The phase diagram of two flavour QCD Jan M. Pawlowski Universitt - - PowerPoint PPT Presentation

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The phase diagram of two flavour QCD Jan M. Pawlowski Universitt - - PowerPoint PPT Presentation

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The phase diagram of two flavour QCD Jan M. Pawlowski Universitt Heidelberg & ExtreMe Matter Institute Quarks, Gluons and the Phase Diagram of QCD St. Goar, September 2nd 2009 Outline Phase diagram of two flavour QCD Quark

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Jan M. Pawlowski

Universität Heidelberg & ExtreMe Matter Institute Quarks, Gluons and the Phase Diagram of QCD

  • St. Goar, September 2nd 2009

The phase diagram of two flavour QCD

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  • Phase diagram of two flavour QCD
  • Quark confinement & chiral symmetry breaking
  • Chiral phase structure at finite density
  • Summary and outlook

Outline

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Phase diagram of QCD

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FAIR, www.gsi.de

Strongly correlated quark-gluon-plasma ’RHIC serves the perfect fluid’

quarkyonic: confinement & chiral symmetry hadronic phase confinement & chiral symmetry breaking

Phase diagram of QCD

massless quarks (chiral symmetry) deconfinement

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SLIDE 5

Phase diagram of two flavour QCD

(chiral limit)

0.2 0.4 0.6 0.8 1 150 160 170 180 190 200 210 220 230 T [MeV]

fπ(T)/fπ(0) Dual density Polyakov Loop 160 180 200 χL,dual

50 100 150 200 250 300 π/3 2π/3 π 4π/3 T [MeV] 2πθ Tconf Tχ

RG-flows in QCD

Braun, Haas, Marhauser,JMP ’09 Schaefer, JMP , Wambach ‘07 (chiral limit)

  • cf. talks by J. Braun & L. Haas
  • cf. talks by K. Fujushima
  • W. Weise

B.-J. Schaefer

PNJL & PQM model Continuum methods

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SLIDE 6

Phase diagram of two flavour QCD

(chiral limit)

0.2 0.4 0.6 0.8 1 150 160 170 180 190 200 210 220 230 T [MeV]

fπ(T)/fπ(0) Dual density Polyakov Loop 160 180 200 χL,dual

50 100 150 200 250 300 π/3 2π/3 π 4π/3 T [MeV] 2πθ Tconf Tχ

Continuum methods

Braun, Haas, Marhauser,JMP ’09 Schaefer, JMP , Wambach ‘07 (chiral limit)

  • cf. talks by J. Braun & L. Haas

Full dynamical QCD

  • cf. talks by K. Fujushima
  • W. Weise

B.-J. Schaefer

PNJL & PQM model RG-flows in QCD

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SLIDE 7

Quark confinement & chiral symmetry breaking

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Confinement

Continuum methods

Braun, Gies, JMP ‘07

p2A A(p2)

p2C ¯ C(p2)

p [GeV]

V [A0] = −1 2Tr logAA[A0] + O(∂tAA) − Tr logC ¯ C[A0] + O(∂tC ¯ C) + O(V ′′[A0])

(Functional RG-flows)

RG-scale k: t = ln k

p0 → 2πTn − gA0

Fischer, Maas, JMP ’08 JMP , in preparation

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SLIDE 9

Confinement

Continuum methods

p2A A(p2)

p2C ¯ C(p2)

p [GeV]

subleading for Tc,conf

V [A0] = −1 2Tr logAA[A0] + O(∂tAA) − Tr logC ¯ C[A0] + O(∂tC ¯ C) + O(V ′′[A0])

‘Polyakov loop potential’

Braun, Gies, JMP ‘07 Fischer, Maas, JMP ’08 JMP , in preparation

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k ∂k

−1 =

−

⊗

−

⊗

+ 1

2

⊗

+ 1

2

⊗

− 1

2

⊗

+

⊗

k ∂k

−1 =

⊗

+

⊗

− 1

2

⊗

+

⊗

Confinement

Continuum methods

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SLIDE 11

Confinement

Continuum methods

Φ[Ac

0] = 1

3(1 + 2 cos 1 2βAc

0)

Φ[8 3π] = 0

Braun, Gies, JMP ‘07

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Confinement

Continuum methods

for SU(N), G(2), Sp(2) cf. talk by Jens Braun Braun, Gies, JMP ‘07

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Universal properties & gauge independence

Continuum methods

JMP , Marhauser ‘08

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Imaginary chemical potential

  • Roberge-Weiss symmetry

Lattice & Continuum QCD

µI = 2πTθ

ψθ(t + β, x) = −e2πiθψθ(t, x)

Zθ = Zθ+1/3

with

deconfining confining

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Dual order parameter

  • Lattice
  • Continuum

Lattice & Continuum QCD

z = e2πiθz

  • rder parameter for confinement

Oθ = O[e2πiθt/βψ] with ψθ(t + β, x) = −e2πiθψθ(t, x)

imaginary chemical potential µ = 2πiθ/β for ψθ = e2πiθt/βψ

Dual order parameter

Braun, Haas, Marhauser, JMP ‘09 Bruckmann, Hagen, Bilgici, Gattringer ‘08 Fischer, ’09; Fischer, Mueller ‘09 Gattringer ‘06 Synatschke, Wipf, Wozar ‘08

imaginary chemical potential

˜ O = 1 dθ Oθe−2πiθ

  • cf. talks by J. Braun, C. Fischer, L. Haas, A. Wipf
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  • no imaginary chemical potential (lattice studies):
  • imaginary chemical potential I: evaluated at equations of motion
  • imaginary chemical potential II: evaluated at a fixed background

Lattice & Continuum QCD ˜ O = 1 dθ Oθe−2πiθ

Dual order parameter

˜ O[A0θ] ≡ 0

˜ O[A0θ] = 0

Roberge-Weiss breaking of Roberge-Weiss DSE: 4 loop and more

˜ O

FRG: 3 loop and more standard FRG & DSE

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  • no imaginary chemical potential (lattice studies):
  • imaginary chemical potential I: evaluated at equations of motion
  • imaginary chemical potential II: evaluated at a fixed background

Lattice & Continuum QCD ˜ O = 1 dθ Oθe−2πiθ

˜ O[A0θ] ≡ 0

˜ O[A0θ] = 0

Roberge-Weiss breaking of Roberge-Weiss DSE: 4 loop and more

˜ O

FRG: 3 loop and more standard FRG & DSE

Dual order parameter

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Dual order parameter

Continuum methods

(Functional RG-flows)

z = e2πiθz

1 dθ Oθe−2πiθ

  • rder parameter for confinement

Braun, Haas, Marhauser, JMP ‘09

fπ

θ

fπ(T, θ)

Oθ = O[e2πiθt/βψ] with ψθ(t + β, x) = −e2πiθψθ(t, x)

T T

imaginary chemical potential µ = 2πiθ/β for ψθ = e2πiθt/βψ

’fermionic pressure difference’ p(T, θ) ≃ P(T, θ) − P(T, 0)

fixed A0: no Roberge-Weiss periodicity

θ

p

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Full dynamical QCD: N_f = 2 & chiral limit

  • RG-flow of Effective Action (Effective Potential)
  • flow of gluon propagator

Continuum methods

(Functional RG-flows)

pure gauge theory flow + +

quark quantum fluctuations mesonic quantum fluctuations

∂tΓk[φ] = 1

2

− − + 1

2

...

  • cf. talk by L. Haas
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Full dynamical QCD: N_f = 2 & chiral limit

Continuum methods

0.2 0.4 0.6 0.8 1 150 160 170 180 190 200 210 220 230 T [MeV]

fπ(T)/fπ(0) Dual density Polyakov Loop 160 180 200 χL,dual

Tχ = Tconf ≃ 180MeV

  • cf. talks by J. Braun & L. Haas

Braun, Haas, Marhauser, JMP ‘09

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Full dynamical QCD: N_f = 2 & chiral limit

Continuum methods

140 160 180 200 220 240

T [MeV]

0% 0.2% 0.4% 0.6% 0.8% 1%

Δn/L

~

Deviation of dual density from Polyakov loop

∆˜

n

Φ

∆˜

n = ˜

n[A0] ˜ n[0] − Φ[A0] :

Braun, Haas, Marhauser, JMP ‘09

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Full dynamical QCD: N_f = 2 & chiral limit

Continuum methods & lattice compatible with Karsch et al ’08 compatible with Fodor et al ’08?

175MeV ≃ Tc,conf > Tc,χ ≃ 150MeV

Nf = 2 + 1 Nf = 2 + 1

Nf = 2

0.2 0.4 0.6 0.8 1 150 160 170 180 190 200 210 220 230 T [MeV]

fπ(T)/fπ(0) Dual density Polyakov Loop 160 180 200 χL,dual

Tχ = Tconf ≃ 180MeV

Braun, Haas, Marhauser, JMP ‘09

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Full dynamical QCD: N_f = 2 & chiral limit

Continuum methods

chemical potential : µ = 2πi T θ

50 100 150 200 250 300 π/3 2π/3 π 4π/3 T [MeV] 2πθ Tconf Tχ

Braun, Haas, Marhauser, JMP ‘09

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SLIDE 24

Full dynamical QCD: N_f = 2 & chiral limit

Continuum methods & lattice lattice results Kratochvila et al ‘06 & Wu et al ‘06 adjust 8-fermi interaction Polyakov-NJL model Sakai et al ‘09

agreement 50 100 150 200 250 300 π/3 2π/3 π 4π/3 T [MeV] 2πθ Tconf Tχ

Tχ

Tconf

Braun, Haas, Marhauser, JMP ‘09

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Chiral phase structure at finite density

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Phase diagram of QCD

Schaefer, JMP , Wambach ‘07

quarkyonic phase?

washed out by quantum fluctuations? Polyakov - Quark-Meson model

Nf = 2

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Summary & Outlook

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Summary & outlook

  • Phase diagram of QCD
  • Confinement & chiral symmetry breaking at finite temperature

0.2 0.4 0.6 0.8 1 150 160 170 180 190 200 210 220 230 T [MeV]

fπ(T)/fπ(0) Dual density Polyakov Loop 160 180 200 χL,dual

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  • Phase diagram of QCD
  • Confinement & chiral symmetry breaking at finite temperature
  • Dynamical hadronisation
  • Next steps: real chemical potential & 2+1 flavours

QCD flows dynamically into hadronic effective theories work in progress

0.2 0.4 0.6 0.8 1 150 160 170 180 190 200 210 220 230 T [MeV]

fπ(T)/fπ(0) Dual density Polyakov Loop 160 180 200 χL,dual

Summary & outlook

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Summary & outlook

  • Phase diagram of QCD
  • Confinement & chiral symmetry breaking at finite temperature
  • Dynamical hadronisation
  • critical point and phase lines in effective theories
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SLIDE 31
  • Phase diagram of QCD
  • Confinement & chiral symmetry breaking at finite temperature
  • Dynamical hadronisation
  • critical point and phase lines in effective theories
  • Hadronic properties
  • Next step

Top-down meets bottom-up Refine effective hadronic theories e.g.

Summary & outlook

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Summary & outlook

  • Phase diagram of QCD
  • Confinement & chiral symmetry breaking at finite temperature
  • Dynamical hadronisation
  • critical point and phase lines in effective theories
  • Hadronic properties
  • non-equilibrium physics