Tracing the
QCD Equation of State
André Peshier, University of Cape Town
--- Wits University, September 2012 ---
QCD thermodynamics … WHY?
• in general: (thermodynamic) properties of matter hard to calculate ab initio
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QCD thermodynamics … WHY?
• Quantum Chromodynamics (QCD) is a THEORY (not a model) … with a rich structure
• Thermodynamic potential ~ generating functional in quantum field theory
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Heavy-ion collisions
LHC @ CERN
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Heavy-ion collisions
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QCD feature: Confinement
• singlet potential
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(string parameterisation)
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QCD feature: Asymptotic freedom
• Running coupling
accessible perturbatively???
hierarchy of thermal scales
• typical momentum
“hard”
• Electric screening
“soft”
• Magnetic screening
“ultrasoft”
[Bethke ...]
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Interaction free limit
• harmonic oscillator
– Partition sum
– mean energy
• free gluon gas (= “colored” black body radiation)
Thermodynamic limit
pressure (= Thermodyn potential)
entropy density
energy density
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MIT bag model
•
Non-perturbative vacuum pressure
•
Confinement: heavy glueballs
(phase) transition
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Perturbative QCD
Shuryak (1978) … Kajantie et al. (2003):
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Perturbative QCD
 no “convergence” for
relevant temperatures
 powers of
(and log’s)
 perturbative limit
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Toy model
• “Lagrangian”
→
“partition fnc”
• perturbative expansion
cut
plane: convergence radius= 0
 at large coupling : truncate pert. expansion at low order
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, or …
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Lattice QCD
• compute QCD path integral in discretized and compactified Euclidean space
quarks:
gluons:
expansive
• continuum limit
• thermodynamic limit
• quarks
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Lattice QCD (here: quenched limit)
(phase) transition
heavy glueballs
deconfined gluons
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Hard Thermal Loops
Bose enhancement can change powercounting:
HTL perturbation theory: expansion in dressed propagators
gauge invariant
trans + long components
depend not only on
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HTL resummations (here massless
theory)
• HTL perturbation theory [Karsch et al 1997]
rearrange Lagrangian
(“by hand”)
• 2PI (self-consistent) approximations [AP 1998]
+
+
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+…
+…
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2PI-HTL for QCD (here: quenched)
• Blaizot et al 2001: entropy
- “simple” 1-loop functional,
manifestly finite
• AP 2001: pressure
- “complicated”: thermal
IR+UV divergencies,
they cancel 
- understand why it breaks
for
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Quasiparticle model
simplified 2PI-HTL approach + added pheno flexibility
massive transverse gluons: effective coupling with IR enhancement
2PI:
QP:
[Gorenstein+Yang, 1995]
Why makes entropy special? … Revisit harmonic oscillator:
field theory:
dof with
divergences cannot be “dropped” for
indicates another contribution:
ground state has no entropy
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Quasiparticle model
NB: O(10%) deviation from free limit
does NOT imply small coupling
[AP et al. 1996]
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Dynamical Quasiparticles
small entropy near
 large quasiparticle mass
 large coupling from lQCD analysis
what about quasiparticle width?
sensitivity to
magnetic screening
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Dynamical Quasiparticles
assume Lorentz spectral function
increase with
decrease with m
increase compatible
with phase transition??
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Dynamical Quasiparticles
extract spectral properties from constrained fit
[AP 2004]
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Dynamical Quasiparticles
implications from width ~ interaction rate [AP+ Cassing 2005]
– plasma parameter
 phase structure “liquid” for temperatures
– enhanced cross section
 percolation for
– very low shear viscosity near
heavy-ion colliders produce
strongly coupled quark-gluon liquid
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Quark chemical potential
• QP concept works quantitatively also when adding in quarks,
• lattice QCD difficult for non-zero quark chemical potential (“sign problem”)
 employ QP model
• Maxwell relation from thermodynamic potential
Flow eqn:
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:
[AP et al. 2001]
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Quark chemical potential
good agreement with new lattice results
dense compact stars
with quark core
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2012 start of projects with Dino Giovannoni ...
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lQCD revisited: integral method
common procedure: compute interaction measure
reconstruct thermodynamics
uncertainties near
uncertainties @ large
free limit for
free limit for
[Boyd et al 1996]
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27
Integral method
bug or feature ...?
Nf =0
[Borsanyi et al. 2012]
continuum extrapolations (based on freelimit scaling) may or may not help ...
Nf = 2+1
[Bazavov et al 2009, Borsanyi et al. 2010]
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QP analysis of lQCD interaction measure
leading-order Ansatz for coupling
fit to lQCD results above certain
SC condition
+ integration constant
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QP analysis of lQCD interaction measure
consistent QP mass results from fits
[email protected], Tracing the QCD EoS, Wits University, September 2012
marked reduction in entropy (as
well as pressure, energy density)
at large T
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Resumé

QCD-quasiparticle concept has provided
– physics insight
– quantitative predictions
– motivation for theory developments

quasiparticle analysis of lattice QCD trace anomaly
indicates slower approach of QCD bulk properties to free
limit
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