Phases and Fluctuations in QCD Bernd-Jochen Schaefer Austria - - PowerPoint PPT Presentation
Phases and Fluctuations in QCD Bernd-Jochen Schaefer Austria Germany Germany October 10 th 2014 Agenda Phase transitions and QCD QCD-like model studies chiral and deconfinement aspects
Germany
October 10th 2014
Austria Germany
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QCD under extreme conditions: active field for the next 20 years ➜ see e.g. FAIR construction (2014)
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QCD under extreme conditions: active field for the next 20 years ➜ see e.g. FAIR construction (2014)
FAIR construction start 2012
Aug.2014
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QCD at finite temperatures and densities ➜ “transitions” partial deconfinement & partial chiral symmetry restoration
For physical quark masses: smooth phase transitions ➜ deconfinement: analytic change of d.o.f. for finite quark masses: both symmetries explicitly broken ➜ associated global QCD symmetries only exact in two mass limits:
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mc
1.) infinite quark masses ➜ center symmetry: Order parameter: VEV of traced Polyakov loop 2.) massless quarks ➜ chiral symmetry: Order parameter: chiral condensate
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QCD at finite temperatures and densities ➜ “transitions” partial deconfinement & partial chiral symmetry restoration
For physical quark masses: smooth phase transitions ➜ deconfinement: analytic change of d.o.f. for finite quark masses: both symmetries explicitly broken ➜ associated global QCD symmetries only exact in two mass limits:
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mc
1.) infinite quark masses ➜ center symmetry: Order parameter: VEV of traced Polyakov loop 2.) massless quarks ➜ chiral symmetry: Order parameter: chiral condensate still conflicting lattice results!
U(2)L×U(2)R/U(2)V?
➜ crit. exp. similar
1st order Z(2) crossover mπ = 0 mπ,c 2nd order crossover mπ = ∞
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Temperature µ
early universe neutron star cores
LHC RHIC SIS AGS
quark−gluon plasma hadronic fluid nuclear matter vacuum
FAIR/JINR SPS
n = 0 n > 0 <ψψ> ∼ 0 <ψψ> = 0 / <ψψ> = 0 /
phases ? quark matter
crossover
CFL
B B
superfluid/superconducting
2SC
crossover
➜ can one improve the model calculations? ➜ remove model ambiguities
Lattice simulations
135 140 145 150 155 160 165 170 175 180 185 190 195 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Tc [MeV] N
Physical ml/ms
Combined continuum extrapolation
HISQ/tree: quadratic in N
Asqtad: quadratic in N
HISQ/tree Asqtad
QCD lattice simulations: no final answer
courtesy of F. Karsch
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Temperature µ
early universe neutron star cores
LHC RHIC SIS AGS
quark−gluon plasma hadronic fluid nuclear matter vacuum
FAIR/JINR SPS
n = 0 n > 0 <ψψ> ∼ 0 <ψψ> = 0 / <ψψ> = 0 /
phases ? quark matter
crossover
CFL
B B
superfluid/superconducting
2SC
crossover
➜ can one improve the model calculations?
Theoretical questions:
chiral & deconfinement transition
chiral CEP/deconfinement CEP?
➜ effects of fluctuations are important e.g. size of critical region around CEP
➜ higher moments more sensitive to criticality
deviation from HRG model
= & > ?
➜ remove model ambiguities
[Braun, Janot, Herbst 12/14]
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Temperature µ
early universe neutron star cores
LHC RHIC SIS AGS
quark−gluon plasma hadronic fluid nuclear matter vacuum
FAIR/JINR SPS
n = 0 n > 0 <ψψ> ∼ 0 <ψψ> = 0 / <ψψ> = 0 /
phases ? quark matter
crossover
CFL
B B
superfluid/superconducting
2SC
crossover
➜ can one improve the model calculations? non-perturbative continuum functional methods (DSE, FRG, nPI) ➜ complementary to lattice
⇒ no sign problem μ>0 ⇒ chiral symmetry/fermions/small masses/chiral limit
Theoretical questions:
chiral & deconfinement transition
➜ effects of fluctuations are important e.g. size of critical region around CEP
➜ higher moments more sensitive to criticality
deviation from HRG model
= & > ?
[Braun, Janot, Herbst 12/14]
➜ remove model ambiguities
chiral CEP/deconfinement CEP?
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Temperature µ
early universe neutron star cores
LHC RHIC SIS AGS
quark−gluon plasma hadronic fluid nuclear matter vacuum
FAIR/JINR SPS
n = 0 n > 0 <ψψ> ∼ 0 <ψψ> = 0 / <ψψ> = 0 /
phases ? quark matter
crossover
CFL
B B
superfluid/superconducting
2SC
crossover
Method of choice: Functional Renormalization Group
(deconfinement sector) e.g. (Polyakov)-quark-meson model truncation
Theoretical questions:
chiral & deconfinement transition
➜ effects of fluctuations are important e.g. size of critical region around CEP
➜ higher moments more sensitive to criticality
deviation from HRG model
= & > ?
chiral CEP/deconfinement CEP?
[Braun, Janot, Herbst 12/14]
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→ ∞ freeze-out close to chiral crossover line How can we probe a transition? ∂np(X) ∂Xn X = T, µ, . . . cn ≡ ∂np(T, µ) ∂(µ/T)n . . .
[HotQCD, QM 2012]
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HRG model: good lattice data description HRG model versus experiment
[Andronic et al. 2011] [Karsch, Redlich 2010]
HRG model: no critical fluctuations ➜ no phase transition
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Grand potential in Mean-field approximation
Ω(T, µ; σ) = Ωvac + ΩT + VMF(σ) (+UPoly(Φ) )
vacuum term: regularize e.g. with sharp three-momentum cutoff for each cutoff: adjust model parameters like fπ, mσ, mπ standard MFA: Λ = 0
Z =
ψDψDφe −
ψ, ψ, φ)
Partition function:
Z Λ d3p (2)3 q ⇥ p2 + m2
q
replace with (const.) condensate σ
15 170 175 180 185 190 195 200 205 210 20 40 60 80 100 120 140 160 180 T [MeV] µ [MeV] R4,2 R6,2 R8,2 R10,2 R12,2 crossover CEP 80 90 100 110 120 130 140 150 160 50 100 150 200 T [MeV] µ [MeV] R4,2 R6,2 R8,2 R10,2 R12,2 crossover CEP
unquenched PQM MFA QM MFA w/o vacuum role of vacuum term in (P)QM models see
→ Rq
n,m = cn/cm
Rn,2 < 0
[Karsch, Redlich, Friman, Koch et al. 2011]
➜ new technique: algorithmic differentiation (ADOL-C)
[M. Wagner, A. Walther, BJS 2010]
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unquenched PQM MFA renormalized QM MFA renormalized
60 80 100 120 140 160 180 200 220 50 100 150 200 250 300 T [MeV] µ [MeV] R4,2 R6,2 R8,2 R10,2 R12,2 crossover CEP 20 40 60 80 100 120 140 160 50 100 150 200 250 300 T [MeV] µ [MeV] R4,2 R6,2 R8,2 R10,2 R12,2 crossover
role of vacuum term in (P)QM models see:
→ Rq
n,m = cn/cm
Rn,2 < 0
[Karsch, Redlich, Friman, Koch et al. 2011] [BJS, Wagner 2011/12]
➜ new technique: algorithmic differentiation (ADOL-C)
[M. Wagner, A. Walther, BJS 2010]
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Γ(2)
k
= δ2Γk δφδφ Γk[φ] scale dependent effective action t = ln(k/Λ) Rk
[Herbst, Mitter, Stiele, Pawlowski, BJS, Schaffner-Bieleich in preparation 2013]
FRG (average effective action)
[Wetterich 1993]
Γk Γk =
q[iµ⌃µ − g(⇤+i⌥ ⌅⌥ ⇥5)]q + 1 2(⌃µ⇤)2 + 1 2(⌃µ⌥ ⇥)2 + Vk(⇧2) Vk=Λ(⌅2) = 4 (⇤2+⇧ ⇥2−v2)2 − c⇤
Leading order derivative expansion
Regulator solutions with grid/polynomial techniques
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full dynamical QCD FRG flow: fluctuations of gluon, ghost, quark and (via hadronization) meson in presence of dynamical quarks: gluon propagator is modified pure Yang Mills flow + matter back-coupling
[Braun, Haas, Pawlowski 2009/12]
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First step: flow for quark-meson model truncation: neglect YM contributions without bosonic fluctuations: MFA
20 [BJS, J Wambach 2005]
21 [BJS, J Wambach 2005]
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pure Yang Mills flow: fluctuations of gluon, ghost
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Polyakov-loop improved quark-meson flow: fluctuations of Polyakov-loop, quark and meson Yang-Mills flow replaced by ➜ effective Polyakov-loop potential fitted to lattice Yang-Mills thermodynamics
[Herbst, Pawlowski, BJS 2007 2013]
→ UPol(Φ) → UPol(Φ)
24 [Herbst, Pawlowski, BJS 2010,2013]
50 100 150 200 50 100 150 200 250 300 350 T [MeV] µ [MeV] mπ=138 MeV χ crossover Φ crossover
—
Φ crossover χ 1st order σ(T=0)/2 50 100 150 200 50 100 150 200 250 300 350 T [MeV] µ [MeV] mπ=138 MeV χ crossover Φ crossover
—
Φ crossover χ 1st order σ(T=0)/2
w/o T0(μ) with T0(μ)
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Pressure and interaction measure in comparison with lattice data (polynomial Polyakov-loop potential)
[Herbst, Mitter, Stiele, Pawlowski, BJS 2014]
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[Herbst, Mitter, Stiele, Pawlowski, BJS 2014]
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[M. Mitter, BJS 2014] 200 400 600 800 1000 1200 50 100 150 200 250 300 masses [MeV] T [MeV] π σ a0 η’ η
with UA(1) breaking term
200 400 600 800 1000 1200 50 100 150 200 250 300 masses [MeV] T [MeV] π, η’ σ a0 η
without UA(1) breaking term fluctuations push CEP down star: with UA(1) breaking term cross: w/o UA(1) breaking term
20 40 60 80 100 120 50 100 150 200 250 300 350 T [MeV] µ [MeV] MF eMF FRG
location of CEP FRG ⇔ MFAs
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[J.T. Lenaghan 2001]
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mu,d ms
2nd order Z(2) 2nd order O(4) Nf=2 Nf=1 2nd order Z(2) 1st
PURE GAUGE Nf=3 physical point mtri
s
1st
mc
1st order Z(2) crossover mπ = 0 mπ,c 2nd order crossover mπ = ∞
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so far:
[C. Fischer, J. Lücker, C. Welzbacher 2014]
50 100 150 200 µq [MeV] 50 100 150 200 T [MeV] Lattice: curvature range κ=0.0066-0.0180 DSE: chiral crossover DSE: critical end point DSE: chiral first order DSE: deconfinement crossover µB/T=2 µB/T=3
Location of CEP not accessible with lattice, FRG & DSE
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[N. Strodthoff, BJS, L. von Smekal 12]
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inhomogeneous chiral symmetry breaking: phases characterized by spatially varying chiral condensate σ(x) which breaks translational variance allowing for inhomogeneous phases ➜ cooper pairs with non-vanishing total momentum near Fermi surface
Gross-Neveu 1+1 ➜ chiral spirals favored solution for μ>0 quark-meson model (renormalizable): include vacuum term in grand potential (Dirac-sea contribution)
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QM model: Phase diagram (two flavor, extended MFA) Influence Dirac sea (left: Λ=0 middle: Λ=600 MeV right: Λ=5 GeV)
30 60 90 120 150 180 50 100 150 200 250 300 350 400 450 T (MeV) µ (MeV) 30 60 90 120 150 180 50 100 150 200 250 300 350 400 450 T (MeV) µ (MeV) 30 60 90 120 150 180 50 100 150 200 250 300 350 400 450 T (MeV) µ (MeV)
CP: Critical point (endpoint of 1st order transition) LP: Lifshitz point (two homogeneous phases meet one inhomogeneous phase) LP LP For mσ = 2Mq LP=CP
1st 1st 2nd 2nd
[S. Carignano, M. Buballa, BJS 2014]
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