Post on 05-Aug-2019
QCD from quark, gluon, and meson correlators
Mario Mitter
Brookhaven National Laboratory
Giessen, January 2018
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 1 / 22
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
µ
early universe
neutron star cores
LHCRHIC
AGS
SIS
quark−gluon plasma
hadronic fluid
nuclear mattervacuum
SPS
FAIR/NICA
n = 0 n > 0
<ψψ> ∼ 0
/<ψψ> = 0
/<ψψ> = 0
phases ?
quark matter
crossover
CFLB B
superfluid/superconducting
2SC
crossover
[Schaefer, Wagner, ’08]
large part of this effort: vacuum QCD and YM-theorywhy?
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 2 / 22
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
µ
early universe
neutron star cores
LHCRHIC
AGS
SIS
quark−gluon plasma
hadronic fluid
nuclear mattervacuum
SPS
FAIR/NICA
n = 0 n > 0
<ψψ> ∼ 0
/<ψψ> = 0
/<ψψ> = 0
phases ?
quark matter
crossover
CFLB B
superfluid/superconducting
2SC
crossover
[Schaefer, Wagner, ’08]
large part of this effort: vacuum QCD and YM-theory
why?
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 2 / 22
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
µ
early universe
neutron star cores
LHCRHIC
AGS
SIS
quark−gluon plasma
hadronic fluid
nuclear mattervacuum
SPS
FAIR/NICA
n = 0 n > 0
<ψψ> ∼ 0
/<ψψ> = 0
/<ψψ> = 0
phases ?
quark matter
crossover
CFLB B
superfluid/superconducting
2SC
crossover
[Schaefer, Wagner, ’08]
large part of this effort: vacuum QCD and YM-theorywhy?
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 2 / 22
QCD from the effective action (gauge fixing necessary).Γ[Φ] =
∑n
∫{pi} Γ
(n)Φ1···Φn
(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)
full information about QFT encoded in Γ[Φ]/correlators:I bound state spectrum: pole structure of the Γ(n)
e.g. [Roberts, Williams, ’94], [Alkofer, Smekal, ’00], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, ’16]
I form factors: photon-particle correlatorse.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, ’08], [Sanchis-Alepuz, Williams, Alkofer, ’13]
⇒ decay constants e.g. [Maris, Roberts, Tandy, ’97], [MM, Pawlowski, Strodthoff, in prep.]
I thermodynamic quantities: Γ[Φ] ∝ grand potentialF equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
F fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
I further quantities: Γ[Φ] ∝ eff. potential, propagators, ’t Hooft determinantF chiral condensate(s)/〈σ〉
e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
F (dressed) Polyakov loope.g. [Fischer, ’09], [Braun, Haas, Marhauser, Pawlowski, ’09], [MM, et al., ’17]
F axial anomaly e.g.[Grahl, Rischke, ’13], [MM, Schaefer, ’13], [Fejos, ’15], [Heller, MM, ’15]
F spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 3 / 22
QCD from the effective action (gauge fixing necessary).Γ[Φ] =
∑n
∫{pi} Γ
(n)Φ1···Φn
(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)
full information about QFT encoded in Γ[Φ]/correlators:
I bound state spectrum: pole structure of the Γ(n)
e.g. [Roberts, Williams, ’94], [Alkofer, Smekal, ’00], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, ’16]
I form factors: photon-particle correlatorse.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, ’08], [Sanchis-Alepuz, Williams, Alkofer, ’13]
⇒ decay constants e.g. [Maris, Roberts, Tandy, ’97], [MM, Pawlowski, Strodthoff, in prep.]
I thermodynamic quantities: Γ[Φ] ∝ grand potentialF equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
F fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
I further quantities: Γ[Φ] ∝ eff. potential, propagators, ’t Hooft determinantF chiral condensate(s)/〈σ〉
e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
F (dressed) Polyakov loope.g. [Fischer, ’09], [Braun, Haas, Marhauser, Pawlowski, ’09], [MM, et al., ’17]
F axial anomaly e.g.[Grahl, Rischke, ’13], [MM, Schaefer, ’13], [Fejos, ’15], [Heller, MM, ’15]
F spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 3 / 22
QCD from the effective action (gauge fixing necessary).Γ[Φ] =
∑n
∫{pi} Γ
(n)Φ1···Φn
(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)
full information about QFT encoded in Γ[Φ]/correlators:I bound state spectrum: pole structure of the Γ(n)
e.g. [Roberts, Williams, ’94], [Alkofer, Smekal, ’00], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, ’16]
I form factors: photon-particle correlatorse.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, ’08], [Sanchis-Alepuz, Williams, Alkofer, ’13]
⇒ decay constants e.g. [Maris, Roberts, Tandy, ’97], [MM, Pawlowski, Strodthoff, in prep.]
I thermodynamic quantities: Γ[Φ] ∝ grand potentialF equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
F fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
I further quantities: Γ[Φ] ∝ eff. potential, propagators, ’t Hooft determinantF chiral condensate(s)/〈σ〉
e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
F (dressed) Polyakov loope.g. [Fischer, ’09], [Braun, Haas, Marhauser, Pawlowski, ’09], [MM, et al., ’17]
F axial anomaly e.g.[Grahl, Rischke, ’13], [MM, Schaefer, ’13], [Fejos, ’15], [Heller, MM, ’15]
F spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 3 / 22
QCD from the effective action (gauge fixing necessary).Γ[Φ] =
∑n
∫{pi} Γ
(n)Φ1···Φn
(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)
full information about QFT encoded in Γ[Φ]/correlators:I bound state spectrum: pole structure of the Γ(n)
e.g. [Roberts, Williams, ’94], [Alkofer, Smekal, ’00], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, ’16]
I form factors: photon-particle correlatorse.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, ’08], [Sanchis-Alepuz, Williams, Alkofer, ’13]
⇒ decay constants e.g. [Maris, Roberts, Tandy, ’97], [MM, Pawlowski, Strodthoff, in prep.]
I thermodynamic quantities: Γ[Φ] ∝ grand potentialF equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
F fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
I further quantities: Γ[Φ] ∝ eff. potential, propagators, ’t Hooft determinantF chiral condensate(s)/〈σ〉
e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
F (dressed) Polyakov loope.g. [Fischer, ’09], [Braun, Haas, Marhauser, Pawlowski, ’09], [MM, et al., ’17]
F axial anomaly e.g.[Grahl, Rischke, ’13], [MM, Schaefer, ’13], [Fejos, ’15], [Heller, MM, ’15]
F spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 3 / 22
QCD from the effective action (gauge fixing necessary).Γ[Φ] =
∑n
∫{pi} Γ
(n)Φ1···Φn
(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)
full information about QFT encoded in Γ[Φ]/correlators:I bound state spectrum: pole structure of the Γ(n)
e.g. [Roberts, Williams, ’94], [Alkofer, Smekal, ’00], [Eichmann, Sanchis-Alepuz, Williams, Alkofer, Fischer, ’16]
I form factors: photon-particle correlatorse.g. [Cloet, Eichmann, El-Bennich, Klahn, Roberts, ’08], [Sanchis-Alepuz, Williams, Alkofer, ’13]
⇒ decay constants e.g. [Maris, Roberts, Tandy, ’97], [MM, Pawlowski, Strodthoff, in prep.]
I thermodynamic quantities: Γ[Φ] ∝ grand potentialF equation of state e.g. [Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
F fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
I further quantities: Γ[Φ] ∝ eff. potential, propagators, ’t Hooft determinantF chiral condensate(s)/〈σ〉
e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
F (dressed) Polyakov loope.g. [Fischer, ’09], [Braun, Haas, Marhauser, Pawlowski, ’09], [MM, et al., ’17]
F axial anomaly e.g.[Grahl, Rischke, ’13], [MM, Schaefer, ’13], [Fejos, ’15], [Heller, MM, ’15]
F spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 3 / 22
e.g. EOS and axial anomaly in “QCD-enhanced” modelsequation of state
Nf = 2 + 1 PQM model with FRG
unquenched Polyakov-loop potentialfrom [Braun, Haas, Marhauser, Pawlowski, ’11]
0
1
2
3
4
5
6
7
8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
(ε -
3P
)/T
4
t
Wuppertal-Budapest, 2010
HotQCD Nt=8, 2012
HotQCD Nt=12, 2012
PQM FRG
PQM eMF
PQM MF
[Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
[Haas, Stiele, Braun, Pawlowski, Schaffner-Bielich, ’13]
η′-meson screening mass
Nf = 2 PQM model, extended MF
running ’t Hooft determinantfrom [MM, Pawlowski, Strodthoff, ’14]
0
200
400
600
800
1000
120 140 160 180 200 220 240
m/[
Me
V]
T/[MeV]
mη
mηPQM
mσPQM
mπPQM
[Heller, MM, ’15]
.
phase diagrams e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 4 / 22
e.g. EOS and axial anomaly in “QCD-enhanced” modelsequation of state
Nf = 2 + 1 PQM model with FRG
unquenched Polyakov-loop potentialfrom [Braun, Haas, Marhauser, Pawlowski, ’11]
0
1
2
3
4
5
6
7
8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
(ε -
3P
)/T
4
t
Wuppertal-Budapest, 2010
HotQCD Nt=8, 2012
HotQCD Nt=12, 2012
PQM FRG
PQM eMF
PQM MF
[Herbst, MM, Pawlowski, Schaefer, Stiele, ’13]
[Haas, Stiele, Braun, Pawlowski, Schaffner-Bielich, ’13]
η′-meson screening mass
Nf = 2 PQM model, extended MF
running ’t Hooft determinantfrom [MM, Pawlowski, Strodthoff, ’14]
0
200
400
600
800
1000
120 140 160 180 200 220 240
m/[
Me
V]
T/[MeV]
mη
mηPQM
mσPQM
mπPQM
[Heller, MM, ’15]
.
phase diagrams e.g. [Schaefer, Wambach ’04], [Fischer, Luecker, Mueller ’11], [MM, Schaefer, ’13]
spectral functions e.g. [Tripolt, Strodthoff, Smekal, Wambach, ’14]
fluctuations of conserved charges e.g. [Fu, Rennecke, Pawlowski, Schaefer, ’16]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 4 / 22
e.g. Center symmetry order parameters [MM, Hopfer, Schaefer, Alkofer, 2017]
quenched (scalar) Quantum Chromodynamics
correlators from Dyson-Schwinger equation (DSE)
lattice gluon input and vertex models
0
0.5
1
1.5
2
2.5
3
100 150 200 250 300
Σ(T
)/Σ
(T=
27
7 M
eV
)
T [MeV]
m=1.5 GeV, d1=0.53m=2.0 GeV, d1=0.53m=1.5 GeV, d1=0.45
from scalar propagator:
2π∫0
dϕT∑n
D2ϕ(~p = ~0, ωn(ϕ))
✥
✥�✥✁
✥�✥✂
✥�✥✄
✥�✥☎
✥�✆
✆✥✥ ✁✥✥ ✝✥✥ ✂✥✥ ✞✥✥ ✄✥✥
❚ ✟✠✡☛☞
❙✶ ✟✌✡☛✲✶☞
❙q ✟✌✡☛✸☞
from quark propagator:
2π∫0
dϕT∑n
[1
4trD S(~0, ωn(ϕ))
]2
cf. e.g. [Fischer ’09], [Braun, Haas, Marhauser, Pawlowski, ’09],. . .
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 5 / 22
e.g. Debye mass in SU(3) YM theory [Cyrol, MM, Pawlowski, Strodthoff, 2017]
correlators from Functional Renormalisation Group (FRG)
screening mass:fit to exponential decay of chromo-electric gluon propagator
FRG
first order HTL
second order HTL, cp = 1
second order HTL, cp = 0.88
0.5 1.0 1.5 2.0
2.0
2.1
2.2
2.3
2.4
2.5
2.6
T [GeV]
mS/T
0.1 0.2 0.3 0.4 0.5
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
T [GeV]m
S[G
eV]
excellent agreement with beyond leading order Debye mass of [Arnold, Yaffe, ’95]for T & 0.6 GeV
smooth transition to nonperturbative regime
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 6 / 22
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, 2014]
pure SU(N) YM-theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, 2016]
Nf = 2 QCD [Cyrol, MM, Strodthoff, Pawlowski, 2017]
YM-theory at finite temperature T > 0 [Cyrol, MM, Strodthoff, Pawlowski, 2017]
use results from lattice gauge theory to check truncation:what do we need from the lattice?
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 7 / 22
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, 2014]
pure SU(N) YM-theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, 2016]
Nf = 2 QCD [Cyrol, MM, Strodthoff, Pawlowski, 2017]
YM-theory at finite temperature T > 0 [Cyrol, MM, Strodthoff, Pawlowski, 2017]
use results from lattice gauge theory to check truncation:what do we need from the lattice?
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 7 / 22
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, 2014]
pure SU(N) YM-theory [Cyrol, Fister, MM, Pawlowski, Strodthoff, 2016]
Nf = 2 QCD [Cyrol, MM, Strodthoff, Pawlowski, 2017]
YM-theory at finite temperature T > 0 [Cyrol, MM, Strodthoff, Pawlowski, 2017]
use results from lattice gauge theory to check truncation:what do we need from the lattice?
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 7 / 22
(Euclidean) Correlation functions with the FRGmass-like IR regulator:
I S [Φ]→ S [Φ] + 〈Φ,RkΦ〉I (renormalised) initial action ΓΛ→∞[Φ] = S [Φ]
use only perturbative QCD input:I αS(Λ = O(10) GeV)I mq(Λ = O(10) GeV)
∂k ⇔ integration of momentum shells: [Wetterich ’93]
∂kΓk [A, c , c , q, q] = 12 − −
⇒ full non-perturbative quantum effective action
gauge-fixed approach (Landau gauge): ghosts appearfunctional derivatives ⇒ equations for correlatorsaim for “apparent convergence” of Γ[Φ] = lim
k→0Γk [Φ]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 8 / 22
(Euclidean) Correlation functions with the FRGmass-like IR regulator:
I S [Φ]→ S [Φ] + 〈Φ,RkΦ〉I (renormalised) initial action ΓΛ→∞[Φ] = S [Φ]
use only perturbative QCD input:I αS(Λ = O(10) GeV)I mq(Λ = O(10) GeV)
∂k ⇔ integration of momentum shells: [Wetterich ’93]
∂kΓk [A, c , c , q, q] = 12 − −
⇒ full non-perturbative quantum effective action
gauge-fixed approach (Landau gauge): ghosts appearfunctional derivatives ⇒ equations for correlatorsaim for “apparent convergence” of Γ[Φ] = lim
k→0Γk [Φ]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 8 / 22
(Euclidean) Correlation functions with the FRGmass-like IR regulator:
I S [Φ]→ S [Φ] + 〈Φ,RkΦ〉I (renormalised) initial action ΓΛ→∞[Φ] = S [Φ]
use only perturbative QCD input:I αS(Λ = O(10) GeV)I mq(Λ = O(10) GeV)
∂k ⇔ integration of momentum shells: [Wetterich ’93]
∂kΓk [A, c , c , q, q] = 12 − −
⇒ full non-perturbative quantum effective action
gauge-fixed approach (Landau gauge): ghosts appearfunctional derivatives ⇒ equations for correlatorsaim for “apparent convergence” of Γ[Φ] = lim
k→0Γk [Φ]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 8 / 22
(Euclidean) Correlation functions with the FRGmass-like IR regulator:
I S [Φ]→ S [Φ] + 〈Φ,RkΦ〉I (renormalised) initial action ΓΛ→∞[Φ] = S [Φ]
use only perturbative QCD input:I αS(Λ = O(10) GeV)I mq(Λ = O(10) GeV)
∂k ⇔ integration of momentum shells: [Wetterich ’93]
∂kΓk [A, c , c , q, q] = 12 − −
⇒ full non-perturbative quantum effective action
gauge-fixed approach (Landau gauge): ghosts appearfunctional derivatives ⇒ equations for correlatorsaim for “apparent convergence” of Γ[Φ] = lim
k→0Γk [Φ]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 8 / 22
(Euclidean) Correlation functions with the FRGmass-like IR regulator:
I S [Φ]→ S [Φ] + 〈Φ,RkΦ〉I (renormalised) initial action ΓΛ→∞[Φ] = S [Φ]
use only perturbative QCD input:I αS(Λ = O(10) GeV)I mq(Λ = O(10) GeV)
∂k ⇔ integration of momentum shells: [Wetterich ’93]
∂kΓk [A, c , c , q, q] = 12 − −
⇒ full non-perturbative quantum effective action
gauge-fixed approach (Landau gauge): ghosts appearfunctional derivatives ⇒ equations for correlatorsaim for “apparent convergence” of Γ[Φ] = lim
k→0Γk [Φ]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 8 / 22
Mesons via dynamical hadronization [Gies, Wetterich, 2002]
change of variables: particular 4-Fermi channels → meson exchangeefficient inclusion of pole structure ⇒ no spurious singularitieslow-energy effective model parameters from QCD - range of validity
∂kΓk = 12 − − + 1
2
0
50
100
150
200
250
0.1 1 10
(bosoniz
ed)
4-f
erm
i-in
tera
ction
RG-scale k [GeV]
h2π/(2 m
2π)
λπ
[MM, Strodthoff, Pawlowski, 2014]
0
5
10
15
20
25
30
1 10
Yukaw
a inte
raction h
π
RG-scale k [GeV]
[Braun, Fister, Pawlowski, Rennecke, 2014]
[MM, Strodthoff, Pawlowski, 2014]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 9 / 22
Mesons via dynamical hadronization [Gies, Wetterich, 2002]
change of variables: particular 4-Fermi channels → meson exchangeefficient inclusion of pole structure ⇒ no spurious singularitieslow-energy effective model parameters from QCD - range of validity
∂kΓk = 12 − − + 1
2
0
50
100
150
200
250
0.1 1 10
(bosoniz
ed)
4-f
erm
i-in
tera
ction
RG-scale k [GeV]
h2π/(2 m
2π)
λπ
[MM, Strodthoff, Pawlowski, 2014]
0
5
10
15
20
25
30
1 10
Yukaw
a inte
raction h
π
RG-scale k [GeV]
[Braun, Fister, Pawlowski, Rennecke, 2014]
[MM, Strodthoff, Pawlowski, 2014]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 9 / 22
Nf = 2 Landau-gauge QCD [Cyrol, MM, Pawlowski, Strodthoff, 2017]
Truncation:
systematics of improving the truncation?
⇒ BRST-invariant operators, e.g. ψ /Dnψ
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 10 / 22
Nf = 2 Landau-gauge QCD [Cyrol, MM, Pawlowski, Strodthoff, 2017]
Truncation:
systematics of improving the truncation?
⇒ BRST-invariant operators, e.g. ψ /Dnψ
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 10 / 22
Some representative equations (numerics-heavy)[MM, Strodthoff, Pawlowski, 2014],
[Cyrol, Fister, MM, Strodthoff, Pawlowski, 2016]
cf. FormTracer [Cyrol, MM, Strodthoff, 2016]
∂t = + + 12
+ −+
−1
∂t = − − − − − 12
+ 2 − + perm.
∂t = − − − −
− −−
2
+ perm.
+
=∂t
+ 12
− 2
− − +2 − + perm.
=∂t + perm.−+2−
=∂t + perm.− −
=∂t
=∂t−1
−1
+ 12
∂t =−1
+− 2
+ perm.∂t = − − − + 2
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 11 / 22
Some representative equations (numerics-heavy)[MM, Strodthoff, Pawlowski, 2014],
[Cyrol, Fister, MM, Strodthoff, Pawlowski, 2016]
cf. FormTracer [Cyrol, MM, Strodthoff, 2016]
∂t = + + 12
+ −+
−1
∂t = − − − − − 12
+ 2 − + perm.
∂t = − − − −
− −−
2
+ perm.
+
=∂t
+ 12
− 2
− − +2 − + perm.
=∂t + perm.−+2−
=∂t + perm.− −
=∂t
=∂t−1
−1
+ 12
∂t =−1
+− 2
+ perm.∂t = − − − + 2
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 11 / 22
Some representative equations (numerics-heavy)[MM, Strodthoff, Pawlowski, 2014],
[Cyrol, Fister, MM, Strodthoff, Pawlowski, 2016]
cf. FormTracer [Cyrol, MM, Strodthoff, 2016]
∂t = + + 12
+ −+
−1
∂t = − − − − − 12
+ 2 − + perm.
∂t = − − − −
− −−
2
+ perm.
+
=∂t
+ 12
− 2
− − +2 − + perm.
=∂t + perm.−+2−
=∂t + perm.− −
=∂t
=∂t−1
−1
+ 12
∂t =−1
+− 2
+ perm.∂t = − − − + 2
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 11 / 22
Chiral symmetry breakingχSB ⇔ resonance in 4-Fermi interaction λ (pion pole):
β-function of momentum independent 4-Fermi interaction:
∂tλ = 2λ+ a λ2 + b λα + c α2, b > 0, a, c ≤ 0
∂t = − −2 + . . .
λ
∂tλ
g > gcr
g = gcr
g = 0
g = 0, T > 0
[Braun, 2011]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 12 / 22
Chiral symmetry breakingχSB ⇔ resonance in 4-Fermi interaction λ (pion pole):
β-function of momentum independent 4-Fermi interaction:
∂tλ = 2λ+ a λ2 + b λα + c α2, b > 0, a, c ≤ 0
∂t = − −2 + . . .
λ
∂tλ
g > gcr
g = gcr
g = 0
g = 0, T > 0
[Braun, 2011]
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 12 / 22
(transverse) running couplings [Cyrol, MM, Pawlowski, Strodthoff, 2017]
0
0.5
1
1.5
2
2.5
0.1 1 10
mπ=247 MeV
run
nin
g c
ou
plin
gs
p [GeV]
αc-cAαA
3
αA4
αq-qAαcr
-0.1
0
0.1
∆A3
∆A4
agreement in perturbative regime required by Slavnov-Taylor identities
non-degenerate in nonperturbative regime: reflects gluon mass gap
αqAq > αcr : necessary for chiral symmetry breaking
area above αcr very sensitive to errors⇒ use STI in perturbative regime
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 13 / 22
Quark propagator [Cyrol, MM, Pawlowski, Strodthoff, 2017]
Γqq(p) = Zq(p)(/p + M(p)
)
0
0.2
0.4
0.6
0.8
1
0.1 1 10
qu
ark
pro
pa
ga
tor
dre
ssin
gs
p [GeV]
error estimate
mπ=140 MeV
mπ=60 MeV
mπ=285 MeV
lattice, β=5.20, mπ=280 MeV
lattice, β=5.29, mπ=295 MeV
SχSB: Mq(0)� Mq(p � ΛQCD)
FRG vs. lattice: bare mass, scale setting, lattice Zq?
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:1605.09632 [hep-lat].
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 14 / 22
Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 2017]
quark-gluon interaction most crucial for chiral symmetry breakingtransverse tensor basis (8 tensors), e.g. γµ, i
(/p + /q
)γµ, 1
2
[/p, /q]γµ
λ(i)(p, q)→ λ(i)(p2, q2, p · q)
-1
0
1
2
3
4
5
0.1 1 10
mπ=140 MeV
qu
ark
-glu
on
ve
rte
x d
ressin
gs
p [GeV]
error estimate
λ(1)q-qΑ
, mπ=285
λ(7)q-qΑ
, mπ=285
λ(4)q-qΑ
, mπ=285
lattice, λ(1)q-qΑ
, β=5.20, mπ=280 MeV
lattice, λ(1)q-qΑ
, β=5.29, mπ=295 MeV
3 leading tensors:I classical tensor:
constrained by STIat large momenta
I chirally symmetricI break chiral symmetry
systematic lattice error?
chirally symmetric tensors from operator q /D3q worsen result
counteracted by tensor structures in Γ(4)AAqq and Γ
(5)A3qq
from q /D3q
⇒ 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:1605.09632 [hep-lat].
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 15 / 22
Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 2017]
quark-gluon interaction most crucial for chiral symmetry breakingtransverse tensor basis (8 tensors), e.g. γµ, i
(/p + /q
)γµ, 1
2
[/p, /q]γµ
λ(i)(p, q)→ λ(i)(p2, q2, p · q)
-1
0
1
2
3
4
5
0.1 1 10
mπ=140 MeV
qu
ark
-glu
on
ve
rte
x d
ressin
gs
p [GeV]
error estimate
λ(1)q-qΑ
, mπ=285
λ(7)q-qΑ
, mπ=285
λ(4)q-qΑ
, mπ=285
lattice, λ(1)q-qΑ
, β=5.20, mπ=280 MeV
lattice, λ(1)q-qΑ
, β=5.29, mπ=295 MeV
3 leading tensors:I classical tensor:
constrained by STIat large momenta
I chirally symmetricI break chiral symmetry
systematic lattice error?
chirally symmetric tensors from operator q /D3q worsen result
counteracted by tensor structures in Γ(4)AAqq and Γ
(5)A3qq
from q /D3q
⇒ 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:1605.09632 [hep-lat].
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 15 / 22
Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 2017]
quark-gluon interaction most crucial for chiral symmetry breakingtransverse tensor basis (8 tensors), e.g. γµ, i
(/p + /q
)γµ, 1
2
[/p, /q]γµ
λ(i)(p, q)→ λ(i)(p2, q2, p · q)
-1
0
1
2
3
4
5
0.1 1 10
mπ=140 MeV
qu
ark
-glu
on
ve
rte
x d
ressin
gs
p [GeV]
error estimate
λ(1)q-qΑ
, mπ=285
λ(7)q-qΑ
, mπ=285
λ(4)q-qΑ
, mπ=285
lattice, λ(1)q-qΑ
, β=5.20, mπ=280 MeV
lattice, λ(1)q-qΑ
, β=5.29, mπ=295 MeV
3 leading tensors:I classical tensor:
constrained by STIat large momenta
I chirally symmetricI break chiral symmetry
systematic lattice error?
chirally symmetric tensors from operator q /D3q worsen result
counteracted by tensor structures in Γ(4)AAqq and Γ
(5)A3qq
from q /D3q
⇒ 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:1605.09632 [hep-lat].
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 15 / 22
Quark-gluon interactions [Cyrol, MM, Pawlowski, Strodthoff, 2017]
quark-gluon interaction most crucial for chiral symmetry breakingtransverse tensor basis (8 tensors), e.g. γµ, i
(/p + /q
)γµ, 1
2
[/p, /q]γµ
λ(i)(p, q)→ λ(i)(p2, q2, p · q)
-1
0
1
2
3
4
5
0.1 1 10
mπ=140 MeV
qu
ark
-glu
on
ve
rte
x d
ressin
gs
p [GeV]
error estimate
λ(1)q-qΑ
, mπ=285
λ(7)q-qΑ
, mπ=285
λ(4)q-qΑ
, mπ=285
lattice, λ(1)q-qΑ
, β=5.20, mπ=280 MeV
lattice, λ(1)q-qΑ
, β=5.29, mπ=295 MeV
3 leading tensors:I classical tensor:
constrained by STIat large momenta
I chirally symmetricI break chiral symmetry
systematic lattice error?
chirally symmetric tensors from operator q /D3q worsen result
counteracted by tensor structures in Γ(4)AAqq and Γ
(5)A3qq
from q /D3q
⇒ 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:1605.09632 [hep-lat].
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 15 / 22
Gluon propagator [Cyrol, MM, Pawlowski, Strodthoff, 2017]
ΓAA(p) = ZA(p) p2(δµν − pµpν/p2
)
0
0.5
1
1.5
2
2.5
3
0.1 1 10
glu
on
pro
pa
ga
tor
dre
ssin
g 1
/ZA
p [GeV]
error estimate
mπ=140 MeV
mπ=60 MeV
mπ=285 MeV
lattice, β=5.29, mπ=150 MeV
infrared suppression ⇔ “confinement”
insensitive to pion mass
smooth transition to pert. theory
scaling solution: lattice comparison?
lattice data: A. Sternbeck, K. Maltman, M. Muller-Preussker, L. von Smekal, PoS LATTICE2012 (2012) 243.
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 16 / 22
More correlators [Cyrol, MM, Pawlowski, Strodthoff, 2017]
0.5 1.0 1.5 2.0 2.5 3.0
0.5
1.0
1.5
2.0
2.5
3.0
gluon momentum k [GeV]
an
tiq
ua
rkm
om
en
tum
p[G
eV]
λ(1)
1.251.501.752.002.252.502.753.00
-5
0
5
10
15
20
0.1 1 10
mπ=140 MeV
fou
r-fe
rmi ve
rte
x d
ressin
gs
p [GeV]
p2λ
(η’)q-q-qq
p2λ
(S+P)-adj
q-q-qq
p2λ
(V-A)
q-q-qq
p2λ
(V+A)
q-q-qq
p2λ
(V-A)adj
q-q-qq
p2λ
(S-P)-q-q-qq
p2λ
(S-P)-adj
q-q-qq
p2λ
(S+P)+q-q-qq
p2λ
(S+P)+adj
q-q-qq
0
2
4
6
8
10
12
0.1 1 10
mπ=140 MeV
Yu
ka
wa
in
tera
ctio
n d
ressin
gs
p [GeV]
h(1)q-qπ
p*h(2)q-qπ
p*h(3)q-qπ
p2h
(4)q-qπ
-4
-3
-2
-1
0
1
2
3
4
5
0.1 1 10
mπ=140 MeV
2-q
ua
rk-2
-glu
on
ve
rte
x d
ressin
gs
p [GeV]
p2λ
(1)q-qΑ
2
p2λ
(2)q-qΑ
2
p2λ
(3)q-qΑ
2
p2λ
(4)q-qΑ
2
p2λ
(5)q-qΑ
2
p2λ
(6)q-qΑ
2
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 17 / 22
Pure SU(N) YM-theory
[Cyrol, Fister, MM, Pawlowski, Strodthoff, ’16]
[Cyrol, MM, Pawlowski, Strodthoff, ’17]
Truncation (blue: magnetic (transverse) leg, red: electric (longitudinal)leg):
1/Zc(p) λMccA(p) λM
A3(p) λMA4(p)
1/ZMA (p) 1/ZE
A(p) λEA3(p) λE
A4(p)
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 18 / 22
Vacuum [Cyrol, Fister, MM, Pawlowski, Strodthoff, 2016]
truncation: momentum dependent dressing functions for all classical tensors
hardest part of solution: fulfilling the modified STI (⇒ scaling solution)
Γ(2)AA(p) ∝ ZA(p) p2
(δµν − pµpν/p2
)IR-suppression ⇔ “confinement”
smooth transition to perturbation theory
0.1 1 10p [GeV]
0
1
2
3
glu
on p
ropag
ator
dre
ssin
g
FRG, scaling
FRG, decoupling
Sternbeck et al.
running couplings
degeneracy at large p due to STI
test of truncation
0.1 1 10 100p [GeV]
10-6
10-4
10-2
100
run
nin
g c
ou
pli
ng
s
0.5
1
1.5
2
αAcc
αA
3
αA
4
lattice data: A. Sternbeck, E. M. Ilgenfritz, M. Muller-Preussker, A. Schiller, and I. L. Bogolubsky, PoS LAT2006, 076.
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 19 / 22
Vacuum [Cyrol, Fister, MM, Pawlowski, Strodthoff, 2016]
truncation: momentum dependent dressing functions for all classical tensors
hardest part of solution: fulfilling the modified STI (⇒ scaling solution)
Γ(2)AA(p) ∝ ZA(p) p2
(δµν − pµpν/p2
)IR-suppression ⇔ “confinement”
smooth transition to perturbation theory
0.1 1 10p [GeV]
0
1
2
3
glu
on p
ropag
ator
dre
ssin
g
FRG, scaling
FRG, decoupling
Sternbeck et al.
running couplings
degeneracy at large p due to STI
test of truncation
0.1 1 10 100p [GeV]
10-6
10-4
10-2
100
run
nin
g c
ou
pli
ng
s0.5
1
1.5
2
αAcc
αA
3
αA
4
lattice data: A. Sternbeck, E. M. Ilgenfritz, M. Muller-Preussker, A. Schiller, and I. L. Bogolubsky, PoS LAT2006, 076.
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 19 / 22
Propagators at T 6= 0 [Cyrol, MM, Pawlowski, Strodthoff, ’17]
Zeroth mode correlation functions
T = 0
T = 0.45 Tc
T = 0.93 Tc
T = 0.98 Tc
T = 1.01 Tc
T = 1.10 Tc
T = 1.81 Tc
0.1 0.2 0.5 1 2 50
1
2
3
4
5
p [GeV]
magnet
icglu
on
pro
pagato
rdre
ssin
g
SU(2)
T = 0
T = 0.45 Tc
T = 0.98 Tc
T = 1.02 Tc
T = 1.07 Tc
T = 1.36 Tc
T = 1.80 Tc
0.1 0.2 0.5 1 2 50
1
2
3
4
5
p [GeV]
magnet
icglu
on
pro
pagato
rdre
ssin
g
SU(3)
T = 0
T = 0.45 Tc
T = 0.93 Tc
T = 0.98 Tc
T = 1.01 Tc
T = 1.10 Tc
T = 1.81 Tc
0.1 0.2 0.5 1 2 50
2
4
6
8
10
12
p [GeV]
elec
tric
glu
on
pro
pagato
rdre
ssin
g T = 0
T = 0.45 Tc
T = 0.98 Tc
T = 1.02 Tc
T = 1.07 Tc
T = 1.36 Tc
T = 1.80 Tc
0.1 0.2 0.5 1 2 50
2
4
6
8
10
12
p [GeV]
elec
tric
glu
on
pro
pagato
rdre
ssin
g
lattice data: A. Maas, J. M. Pawlowski, L. von Smekal, D. Spielmann, Phys.Rev. D85 (2012) 034037. (SU(2))
P. J. Silva, O. Oliveira, P. Bicudo, and N. Cardoso, Phys. Rev. D89, 074503 (2014). (SU(3))
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 20 / 22
Propagators at T 6= 0 [Cyrol, MM, Pawlowski, Strodthoff, ’17]
Zeroth mode correlation functions
T = 0
T = 0.45 Tc
T = 0.93 Tc
T = 0.98 Tc
T = 1.01 Tc
T = 1.10 Tc
T = 1.81 Tc
0.1 0.2 0.5 1 2 50
1
2
3
4
5
p [GeV]
magnet
icglu
on
pro
pagato
rdre
ssin
g
SU(2)
T = 0
T = 0.45 Tc
T = 0.98 Tc
T = 1.02 Tc
T = 1.07 Tc
T = 1.36 Tc
T = 1.80 Tc
0.1 0.2 0.5 1 2 50
1
2
3
4
5
p [GeV]
magnet
icglu
on
pro
pagato
rdre
ssin
g
SU(3)
T = 0
T = 0.45 Tc
T = 0.93 Tc
T = 0.98 Tc
T = 1.01 Tc
T = 1.10 Tc
T = 1.81 Tc
0.1 0.2 0.5 1 2 50
2
4
6
8
10
12
p [GeV]
elec
tric
glu
on
pro
pagato
rdre
ssin
g T = 0
T = 0.45 Tc
T = 0.98 Tc
T = 1.02 Tc
T = 1.07 Tc
T = 1.36 Tc
T = 1.80 Tc
0.1 0.2 0.5 1 2 50
2
4
6
8
10
12
p [GeV]
elec
tric
glu
on
pro
pagato
rdre
ssin
g
lattice data: A. Maas, J. M. Pawlowski, L. von Smekal, D. Spielmann, Phys.Rev. D85 (2012) 034037. (SU(2))
P. J. Silva, O. Oliveira, P. Bicudo, and N. Cardoso, Phys. Rev. D89, 074503 (2014). (SU(3))
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 20 / 22
Backgrounds, ghost and zero crossing [Cyrol, MM, Pawlowski, Strodthoff, ’17]
〈A0〉 important near Tc , cf. [Herbst et al., ’15]
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5
T [GeV]
Kaczmarek et al. ’02Huebner ’06L[ϕ]
<L>ren+mult
magnetic zero crossing in 3g -vertex
0.0 0.2 0.4 0.6 0.8
0.20
0.25
0.30
0.35
0.40
0.45
T [GeV]
p0[G
eV]
T = 0
T = 0.45 Tc
T = 0.93 Tc
T = 0.98 Tc
T = 1.01 Tc
T = 1.10 Tc
T = 1.81 Tc
0.5 1 2 51.0
1.5
2.0
2.5
3.0
p [GeV]
ghost
pro
pagato
rdre
ssin
g
T = 0
T = 0.075 GeV
T = 0.125 GeV
T = 0.200 GeV
T = 0.400 GeV
T = 0.800 GeV
0.05 0.10 0.50 1 5 10-1.5
-1.0
-0.5
0.0
0.5
1.0
p [GeV]
magnet
icth
ree-
glu
on
ver
tex
dre
ssin
g
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 21 / 22
Backgrounds, ghost and zero crossing [Cyrol, MM, Pawlowski, Strodthoff, ’17]
〈A0〉 important near Tc , cf. [Herbst et al., ’15]
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5
T [GeV]
Kaczmarek et al. ’02Huebner ’06L[ϕ]
<L>ren+mult
magnetic zero crossing in 3g -vertex
0.0 0.2 0.4 0.6 0.8
0.20
0.25
0.30
0.35
0.40
0.45
T [GeV]
p0[G
eV]
T = 0
T = 0.45 Tc
T = 0.93 Tc
T = 0.98 Tc
T = 1.01 Tc
T = 1.10 Tc
T = 1.81 Tc
0.5 1 2 51.0
1.5
2.0
2.5
3.0
p [GeV]
ghost
pro
pagato
rdre
ssin
g
T = 0
T = 0.075 GeV
T = 0.125 GeV
T = 0.200 GeV
T = 0.400 GeV
T = 0.800 GeV
0.05 0.10 0.50 1 5 10-1.5
-1.0
-0.5
0.0
0.5
1.0
p [GeV]
magnet
icth
ree-
glu
on
ver
tex
dre
ssin
g
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 21 / 22
Status and Outlook
vacuum QCDI QCD from αS(Λ = O(10) GeV) and mq(Λ = O(10) GeV)I good agreement with lattice correlatorsI more checks on convergence of vertex expansion
finite temperature YM-theory:I good agreement with magnetic lattice correlatorsI electric correlators: argued for importance of backgrounds near Tc
I Debye mass consistent with perturbation theory at T & 0.6 GeV
next stop: QCD @ T , µ > 0I equation of stateI fluctuations of conserved chargesI order parameters
further applications:I input for “QCD-enhanced” modelsI other strongly-interacting theories
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 22 / 22
Status and Outlook
vacuum QCDI QCD from αS(Λ = O(10) GeV) and mq(Λ = O(10) GeV)I good agreement with lattice correlatorsI more checks on convergence of vertex expansion
finite temperature YM-theory:I good agreement with magnetic lattice correlatorsI electric correlators: argued for importance of backgrounds near Tc
I Debye mass consistent with perturbation theory at T & 0.6 GeV
next stop: QCD @ T , µ > 0I equation of stateI fluctuations of conserved chargesI order parameters
further applications:I input for “QCD-enhanced” modelsI other strongly-interacting theories
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 22 / 22
Status and Outlook
vacuum QCDI QCD from αS(Λ = O(10) GeV) and mq(Λ = O(10) GeV)I good agreement with lattice correlatorsI more checks on convergence of vertex expansion
finite temperature YM-theory:I good agreement with magnetic lattice correlatorsI electric correlators: argued for importance of backgrounds near Tc
I Debye mass consistent with perturbation theory at T & 0.6 GeV
next stop: QCD @ T , µ > 0I equation of stateI fluctuations of conserved chargesI order parameters
further applications:I input for “QCD-enhanced” modelsI other strongly-interacting theories
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 22 / 22
Status and Outlook
vacuum QCDI QCD from αS(Λ = O(10) GeV) and mq(Λ = O(10) GeV)I good agreement with lattice correlatorsI more checks on convergence of vertex expansion
finite temperature YM-theory:I good agreement with magnetic lattice correlatorsI electric correlators: argued for importance of backgrounds near Tc
I Debye mass consistent with perturbation theory at T & 0.6 GeV
next stop: QCD @ T , µ > 0I equation of stateI fluctuations of conserved chargesI order parameters
further applications:I input for “QCD-enhanced” modelsI other strongly-interacting theories
M. Mitter (BNL) Correlators of QCD Giessen, January 2018 22 / 22