qcd phase diagram with functional methods -...

Christian S. Fischer

Justus Liebig Universität Gießen

Christian Fischer (University of Gießen) QCD phase diagram / 34

work together with

Jan Lücker, Axel Maas and Jens Müller

28. August 2012

QCD phase diagram with functional methods

1


0 50 100 150 200 250 300µ [Mev]

100

150

200

T [M

eV]

CEP, Nf=2CEP, Nf=2+1Chiral crossoverChiral 1st order

1.Introduction

2.Gluons at zero and finite temperature

3.Quarks and the QCD phase diagram

Overview

2


Phase diagram of water

3

first order

second order

Pressure

Temperature

Source: Wikipedia


Connecting small and large scales

4

History of our universe...

© CERN

RHIC, ALICE, CBM

...studied in laboratory


baryons, mesons (and glueballs ?) linear rising potential at large distance: string breaking

Properties of QCD: Confinement

5

Quark confinement

Millenium-Prize (1 Mio Dollar)Clay Mathematics Institute

Bali, Phys. Rept 343 (2001)


Properties of QCD: Dynamical mass generation

6

Dynamical quark masses via weak and strong force Yoichiro Nambu,

Nobel prize 2008

u d s c b tMweak 3 5 80 1200 4500 176000Mstrong 350 350 350 350 350 350Mtotal 350 350 450 1500 4800 176000[MeV/c2]

[MeV/c2]

[MeV/c2]

S−1(p) = [ip/ +M(p2)]/Zf (p2)

Input parameters in Nf=2+1 QCD


Properties of QCD: Dynamical mass generation

7

S−1(p) = [ip/ +M(p2)]/Zf (p2)


Details of phase transitions Existence and location of critical point Properties of quarks and gluons in different phases Consequences for astrophysics

QCD phase diagram

8

Interesting open questions:

Quarks confinedand massive

Quarks de-confinedand (almost) massless


QCD phase transitions I

9

S−1(p) = [ip/ +M(p2)]/Zf (p2)


QCD phase transitions II

10

Static Quarks (Mweak ➝∞)

Chiral Limit Nf=3 (Mweak ➝ 0)

Chiral Limit

Is this happening ??

P. de Forcrand and O. Philipsen, PoS LATTICE 2008 (2008) 208


0 50 100 150 200 250 300µ [Mev]

100

150

200

T [M

eV]


1.Introduction



Overview

11


QCD in covariant gauge

12


Lattice QCD vs. DSE/FRG: Complementary!

13

Models: PNJL, PQM

Technically easierExploratory


DSE vs. Lattice (T=0)

14

0 1 2 3 4 5p [GeV]

0

0.5

1

1.5

Z(p2 )

Sternbeck et. al. (2006)Funktionalzugang

CF, Maas, Pawlowski, Annals Phys. 324 (2009) 2408.


analytic away from real axis cut structure for time-like real momenta positivity violations for gluon ‘quasiparticle mass’ of about 600-700 MeV

Analytic structure of gluon propagator

15

GluonPropagator-RealPart

GluonPropagator-RealPart

-2 -1 0 1 2!p2 -2-1

01

2

"p2-15

-10

-5

0

5

10

15

-15-10-5051015

-2 -1 0 1 2!p2 -2-1

01

2

"p2-15

-10

-5

0

5

10

15

-15-10-5051015

spectral function

Alkofer, Detmold, CF, Maris, PRD 70 (2004) 014014 Strauss, CF, Kellermann, to appear


Glue at finite temperature (T≠0)

16


Gluon screening mass: SU(2) vs. SU(3)

17

Bali, Phys. Rept 343 (2001)


0 50 100 150 200 250 300µ [Mev]

100

150

200

T [M

eV]


1.Introduction



Overview

18


much studied at T=0

T≠0: ansatz, T,m,μ dependent

DSEs of QCD

19

quenched latticepropagator

quark gluon vertex


Order parameter: the dressed Polyakov-loop

20

ordinary Polyakov-loop: Φ = P̂ exp

�ig

� 1/T

0dτA4(τ, �x)

�

zn

sensitive to center transformation

Now consider general U(1)-valued boundary conditions intemporal direction for quark fields:

i!

e ψ(�x, 1/T ) = eiϕ ψ(�x, 0)

ω(nt) = (2πT )(nt + ϕ/2π)

x

t

zn = exp[2πi n/Nc] , n = 0..Nc − 1


Order parameter: the dressed Polyakov-loop II

21

�ψψ�ϕ =1

V m

�

l

eiϕn(l)

(2am)|l|TrcU(l)

m :explicit quark mass

a :lattice spacing

V :volume

|l| :Loop length

winding number

closed loops

m → ∞ : n(l) = 1

are ordinary Polyakov-loops

!

ei


The dual condensate/dressed Polyakov loop

22


QCD phase transition: heavy quark limit/quenched

23


Transition temperatures, quenched

24

ConfinementDeconfinement

1st order


T>Tc: positive curvature - quasiparticle picture possibleT<Tc: negative curvature - positivity violations

Quenched QCD: Positivity violations I

25

Schwinger function: S(τ) = T�

np

eiτωp

�iωnC(iωn) +B(iωn)

ω2nC

2(iωn) +B2(iωn)

�

Karsch and Kitazawa, PRD 80, 056001 (2009)Mueller, CF, Nickel, EPJC 70 (2010) 1037-1049


QCD phase transitions: Nf=2

26


Tχ ≈185 MeVTconf ≈195 MeVsimilar results in FRG-approach J. Braun, L. Haas, F. Marhauser, J. M. Pawlowski, PRL 106 (2011) 022002

Nf=2: Transition temperatures at μ=0

27

Crossover!

CF, Luecker, Mueller, PLB 702 (2011) 438-441CF, Luecker, arXiv:1206.5191.


chiral CEPcrucial: backreaction of quark onto gluonqualitative agreement with RG-improved PQM model

Herbst, Pawlowski, Schaefer, PLB 696 (2011)

Nf=2: QCD phase diagram

28

CF., J. Luecker, J. A. Mueller, PLB 702 (2011) 438-441CF., J Luecker, arXiv:1206.5191


Physical up/down and strange quark masses Transition controlled by chiral dynamics at μ=0: compare to available lattice results

QCD phase transitions: Nf=2+1

29


Lattice extrapolation reliable for μ/T ≤ 1No CEP for small chemical potentialPQM plus RG-methods (functional methods)

Phase diagram: Lattice - PQM

30

Endrodi, Fodor, Katz, Szabo, JHEP 1104 (2011) 001 Herbst, Pawlowski, Schaefer, PLB 696 (2011) 58

100 200


solve coupled system of three equations

DSEs with Nf=2+1

31


semi-quantitative agreement

Nf=2+1, zero chemical potential

32

Lattice: Borsanyi et al. [Wuppertal-Budapest Collaboration], JHEP 1009(2010) 073DSE: CF, Luecker, arXiv:1206.5191

100 150 200 250T [MeV]

0

0.2

0.4

0.6

0.8

1

Δl,s

(T)/Δ

l,s(0

)

DSELattice QCD

zero chemical potential

Crossover

quark-gluon interaction not adjusted to restored phase


large temperatures: behavior as expected from HTLfirst order transition at large chemical potential

Nf=2+1: thermal electric gluon mass

33

CF., J Luecker, arXiv:1206.5191


no quarkyonic regionno CEP at μc/Tc < 1 in agreement with lattice

Nf=2+1: phase diagram

34

CF, Luecker, arXiv:1206.5191

Quarks are screening

CEP at large μ

??

de Forcrand, Philipsen, JHEP 0811 (2008) 012; Nucl Phys. B642 (2002) 290-306Endrodi, Fodor, Katz, Szabo, JHEP 1104 (2011) 001.


Temperature dependent gluon propagatorcharacteristic behavior of electric gluon‘melting’ of magnetic gluon with temperature

Deconfinement Tc from dressed Polyakov-loop via DSEs

QCD with finite chemical potential (beyond mean field)backreaction of quarks onto gluons importantNf=2+1: CEP at μc/Tc > 1

Summary

35

QCD phase diagram:

Other topics:Meson structure (pion cloud, form factors etc.)

CF and R. Williams, PRL 103, 122001 (2009)

Baryon structure (3-body problem, form factors etc.) G. Eichmann and CF, PRD 85 (2012) 034015, EPJA 48 (2012) 9

Hadronic contributions to (g-2)μ T. Goecke, CF, R. Williams, PLB 704 (2011); PRD 83 (2011)

qcd phase diagram with functional methods -...

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