II missing strength? M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
56 Quark-gluon interactions II missing strength? expansion in tensor structures expansion in operators ψ /D n ψ [MM, Pawlowski, Strodthoff, 2014] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
57 Quark-gluon interactions II missing strength? expansion in tensor structures expansion in operators ψ /D n ψ [MM, Pawlowski, Strodthoff, 2014] in particular qγ 5 γ µ ɛ µνρσ {F νρ, D σ }q: contributes to qaq, qa 2 q and qa 3 q contains important non-classical tensors ( qaq) considerable contribution to quark-gluon vertex ( qa 2 q) contribution to qa 3 q seems unimportant M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
58 Quark-gluon interactions II missing strength? expansion in tensor structures expansion in operators ψ /D n ψ [MM, Pawlowski, Strodthoff, 2014] in particular qγ 5 γ µ ɛ µνρσ {F νρ, D σ }q: contributes to qaq, qa 2 q and qa 3 q contains important non-classical tensors ( qaq) considerable contribution to quark-gluon vertex ( qa 2 q) contribution to qa 3 q seems unimportant M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
59 Quark-gluon interactions II missing strength? expansion in tensor structures expansion in operators ψ /D n ψ [MM, Pawlowski, Strodthoff, 2014] in particular qγ 5 γ µ ɛ µνρσ {F νρ, D σ }q: contributes to qaq, qa 2 q and qa 3 q contains important non-classical tensors ( qaq) considerable contribution to quark-gluon vertex ( qa 2 q) contribution to qa 3 q seems unimportant explicit calculations of AA qq-vertex: full basis: 63 chirally symmetric tensor elements 3 15 chirally symmetric tensor elements ( ψ /D ψ): all seem important order of effect similar to qγ 5γ µɛ µνρσ{f νρ, D σ}q why? underlying principle? [MM, Pawlowski, Strodthoff, in prep.] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
60 Stability of truncation (apparent convergence) Expansion of effective action in 1PI correlators full mom. dep. classical tensor structure mom. dep. (sym. channel) under investigation: full tensor structure mom. dep. (sym. channel) full tensor structure full mom. dep. partial tensor structure mom. dep. (sym. channel) full tensor structure mom. dep. (single channel) full mom. dep. via effective potential full tensor structure mom. dep. (sym. channel) M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
61 Outlook: unquenched gluon propagator gluon propagator dressing 1/Z A Sternbeck et al., 2012 FRG p [GeV] self-consistent solution of classical propagators and vertices (1D) massless quarks [Cyrol, MM, Pawlowski, Strodthoff, in preparation] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
62 η -meson (screening) mass at chiral crossover small η -meson mass above chiral crossover? [Kapusta, Kharzeev, McLerran, 1998]?drop in η mass at chiral crossover? [Csörgo et al., 2010] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
63 η -meson (screening) mass at chiral crossover small η -meson mass above chiral crossover? [Kapusta, Kharzeev, McLerran, 1998]?drop in η mass at chiral crossover? [Csörgo et al., 2010] chiral crossover: Polyakov-Quark-Meson model (extended mean-field) [1] <σ>/f πφ N f = 2 quark and meson degrees of freedom describes chiral crossover (de-)confinement via Polyakov loop potential T/[MeV] U(1) A -anomaly: mesonic t Hooft determinant M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
64 η -meson (screening) mass at chiral crossover small η -meson mass above chiral crossover? [Kapusta, Kharzeev, McLerran, 1998]?drop in η mass at chiral crossover? [Csörgo et al., 2010] chiral crossover: Polyakov-Quark-Meson model (extended mean-field) [1] <σ>/f πφ N f = 2 quark and meson degrees of freedom describes chiral crossover (de-)confinement via Polyakov loop potential U(1) A -anomaly: mesonic t Hooft determinant T/[MeV] t Hooft determinant [Heller, MM, 2015] λ (S-P)+ [MeV] RG-scale dependence from fqcd temperature dependence k(t ): λ (S P)+,fQCD(k) λ (S P)+,PQM(T ) k/[mev] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
65 η -meson (screening) mass at chiral crossover: result 1200 Masses as function of temperature with Polyakov-Loop m π m η screening masses! m σ m/[mev] T/[MeV] [Heller, MM, 2015] M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
66 η -meson (screening) mass at chiral crossover: result 1200 Masses as function of temperature with Polyakov-Loop m π m η m σ screening masses! QM-Model N f = 2 + 1: π σ a 0 η η m/[mev] masses [MeV] T [MeV] [MM, Schaefer, 2013] T/[MeV] [Heller, MM, 2015] chiral symmetry restoration: drop in m η M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
67 Summary and Outlook (quenched) QCD with functional RG QCD phase diagram: need for quantitative precision vacuum: sole input αs (Λ = O(10) GeV) and m q (Λ = O(10) GeV) good agreement with lattice simulations (sufficient?) (non-perturbative) results: YM-system quark-propagator quark-gluon vertex 4-Fermi interaction channels phenomenology: η -meson and pion mass splitting M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
68 Summary and Outlook (quenched) QCD with functional RG QCD phase diagram: need for quantitative precision vacuum: sole input αs (Λ = O(10) GeV) and m q (Λ = O(10) GeV) good agreement with lattice simulations (sufficient?) (non-perturbative) results: YM-system quark-propagator quark-gluon vertex 4-Fermi interaction channels phenomenology: η -meson and pion mass splitting unquenching (first results) finite temperature/chemical potential more checks on convergence of vertex expansion bound-state properties (form factor,pda... ) M. Mitter (U Heidelberg) χsb in continuum QCD Graz, April 19, / 34
Chiral symmetry breaking in continuum QCD
Chiral symmetry breaking in continuum QCD Mario Mitter Ruprecht-Karls-Universität Heidelberg GSI, February 9, 216 M. Mitter (U Heidelberg) χsb in continuum QCD GSI, February 216 1 / 29 fqcd collaboration
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
QCD phase structure from the functional RG
QCD phase structure from the functional RG Mario Mitter Ruprecht-Karls-Universität Heidelberg Dubna, November 216 M. Mitter (U Heidelberg) QCD phase structure from the frg Dubna, November 216 1 / 23 fqcd
QCD from quark, gluon, and meson correlators
QCD from quark, gluon, and meson correlators Mario Mitter Brookhaven National Laboratory Frankfurt, October 7 M. Mitter (BNL) Correlators of QCD Frankfurt, October 7 / fqcd collaboration - QCD (phase diagram)
QCD Phases with Functional Methods
QCD Phases with Mario PhD-Advisors: Bernd-Jochen Schaefer Reinhard Alkofer Karl-Franzens-Universität Graz Institut für Physik Fachbereich Theoretische Physik Rab, September 2010 QCD Phases with Table of
On the role of fluctuations in (2+1)-flavor QCD
On the role of fluctuations in (2+1)-flavor QCD Bernd-Jochen Schaefer Germany Germany November 29 th, 217 Conjectured QC3D phase diagram Temperature early universe LHC crossover vacuum RHIC SPS =
Functional renormalization group approach of QCD and its application in RHIC physics
Functional renormalization group approach of QCD and its application in RHIC physics Wei-jie Fu Dalian University of Technology wjfu@dlut.edu.cn The Third Symposium on Theoretical Physics at Peking U.
On bound states in gauge theories with different matter content
On bound states in gauge theories with different matter content Reinhard Alkofer Institute of Physics, Department of Theoretical Physics, University of Graz Bound states in QCD and beyond St. Goar, March
t Hooft Determinant at Finite Temperature with Fluctuations
t Hooft Determinant at Finite Temperature with Fluctuations Mario Mitter In collaboration with: Bernd-Jochen Schaefer, Nils Strodthoff, Lorenz von Smekal (former) PhD Advisers: Reinhard Alkofer, Bernd-Jochen
Yang-Mills Propagators in Landau Gauge at Non-Vanishing Temperature
Yang-Mills Propagators in Landau Gauge at Non-Vanishing Temperature Leonard Fister, Jan M. Pawlowski, Universität Heidelberg... work in progress ERG Corfu - September 2 Motivation ultimate goal: computation
Can we locate the QCD critical endpoint with a Taylor expansion?
Can we locate the QCD critical endpoint with a Taylor expansion? Bernd-Jochen Schaefer Karl-Franzens-Universität Graz, Austria 7 th February - 6 th March, 1 48. Internationale Universitätswochen für Theoretische
On the Landau gauge three-gluon vertex
On the Landau gauge three-gluon vertex M. Vujinovic, G. Eichmann, R. Williams, R. Alkofer Karl Franzens University, Graz PhD Seminar talk Graz, Austria, 13.11.2013. M. Vujinovic et al. (KFU, Graz) On the
Aspects of Two- and Three-Flavor Chiral Phase Transitions
Aspects of Two- and Three-Flavor Chiral Phase Transitions Mario Karl-Franzens-Universität Graz Institut für Physik Fachbereich Theoretische Physik Kyoto, September 6, 211 Table of Contents 1 Motivation
The Phase Structure of the Polyakov Quark-Meson Model beyond Mean Field
The Phase Structure of the Polyakov Quark-Meson Model beyond Mean Field Tina Katharina Herbst In Collaboration with B.-J. Schaefer and J.M. Pawlowski arxiv: 18.81 [hep-ph] (to appear in Phys. Lett. B)
With the FRG towards the QCD Phase diagram
With the FRG towards the QCD Phase diagram Bernd-Jochen Schaefer University of Graz, Austria RG Approach from Ultra Cold Atoms to the Hot QGP 22 nd Aug - 9 th Sept, 211 Helmholtz Alliance Extremes of Density
The Role of the Quark-Gluon Vertex in the QCD Phase Transition
The Role of the Quark-Gluon Vertex in the QCD Phase Transition PhD Seminar, 05.12.2012 Markus Hopfer University of Graz (A. Windisch, R. Alkofer) Outline 1 Motivation A Physical Motivation Calculations
Recent results for propagators and vertices of Yang-Mills theory
Introduction Dyson-Schwinger equations Extending truncations Summary and conclusions Recent results for propagators and vertices of Yang-Mills theory Markus Q. Huber arxiv:1808.05227 Institute of Theoretical
From Quarks and Gluons to Hadrons: Functional RG studies of QCD at finite Temperature and chemical potential
From Quarks and Gluons to Hadrons: Functional RG studies of QCD at finite Temperature and chemical potential Jens Braun Theoretisch-Physikalisches Institut Friedrich-Schiller Universität Jena Quarks, Hadrons
Bethe Salpeter studies of mesons beyond rainbow-ladder
Bethe Salpeter studies of mesons beyond rainbow-ladder Richard Williams 1 st June 2010 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon College of William and Mary,
Baryon number fluctuations within the functional renormalization group approach
Baryon number fluctuations within the functional renormalization group approach Wei-jie Fu Dalian University of Technology wjfu@dlut.edu.cn The Third Symposium on Chiral Effective Field Theory, Oct. 28-Nov.
The phase diagram of two flavour QCD
The phase diagram of two flavour QCD Jan M. Pawlowski Universität Heidelberg & ExtreMe Matter Institute Quarks, Gluons and the Phase Diagram of QCD St. Goar, September 2nd 2009 Outline Phase diagram of
Renormalization Group Study of the Chiral Phase Transition
Renormalization Group Study of the Chiral Phase Transition Ana Juričić, Bernd-Jochen Schaefer University of Graz Graz, May 23, 2013 Table of Contents 1 Proper Time Renormalization Group 2 Quark-Meson Model
(De-)Confinement from QCD Green s functions
(De-)Confinement from QCD Green s functions Christian S. Fischer JLU Giessen March 2012 with Jan Luecker, Jens Mueller, Christian Kellermann, Stefan Strauss Christian S. Fischer (JLU Giessen) (De-)Confinement
Spectral Functions from the Functional RG
Spectral Functions from the Functional RG 7 th International Conference on the Exact Renormalization Group ERG 2014 22/09/14 Lefkada, Greece Nils Strodthoff, ITP Heidelberg 2-Point Functions and their
The Phase Structure of the Polyakov Quark-Meson Model beyond Mean Field
The Phase Structure of the Polyakov Quark-Meson Model beyond Mean Field Tina Katharina Herbst In Collaboration with B.-J. Schaefer and J.M. Pawlowski arxiv: 18.81 [hep-ph] 5th International Conference
Non-perturbative Study of Chiral Phase Transition
Non-perturbative Study of Chiral Phase Transition Ana Juričić Advisor: Bernd-Jochen Schaefer University of Graz Graz, January 9, 2013 Table of Contents Chiral Phase Transition in Low Energy QCD Renormalization
QCD at finite density with Dyson-Schwinger equations
QCD at finite density with Dyson-Schwinger equations Daniel Müller, Michael Buballa, Jochen Wambach KFU Graz, January 3, 213 January 3, 213 TU Darmstadt 1 Outline Introduction: QCD phase diagram Dyson-Schwinger
Locating QCD s critical end point
Locating QCD s critical end point Christian S. Fischer Justus Liebig Universität Gießen 31st of Oct 2016 Eichmann, CF, Welzbacher, PRD93 (2016) [1509.02082] Eichmann, Sanchis-Alepuz, Williams, Alkofer,
Functional RG methods in QCD
methods in QCD Institute for Theoretical Physics University of Heidelberg LC2006 May 18th, 2006 methods in QCD motivation Strong QCD QCD dynamical symmetry breaking instantons χsb top. dofs link?! deconfinement
Dynamical Locking of the Chiral and the Deconfinement Phase Transition
Dynamical Locking of the Chiral and the Deconfinement Phase Transition Jens Braun Friedrich-Schiller-University Jena Quarks, Gluons, and Hadronic Matter under Extreme Conditions St. Goar 17/03/2011 J.
QCD chiral phase boundary from RG flows. Holger Gies. Heidelberg U.
Heidelberg U. From Micro to Macro DoF From Micro to Macro DoF UV PLM PNJL NJL Quark Meson model Quark models Bag models Skyrmions... IR From Micro to Macro DoF UV PLM PNJL NJL Quark Meson model Quark models
Richard Williams. Collaborators: Alkofer, Eichmann, Fischer, Heupel, Sanchis-Alepuz
Richard Williams Collaborators: Alkofer, Eichmann, Fischer, Heupel, Sanchis-Alepuz 2 baryons mesons glueballs hybrids tetraquarks pentaquarks Extracting hadron poles from Green s functions 3 Extracting
Introduction to Strong Interactions and the Hadronic Spectrum
Introduction to Strong Interactions and the Hadronic Spectrum Milan Vujinovic University of Graz, Graz, Austria Support by FWF Doctoral Program W1203 Hadrons in Vacuum, Nuclei and Stars Institute of Physics,
Richard Williams C. S. Fischer, W. Heupel, H. Sanchis-Alepuz
Richard Williams C. S. Fischer, W. Heupel, H. Sanchis-Alepuz Overview 2 1.Motivation and Introduction 4. 3PI DSE results 2. DSEs and BSEs 3. npi effective action 6. Outlook and conclusion 5. 3PI meson
Triple-gluon and quark-gluon vertex from lattice QCD in Landau gauge
Triple-gluon and quark-gluon vertex from lattice QCD in Landau gauge André Sternbeck Friedrich-Schiller-Universität Jena, Germany Lattice 2016, Southampton (UK) Overview in collaboration with 1) Motivation
The Infrared Behavior of Landau Gauge Yang-Mills Theory in d=2, 3 and 4 Dimensions
The Infrared Behavior of Landau Gauge Yang-Mills Theory in d=2, 3 and 4 Dimensions Markus Huber 1 R. Alkofer 1 C. S. Fischer 2 K. Schwenzer 1 1 Institut für Physik, Karl-Franzens Universität Graz 2 Institut
Confinement from Correlation Functions
Department of Mathematical Physics, National University of Ireland Maynooth, Maynooth Co. Kildare, Ireland, and Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg,
Scalar particles. Axel Maas. 7 th of May 2010 Delta 2010 Heidelberg Germany
Scalar particles Axel Maas 7 th of May 2010 Delta 2010 Heidelberg Germany Scalar particles - Properties in Landau gauge(s) Axel Maas 7 th of May 2010 Delta 2010 Heidelberg Germany Aim Describe gauge theories
QCD at finite density with Dyson-Schwinger equations
QCD at finite density with Dyson-Schwinger equations Daniel Müller, Michael Buballa, Jochen Wambach Quark Gluon Plasma meets Cold Atoms Episode III August 3, 212 TU Darmstadt 1 Outline Motivation Dyson-Schwinger
Sarma phase in relativistic and non-relativistic systems
phase in relativistic and non-relativistic systems Tina Katharina Herbst In Collaboration with I. Boettcher, J. Braun, J. M. Pawlowski, D. Roscher, N. Strodthoff, L. von Smekal and C. Wetterich arxiv:149.5232
arxiv: v1 [hep-ph] 17 Apr 2014
![arxiv: v1 [hep-ph] 17 Apr 2014](/thumbs/94/120105611.jpg "arxiv: v1 [hep-ph] 17 Apr 2014")
Non-perturbative features of the three-gluon vertex in Landau gauge Milan Vujinovic, Reinhard Alkofer arxiv:404.4474v [hep-ph] 7 Apr 204 Institut für Physik, Karl-Franzens-Universität Graz, Universitätsplatz
Richard Williams. Hèlios Sanchis-Alepuz
Richard Williams Hèlios Sanchis-Alepuz Introduction 2 Idea: Information on hadron properties encoded in Green s functions EM form-factors Dyson-Schwinger Approach Nonpert. Covariant Multi-scale Symmetries
Phase transitions in strong QED3
Phase transitions in strong QED3 Christian S. Fischer Justus Liebig Universität Gießen SFB 634 30. November 2012 Christian Fischer (University of Gießen) Phase transitions in strong QED3 1 / 32 Overview
Joannis Papavassiliou Department of Theoretical Physics and IFIC University of Valencia-CSIC
The dynamics of the gluon mass Joannis Papavassiliou Department of Theoretical Physics and IFIC University of Valencia-CSIC Worshop on Functional Methods in Hadron and Nuclear Physics 2-25 August, 27 ECT*
Tetraquarks and Goldstone boson physics
Tetraquarks and Goldstone boson physics Christian S. Fischer Justus Liebig Universität Gießen February 2017 Eichmann, CF, Heupel, PLB 753 (2016) 282-287 Review: Eichmann, Sanchis-Alepuz, Williams, Alkofer,
Critical Region of the QCD Phase Transition
Critical Region of the QCD Phase Transition Mean field vs. Renormalization group B.-J. Schaefer 1 and J. Wambach 1,2 1 Institut für Kernphysik TU Darmstadt 2 GSI Darmstadt 18th August 25 Uni. Graz B.-J.
HLbl from a Dyson Schwinger Approach
HLbl from a Dyson Schwinger Approach Richard Williams KFUni Graz Tobias Göcke TU Darmstadt Christian Fischer Uni Gießen INT Workshop on Hadronic Light-by-Light contribution to the Muon Anomaly February
QCD-like theories at finite density
QCD-like theories at finite density 34 th International School of Nuclear Physics Probing the Extremes of Matter with Heavy Ions Erice, Sicily, 23 September 212 Lorenz von Smekal 23. September 212 Fachbereich
Mesonic and nucleon fluctuation effects at finite baryon density
Mesonic and nucleon fluctuation effects at finite baryon density Research Center for Nuclear Physics Osaka University Workshop on Strangeness and charm in hadrons and dense matter Yukawa Institute for
Inverse square potential, scale anomaly, and complex extension
Inverse square potential, scale anomaly, and complex extension Sergej Moroz Seattle, February 2010 Work in collaboration with Richard Schmidt ITP, Heidelberg Outline Introduction and motivation Functional
Thermodynamics of the Polyakov-Quark-Meson Model
Thermodynamics of the Polyakov-Quark-Meson Model Bernd-Jochen Schaefer 1, Jan Pawlowski and Jochen Wambach 3 1 KFU Graz, Austria U Heidelberg, Germany 3 TU and GSI Darmstadt, Germany Virtual Institute
Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory Universität Tübingen Institut für Theoretische Physi Auf der Morgenstelle 4 D-7076 Tübingen Germany E-mail: hugo.reinhardt@uni-tuebingen.de Marus Leder
Gluon Propagator and Gluonic Screening around Deconfinement
Gluon Propagator and Gluonic Screening around Deconfinement Tereza Mendes Instituto de Física de São Carlos University of São Paulo Work in collaboration with Attilio Cucchieri Screening at High T At high
Deconfinement and Polyakov loop in 2+1 flavor QCD
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
Towards thermodynamics from lattice QCD with dynamical charm Project A4
Towards thermodynamics from lattice QCD with dynamical charm Project A4 Florian Burger Humboldt University Berlin for the tmft Collaboration: E.-M. Ilgenfritz (JINR Dubna), M. Müller-Preussker (HU Berlin),
STRANGENESS NEUTRALITY AND THE QCD PHASE STRUCTURE
STRANGENESS NEUTRALITY AND THE QCD PHASE STRUCTURE Fabian Rennecke Brookhaven National Laboratory [Fu, Pawlowski, FR, hep-ph/1808.00410] [Fu, Pawlowski, FR, hep-ph/1809.01594] NUCLEAR PHYSICS COLLOQUIUM
The Phases of QCD. Thomas Schaefer. North Carolina State University
The Phases of QCD Thomas Schaefer North Carolina State University 1 Motivation Different phases of QCD occur in the universe Neutron Stars, Big Bang Exploring the phase diagram is important to understanding
Infra-Red. Infra-red dog
A Ghost Story Gluons and ghosts in the IR and the UV Berlin, June 15, 2009 Ph.,Boucaud, F De soto, J.-P. Leroy, A. Le Yaouanc, J. Micheli, O. Pène, J. Rodriguez- Quintero, A.Lokhov and C. Roiesnel I. Gluons
QCD Green Functions:
QCD Green Functions: What their Infrared Behaviour tells us about Confinement! Reinhard Alkofer FWF-funded Doctoral Program Hadrons in Vacuum, Nuclei and Stars Institute of Physics Theoretical Physics
Phases and facets of 2-colour matter
Phases and facets of 2-colour matter Jon-Ivar Skullerud with Tamer Boz, Seamus Cotter, Leonard Fister Pietro Giudice, Simon Hands Maynooth University New Directions in Subatomic Physics, CSSM, 10 March
G2 gauge theories. Axel Maas. 14 th of November 2013 Strongly-Interacting Field Theories III Jena, Germany
G2 gauge theories Axel Maas 14 th of November 2013 Strongly-Interacting Field Theories III Jena, Germany Overview Why G2? Overview Why G2? G2 Yang-Mills theory Running coupling [Olejnik, Maas JHEP'08,
Infrared Propagators and Confinement: a Perspective from Lattice Simulations
Infrared Propagators and Confinement: a Perspective from Lattice Simulations Tereza Mendes University of São Paulo & DESY-Zeuthen Work in collaboration with Attilio Cucchieri Summary Lattice studies of
Hamiltonian approach to QCD: The Polyakov loop potential H. Reinhardt
Hamiltonian approach to QCD: The Polyakov loop potential H. Reinhardt H. R. & J. Heffner Phys. Lett.B718(2012)672 PRD(in press) arxiv:1304.2980 Phase diagram of QCD non-perturbative continuum approaches
Dual quark condensate and dressed Polyakov loops
Dual quark condensate and dressed Polyakov loops Falk Bruckmann (Univ. of Regensburg) Lattice 28, William and Mary with Erek Bilgici, Christian Hagen and Christof Gattringer Phys. Rev. D77 (28) 947, 81.451
Quark tensor and axial charges within the Schwinger-Dyson formalism
Quark tensor and axial charges within the Schwinger-Dyson formalism, Takahiro M. Doi, Shotaro Imai, Hideo Suganuma Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa-oiwake,
A Dyson-Schwinger equation study of the baryon-photon interaction.
A Dyson-Schwinger equation study of the baryon-photon interaction. Diana Nicmorus in collaboration with G. Eichmann A. Krassnigg R. Alkofer Jefferson Laboratory, March 24, 2010 What is the nucleon made
Describing Gluons. Axel Maas. 28 th of July 2009 Pathways to Confinement Rio de Janeiro Brazil
Describing Gluons Axel Maas 28 th of July 2009 Pathways to Confinement Rio de Janeiro Brazil Overview Gauge freedom in Yang-Mills theory Supported by the FWF Slides left: 56 (in this section: 0) Overview
Jochen Wambach. to Gerry Brown
Real-Time Spectral Functions from the Functional Renormalization Group Jochen Wambach TU-Darmstadt and GSI Germany to Gerry Brown an inspring physicist and a great human being November 24, 203 TU Darmstadt
Quark-Gluon Vertex Dressing And Meson Masses Beyond Ladder-Rainbow Truncation.
Quark-Gluon Vertex Dressing And Meson Masses Beyond Ladder-Rainbow Truncation. nucl-th/0605057 H.H. Matevosyan 1,2, A.W. Thomas 2, P.C. Tandy 3 1 Department of Physics & Astronomy, Louisiana State University
Analytical study of Yang-Mills theory from first principles by a massive expansion
Analytical study of Yang-Mills theory from first principles by a massive expansion Department of Physics and Astronomy University of Catania, Italy Infrared QCD APC, Paris Diderot University, 8-10 November
Cold and dense QCD matter
Cold and dense QCD matter GCOE sympodium Feb. 15, 2010 Yoshimasa Hidaka Quantum ChromoDynamics Atom Electron 10-10 m Quantum ChromoDynamics Atom Nucleon Electron 10-10 m 10-15 m Quantum ElectroDynamics
Mesonic and nucleon fluctuation effects in nuclear medium
Mesonic and nucleon fluctuation effects in nuclear medium Research Center for Nuclear Physics Osaka University Workshop of Recent Developments in QCD and Quantum Field Theories National Taiwan University,
arxiv: v2 [hep-ph] 18 Dec 2017
![arxiv: v2 [hep-ph] 18 Dec 2017](/thumbs/75/72272576.jpg "arxiv: v2 [hep-ph] 18 Dec 2017")
Center phase transition from matter propagators in (scalar) QCD M. Mitter a,b, M. Hopfer a, B.-J. Schaefer c, R. Alkofer a arxiv:179.99v [hep-ph] 18 Dec 17 Abstract a Institut für Physik, NAWI Graz, Karl-Franzens-Universität
1/N Expansions in String and Gauge Field Theories. Adi Armoni Swansea University
1/N Expansions in String and Gauge Field Theories Adi Armoni Swansea University Oberwoelz, September 2010 1 Motivation It is extremely difficult to carry out reliable calculations in the strongly coupled
Bethe Salpeter studies of mesons beyond rainbow-ladder Complutense Unviversity of Madrid
Bethe Salpeter studies of mesons beyond rainbow-ladder Complutense Unviversity of Madrid Richard Williams C. S. Fischer and RW, Phys. Rev. D 78 2008 074006, [arxiv:0808.3372] C. S. Fischer and RW, Phys.
Confinement in Polyakov gauge
Confinement in Polyakov gauge Florian Marhauser arxiv:812.1144 QCD Phase Diagram chiral vs. deconfinement phase transition finite density critical point... Confinement Order Parameter ( β ) φ( x) = L(
G 2 QCD Neutron Star. Ouraman Hajizadeh in collaboration with Axel Maas. November 30, 2016
G 2 QCD Neutron Star Ouraman Hajizadeh in collaboration with Axel Maas November 30, 2016 Motivation Why Neutron Stars? Neutron Stars: Laboratory of Strong Interaction Dense Objects: Study of strong interaction
The Phases of QCD. Thomas Schaefer. North Carolina State University
The Phases of QCD Thomas Schaefer North Carolina State University 1 Plan of the lectures 1. QCD and States of Matter 2. The High Temperature Phase: Theory 3. Exploring QCD at High Temperature: Experiment
Spectral Properties of Quarks in the Quark-Gluon Plasma
Lattice27 : 2, Aug., 27 Spectral Properties of Quarks in the Quark-Gluon Plasma Masakiyo Kitazawa (Osaka Univ.) F. Karsch and M.K., arxiv:78.299 Why Quark? Because there are quarks. in the deconfined phase
UV completion of the Standard Model
UV completion of the Standard Model Manuel Reichert In collaboration with: Jan M. Pawlowski, Tilman Plehn, Holger Gies, Michael Scherer,... Heidelberg University December 15, 2015 Outline 1 Introduction
Hadronic light-by-light from Dyson-Schwinger equations
Hadronic light-by-light from Dyson-Schwinger equations Christian S. Fischer Justus Liebig Universität Gießen 23rd of October 2014 Together with Richard Williams, Gernot Eichmann, Tobias Goecke, Jan Haas
Lecture II: Owe Philipsen. The ideal gas on the lattice. QCD in the static and chiral limit. The strong coupling expansion at finite temperature
Lattice QCD, Hadron Structure and Hadronic Matter Dubna, August/September 2014 Lecture II: Owe Philipsen The ideal gas on the lattice QCD in the static and chiral limit The strong coupling expansion at
Polyakov Loop in a Magnetic Field
Polyakov Loop in a Magnetic Field Kenji Fukushima (Department of Physics, Keio University) March 17, 11 @ St.Goar 1 Talk Contents Relativistic Heavy-Ion Collision and Strong Magnetic Fields eb ~m ~118
The Chiral and Deconfinement Phase Transitions in Strongly-Interacting Matter
The Chiral and Deconfinement Phase Transitions in Strongly-Interacting Matter in collaboration with: B-J. Schaefer & J. Wambach Schaefer, MW: PRD 79 (1418) arxiv: 812.2855 [hep-ph] 9.3.29 Mathias Wagner
The Big Picture. Thomas Schaefer. North Carolina State University
The Big Picture Thomas Schaefer North Carolina State University 1 Big Questions What is QCD? What is a Phase of QCD? What is a Plasma? What is a (perfect) Liquid? What is a wqgp/sqgp? 2 What is QCD (Quantum
The Strong Interaction and LHC phenomenology
The Strong Interaction and LHC phenomenology Juan Rojo STFC Rutherford Fellow University of Oxford Theoretical Physics Graduate School course Lecture 2: The QCD Lagrangian, Symmetries and Feynman Rules
Chiral Symmetry Breaking. Schwinger-Dyson Equations
Critical End Point of QCD Phase-Diagram: A Schwinger-Dyson Equation Perspective Adnan Bashir Michoacán University, Mexico Collaborators: E. Guadalupe Gutiérrez, A Ahmad, A. Ayala, A. Raya, J.R. Quintero
SUNY Stony Brook August 16, Wolfram Weise. with. Thomas Hell Simon Rössner Claudia Ratti
SUNY Stony Brook August 16, 27 PHASES of QCD POLYAKOV LOOP and QUASIPARTICLES Wolfram Weise with Thomas Hell Simon Rössner Claudia Ratti C. Ratti, M. Thaler, W. Weise: Phys. Rev. D 73 (26) 1419 C. Ratti,
Probing the QCD phase diagram with higher moments
Probing the QCD phase diagram with higher moments in collaboration with: F. Karsch B.-J. Schaefer A. Walther J. Wambach Outline Why higher moments? Algorithmic differentiation Lattice Taylor expansion
LQCD at non-zero temperature : strongly interacting matter at high temperatures and densities Péter Petreczky
LQCD at non-zero temperature : strongly interacting matter at high temperatures and densities Péter Petreczky QCD and hot and dense matter Lattice formulation of QCD Deconfinement transition in QCD : EoS
Quark condensates and the deconfinement transition
Quark condensates and the deconfinement transition Institute for Nuclear Physics, Darmstadt University of Technology, Schlossgartenstraße 9, 64289 Darmstadt, Germany GSI Helmholtzzentrum für Schwerionenforschung
Scalar QCD. Axel Maas with Tajdar Mufti. 5 th of September 2013 QCD TNT III Trento Italy
Scalar QCD Axel Maas with Tajdar Mufti 5 th of September 2013 QCD TNT III Trento Italy Scalar QCD Bound States, Elementary Particles & Interaction Vertices Axel Maas with Tajdar Mufti 5 th of September
Quark matter and the high-density frontier. Mark Alford Washington University in St. Louis
Quark matter and the high-density frontier Mark Alford Washington University in St. Louis Outline I Quarks at high density Confined, quark-gluon plasma, color superconducting II Color superconducting phases
Confined chirally symmetric dense matter
Confined chirally symmetric dense matter L. Ya. Glozman, V. Sazonov, R. Wagenbrunn Institut für Physik, FB Theoretische Physik, Universität Graz 28 June 2013 L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut
Termodynamics and Transport in Improved Holographic QCD
Termodynamics and Transport in Improved Holographic QCD p. 1 Termodynamics and Transport in Improved Holographic QCD Francesco Nitti APC, U. Paris VII Large N @ Swansea July 07 2009 Work with E. Kiritsis,
Equation of state. Pasi Huovinen Uniwersytet Wroc lawski. Collective Flows and Hydrodynamics in High Energy Nuclear Collisions
Equation of state Pasi Huovinen Uniwersytet Wroc lawski Collective Flows and Hydrodynamics in High Energy Nuclear Collisions Dec 14, 2016, University of Science and Technology of China, Hefei, China The
G 2 -QCD at Finite Density
G 2 -QCD at Finite Density A. Wipf Theoretisch-Physikalisches Institut, FSU Jena collaboration with Axel Maas (Jena) Lorenz von Smekal (Darmstadt/Gießen) Bjoern Wellegehausen (Gießen) Christian Wozar (Jena)
QCD on the lattice - an introduction
QCD on the lattice - an introduction Mike Peardon School of Mathematics, Trinity College Dublin Currently on sabbatical leave at JLab HUGS 2008 - Jefferson Lab, June 3, 2008 Mike Peardon (TCD) QCD on the
QCD and Instantons: 12 Years Later. Thomas Schaefer North Carolina State
QCD and Instantons: 12 Years Later Thomas Schaefer North Carolina State 1 ESQGP: A man ahead of his time 2 Instanton Liquid: Pre-History 1975 (Polyakov): The instanton solution r 2 2 E + B A a µ(x) = 2
Properties of gauge orbits
Properties of gauge orbits Axel Maas 18 th of June 2010 XXVIII International Symposium on Lattice Field Theory Villasimius Sardinia/Italy Why gauge-fixing? Slides left: 16 (in this section: 2) Why gauge-fixing?