Introduction Effective Description Phase Structure Conclusion

The Impact of Fluctuations

on QCD Matter

Tina Katharina Herbst

In Collaboration with: B.-J. Schaefer, J. M. Pawlowski, M. Wagner

TKH, J.M. Pawlowski, B.-J. Schaefer, Phys.Lett. B696 (2011) 58

“Three Days on Quarkyonic Island”

May 19th - 21st, 2011

Recipient of a DOC-fFORTE-fellowship of the Austrian Academy of Sciences

at the Institute of Physics.

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Motivation

Lattice

Models

Critical Point

Quarkyonic Island

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Motivation

Lattice

Models

Critical Point

Quarkyonic Island

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Motivation

Lattice

Models

Critical Point

Quarkyonic Island

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Motivation

Lattice

Models

Critical Point

Quarkyonic Island

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Motivation

Lattice

Models

Critical Point

Quarkyonic Island

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Renormalization Group

Phase Transitions:

Fluctuations on all Scales contribute

Microscopic Description →Macroscopic Description

UV → IR

Wetterich Equation [Wetterich, 1993]

∂kΓk [φ] =1

2Tr

{∂kRk

(Γ

(2)k [φ] + Rk

)−1}

Rk . . . regulator

Γk · · · scale dependent effective action

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Renormalization Group

Phase Transitions:

Fluctuations on all Scales contribute

Microscopic Description →Macroscopic Description

UV → IR

Wetterich Equation [Wetterich, 1993]

∂kΓk [φ] =1

2Tr

{∂kRk

(Γ

(2)k [φ] + Rk

)−1}

Rk . . . regulator

Γk · · · scale dependent effective action

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Polyakov-Quark-Meson ModelLagrangian

LPQM = q̄[i /D − h(σ + iγ5~τ · ~π)

]q +

1

2(∂µφ)2

− U(σ, ~π) − U(Φ, Φ̄)

φ = (σ, ~π) . . . O(4)-representation of the meson field (Nf = 2)

Φ, Φ̄ . . . Polyakov loop, D/ (Φ) = γµ∂µ − i gγ0A0(Φ)

g . . . gauge coupling

h . . . Yukawa coupling

Meson Potential

U(σ, ~π) =λ

4(σ2 + ~π2 − v2)2 − cσ

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Polyakov-Quark-Meson ModelLagrangian

LPQM = q̄[i /D − h(σ + iγ5~τ · ~π)

]q +

1

2(∂µφ)2

− U(σ, ~π) − U(Φ, Φ̄)

φ = (σ, ~π) . . . O(4)-representation of the meson field (Nf = 2)

Φ, Φ̄ . . . Polyakov loop, D/ (Φ) = γµ∂µ − i gγ0A0(Φ)

g . . . gauge coupling

h . . . Yukawa coupling

Polyakov Loop Potential

U(Φ, Φ̄)

T 4= −b2(T ,T0)

2ΦΦ̄− b3

6(Φ3 + Φ̄3) +

b4

4(ΦΦ̄)2

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Polyakov-Quark-Meson ModelLagrangian

LPQM = q̄[i /D − h(σ + iγ5~τ · ~π)

]q +

1

2(∂µφ)2

− U(σ, ~π) − U(Φ, Φ̄)

φ = (σ, ~π) . . . O(4)-representation of the meson field (Nf = 2)

Φ, Φ̄ . . . Polyakov loop, D/ (Φ) = γµ∂µ − i gγ0A0(Φ)

g . . . gauge coupling

h . . . Yukawa coupling

Polyakov Loop Potential

U(Φ, Φ̄)

T 4= −b2(T ,T0)

2ΦΦ̄− b3

6(Φ3 + Φ̄3) +

b4

4(ΦΦ̄)2

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Backcoupling of Matter Sector I

[Schaefer, Pawlowski, Wambach, PRD 2007]

FRG flow for QCD: [J. Braun et al., PRL 2011]

gluons ghosts quarks mesons

∂tΓk[φ] =12 − − + 1

2∂tΓk[A,C,ψ,φ]

Polyakov Loop potential: ∂tΓk[φ] =12 −∂tΓk[A,C]

T0 → T0(Nf , µ)

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Backcoupling of Matter Sector I

[Schaefer, Pawlowski, Wambach, PRD 2007]

FRG flow for QCD: [J. Braun et al., PRL 2011]

gluons ghosts quarks mesons

∂tΓk[φ] =12 − − + 1

2∂tΓk[A,C,ψ,φ]

Polyakov Loop potential: ∂tΓk[φ] =12 −∂tΓk[A,C]

T0 → T0(Nf , µ)

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Backcoupling of Matter Sector I

[Schaefer, Pawlowski, Wambach, PRD 2007]

FRG flow for QCD: [J. Braun et al., PRL 2011]

gluons ghosts quarks mesons

∂tΓk[φ] =12 − − + 1

2∂tΓk[A,C,ψ,φ]

Polyakov Loop potential: ∂tΓk[φ] =12 −∂tΓk[A,C]

T0 → T0(Nf , µ)

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Backcoupling of Matter Sector II[Fukushima, 2010]

Experiment:chemical freezeout points

entropy (red band)and density suggests position of phasetransition

pure PNJL computation(T0 = 200 MeV, green band)inconsistent

polynomial ansatz for T0(µ)⇒ greater overlap (blue band)

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[in these plots: Nc = Nf = 3]

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

T0(µ) - How To[Schaefer, Pawlowski, Wambach, PRD 2007]

[TKH, Pawlowski, Schaefer, PLB 2011]

T0 ←→ ΛQCD

perturbative 1-loop estimate:

β(α) = −b(Nf ) α2 +O(α3)

µ 6= 0⇒ HDL/HTL:

b(Nf )→ b(Nf , µ)[Bethke, NPPS 2004]

T0(Nf , µ) = Tτe−1/(α0b(Nf ,µ))

Nf 0 1 2 2 + 1 3

T0 [ MeV] 270 240 208 187 178

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

R E S U L T S

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Mean Field: T0 = 208 MeV, mπ = 138 MeV

[Schaefer, Pawlowski, Wambach, PRD 2007]

CEP↗

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

RG - PQM: T0 = 208MeV, mπ = 138 MeV

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

χ crossoverΦ crossoverΦ* crossoverχ 1st order

[TKH, Pawlowski, Schaefer, PLB 2011; TKH et al., in prep. 2011]

↙ CEP

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

RG - PQM: T0(µ),T0(0) = 208MeV, mπ = 138 MeV

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

χ crossoverΦ crossoverΦ* crossoverχ 1st order

[TKH, Pawlowski, Schaefer, PLB 2011; TKH et al., in prep. 2011]

↙ CEP

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

RG - QM: mπ = 0

0

20

40

60

80

100

120

140

160

0 50 100 150 200 250 300

Tc

[MeV

]

µ [MeV]

0

5

10

15

20

240 250 260 270 280 290

[Schaefer, Wambach, NPA 2005]

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

RG - PQM: T0 = 208MeV, mπ = 0

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

2nd order1st orderTCP

[TKH et al., in prep. 2011]

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

RG - PQM: T0 = 208MeV, mπ = 50 MeV

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

crossover1st orderCEP

[TKH et al., in prep. 2011]

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

RG - PQM: T0 = 208MeV, mπ = 138 MeV

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

crossover1st orderCEP

[TKH et al., in prep. 2011]

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Summary

PQM model beyond Mean Field

quark-meson fluctuations included within FRG approachImportant feature:back-reaction to gluonic sector

T0 → T0(Nf , µ)

Modifications of the Phase Structure

fluctuations push CEP downwardsT0(µ): chiral and deconfinementtransitions coincide quarkyonic phase shrinks

Mass

splitting in chiral transitionat small T disappears for physical mπ

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

χ crossoverΦ crossoverΦ* crossoverχ 1st order

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Summary

PQM model beyond Mean Field

quark-meson fluctuations included within FRG approachImportant feature:back-reaction to gluonic sector

T0 → T0(Nf , µ)

Modifications of the Phase Structure

fluctuations push CEP downwardsT0(µ): chiral and deconfinementtransitions coincide quarkyonic phase shrinks

Mass

splitting in chiral transitionat small T disappears for physical mπ

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

χ crossoverΦ crossoverΦ* crossoverχ 1st order

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)

Introduction Effective Description Phase Structure Conclusion

Summary

PQM model beyond Mean Field

quark-meson fluctuations included within FRG approachImportant feature:back-reaction to gluonic sector

T0 → T0(Nf , µ)

Modifications of the Phase Structure

fluctuations push CEP downwardsT0(µ): chiral and deconfinementtransitions coincide quarkyonic phase shrinks

Mass

splitting in chiral transitionat small T disappears for physical mπ

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

χ crossoverΦ crossoverΦ* crossoverχ 1st order

The Impact of Fluctuations on QCD Matter Tina K. Herbst (KFU Graz)