QCD from quark, gluon, and meson correlators fileQCD from quark, gluon, and meson correlators Mario Mitter Brookhaven National Laboratory Giessen, January 2018 M. Mitter (BNL) Correlators

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?




Temperature

µ

early universe

neutron star cores

LHCRHIC

AGS

SIS


hadronic fluid


SPS

FAIR/NICA

n = 0 n > 0

<ψψ> ∼ 0

/<ψψ> = 0

/<ψψ> = 0

phases ?

quark matter

crossover

CFLB B


2SC

crossover


large part of this effort: vacuum QCD and YM-theory

why?




Temperature

µ

early universe

neutron star cores

LHCRHIC

AGS

SIS


hadronic fluid


SPS

FAIR/NICA

n = 0 n > 0

<ψψ> ∼ 0

/<ψψ> = 0

/<ψψ> = 0

phases ?

quark matter

crossover

CFLB B


2SC

crossover


large part of this effort: vacuum QCD and YM-theorywhy?


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]



∑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)













∑n

∫{pi} Γ

(n)Φ1···Φn

(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)














∑n

∫{pi} Γ

(n)Φ1···Φn

(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)














∑n

∫{pi} Γ

(n)Φ1···Φn

(p1, . . . , pn−1)Φ1(p1) · · ·Φn(−p1 − · · · − pn−1)













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]


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]


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],. . .


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


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?


Nonperturbative QCD











Nonperturbative QCD











(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]






∂kΓk [A, c , c , q, q] = 12 − −



k→0Γk [Φ]






∂kΓk [A, c , c , q, q] = 12 − −



k→0Γk [Φ]






∂kΓk [A, c , c , q, q] = 12 − −



k→0Γk [Φ]






∂kΓk [A, c , c , q, q] = 12 − −



k→0Γk [Φ]


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]



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


0

5

10

15

20

25

30

1 10

Yukaw

a inte

raction h

π

RG-scale k [GeV]

[Braun, Fister, Pawlowski, Rennecke, 2014]



Nf = 2 Landau-gauge QCD [Cyrol, MM, Pawlowski, Strodthoff, 2017]

Truncation:

systematics of improving the truncation?

⇒ BRST-invariant operators, e.g. ψ /Dnψ


Nf = 2 Landau-gauge QCD [Cyrol, MM, Pawlowski, Strodthoff, 2017]

Truncation:

systematics of improving the truncation?

⇒ BRST-invariant operators, e.g. ψ /Dnψ


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





∂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





∂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


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]


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]


(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


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


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].


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?





(/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







(5)A3qq

from q /D3q






(/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







(5)A3qq

from q /D3q






(/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







(5)A3qq

from q /D3q




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


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.


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


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)


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.


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.


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))


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))


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


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


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


Status and Outlook







Status and Outlook







Status and Outlook







Documents

QCD from quark, gluon, and meson correlators fileQCD from quark, gluon, and meson correlators Mario Mitter Brookhaven National Laboratory Giessen, January 2018 M. Mitter (BNL) Correlators