QCD thermodynamic on the lattice and the

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QCD thermodynamic on the lattice and the
hadron resonance gas
Péter Petreczky
Physics Department and
RIKEN-BNL

• Lattice artifacts in staggered fermion
  formulation
• Thermodynamics at high temperaure EoS,
  fluctuations
• HotQCD , RBC-Bielefeld, MILC
• Thermodynamics at low temperatures and the
  hadron resonance gas (HRG)
• Parametrization of the EoS based on latticeHRG
  and its effect on elliptic flow
• Deconfinement and chiral aspects of the QCD
  transition
• Budapest-Wuppertal, HotQCD results and highly
  improved staggered quark (HISQ) action

ECT/LOEWE/NIKHEF/CATHIE workshop, Trento,
September 14-18, 2009
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Improved staggered calculations at finite
temperature
cutoff effects are different in
high-T region Tgt200MeV
low T region Tlt200 MeV
alt0.125fm
agt0.125fm
hadronic degrees of freedom
quark degrees of freedom
improvement of the flavor symmetry is important
quark dispersion relation
for flavors lt 4 rooting trick
p4, asqtad, HISQ
stout
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Lattice results on trace anomaly
(21)-flavor calculations with p4 and asqtad and
nearly physical
Bernard et al, (MILC) PRD 75 (07) 094505, Cheng
et al, (RBC-Bielefeld) PRD 77 (08) 014511
Bazavov et al, (HotQCD) , arXiv0903.4379
lattice spacing from the heavy quark potential
arXiv0903.4379
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Pressure, energy density and speed of sound
Bazavov et al, (HotQCD Coll.) , arXiv0903.4379
For energy densities relevant for RHIC the speed
of sound is smaller than the ideal gas value The
softest point corresponds to
rapid rise in number of d.o.f at T185-195 MeV
about 10 deviation from the ideal gas
limit lattice discretization errors are small
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Equation of State for physical quark masses

• Thermodynamics quantities are quark mass
  independent for Tgt200MeV
• The quark mass effect is also very small at low
  temperatures (Tlt170MeV) because
• cutoff effects dominate, no agreement with
  hadron resonance gas
• In the transition region thermodynamic
  quantities are larger for the smaller quark mass,
• the enhancement of thermodynamic quantities is
  consistent with 5MeV shift of the
• transition region towards lower temperatures

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QCD thermodynamics at non-zero chemical potential
Taylor expansion
hadronic
quark
Physics at non-zero baryon density Isentropic
EoS radius of convergence, critical end-point
Fluctuation of conserved quantum numbers at zero
baryon density probe of deconfinement
and chiral aspects of the QCD transitions at zero
baryon density and also related to event-by-event
fluctuations in RHIC
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Deconfinement fluctuations of conserved charges

baryon number
electric charge
strange quark number
Ideal gas of quarks
conserved charges carried by light quarks
conserved charges are carried by massive hadrons
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Deconfinement fluctuations of conserved charges

baryon number
electric charge
strange quark number
Ideal gas of quarks
conserved charges carried by light quarks
conserved charges are carried by massive hadrons
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Thermodynamics at high temperature
The quark number susceptibilities for Tgt300MeV
agree with resummed petrurbative predictions
A. Rebhan, arXivhep-ph/0301130 Blaizot et al,
PLB 523 (01) 143 and are in contrrast with
AdS/CFT expectations Teaney, PRD 74 (06) 045025
no constant non-perturbative term is present in
the entropy density
good agreement between lattice and resummed
perturbative (NLA) calculations of the
entropy Rebhan, arXivhep-ph/0301130 Blaizot et
al, PRL 83 (99) 2906
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Fluctuations in the hadron resonance gas model
Kurtosis ratio of the quartic fluctuations to
quadratic fluctuations, can be studied
also experimentally, see e.g. Schuster,
arXiv0903.2911
Hadron resonance gas (HRG) can be used as a
reference at low temperatures
Cheng et al., arXiv0811.1006
reasonable agreement with HRG for certain ratios
at low T
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Lattice results vs. hadron resonance gas model
Include all resonances up to 2.5GeV Use ground
state hadron masses modified according to know
lattice corrections Modify the masses of baryon
resonances up to threshold 1.8GeV and 2.5GeV in
the same way as the ground state baryons
Huovinen, P.P. arXiv0909.xxxx
Baryon number fluctuations
Strangeness fluctuations
discretization effects result in effective
shift of T-scale
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Interpolating between HRG and lattice results
Use interpolation of lattice data above 200MeV
and match it to HRG at lower temperature with
constrain that a s0.95sSB at T800MeV
Huovinen, P.P. arXiv0909.xxxx
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Speed of sound and elliptic flow
Huovinen, P.P. arXiv0909.xxxx
softest point cs20.15 _at_ e1GeV/fm3
significant enhancement of v2 compared to the Bag
EoS
(see Huovinen, NPA761 (2005) 296 for similar
results )
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Deconfinement and chiral transition
stout Budapest-Wuppertal Group, Aoki et al.,
PLB 643 (06) 46 arXiv0903.4155
5MeV, quark mass
6MeV, continuum extrapolation
Renormalized Polyakov loop
Renormalized chiral condensate
no qualitative change, but significant shift of
the transition region toward smaller T
stout action is optimized to reduce the effect of
flavor symmetry breaking, but not the quark the
quark dispersion relation
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Deconfinement and chiral transition
stout Budapest-Wuppertal Group, Aoki et al.,
PLB 643 (06) 46 arXiv0903.4155
Strangeness fluctuations
Renormalized chiral condensate
agreement between HotQCD results and
Budapest-Wuppertal results at high T
stout action is optimized to reduce the effect of
flavor symmetry breaking, but not the quark the
quark dispersion relation gt significant
discretization effects at Tgt200MeV
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Deconfinement and chiral transition
stout Budapest-Wuppertal Group, Aoki et al.,
PLB 643 (06) 46 arXiv0903.4155
Strangeness fluctuations agree quite well with
HRG for Tlt200MeV !
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Deconfinement and chiral transition for HISQ
action
The highly improved staggered fermion action
(HISQ) improves the quark dispersion and is the
most efficient in the improvement of flavor
symmetry breaking (smallest pion splitting)
Preliminary results for Nt6 and 8 HISQ
calculations (Bazavov, P.P., Lattice 2009)
Renormalized chiral condensate
Renormalized Polyakov loop
significant shift of the transition region for
the chiral condensate (much closer to stout) no
apparent shift in the renormalized Polyakov loop
(HISQ results differ significantly from the stout
results)
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Summary and outlook

• Rapid increase in thermodynamic quantities at
  T185-195 MeV for p4 and asqtad action
• and Nt8 things maybe different as continuum
  limit is approach
• Taking into account the lattice spacing
  dependence of hadron masses it is possible to
• get agreement between the HRG and lattice QCD
• Interpolating between HRG at low T and lattice
  QCD at high T it is possible construct
• realistic equation of state to be used in
  hydrodynamic modeling. Significant effect on
• the proton elliptic flow was observed in
  ideal hydro compared to bag EoS
• Comparison with HRG indicate significant cutoff
  effects in the low temperature region
• for p4 and asqtad actions. These
  discretization effects maybe responisble for
  discrepancy
• between HotQCD and stout results. The ongoing
  calculations with HISQ on Nt8 and
• asqtad calculations with Nt12 should clarify
  this problem

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Back-upResults from improved staggered
calculations at T0
a0.125fm, 0.09fm, 0.06fm, chiral and continuum
extrapolations
HPQCD, UKQCD, MILC and Fermilab, PRL 92 (04)
022001
Fermilab, HPQCD, MILC PRL 94 (05) 011601
(hep-ph/0408306 ) Exp. Belle, hep-ex/0510003
Bernard et al (MILC), PoSLAT2007 (07) 137 Aoki
et al, arXiv0903.4155v1 hep-lat
To obtain these results it was necessary to
implement 1) improvement of quark
dispersion relation 2) reduce the flavor
symmetry breaking in the staggered fermion
formulation
LQCD Fermilab, HPQCD, UKQCD PRL 94 (05)
172001 hep-lat/0411027 Exp CDF, PRL 96 (06)
082002 hep-exp/0505076
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Backup weak coupling results versus lattice data