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 lattice+HRG 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
Improved staggered calculations at finite temperature
low T region
T<200 MeV
cutoff effects are different in :
a<0.125fm
a>0.125fm
hadronic degrees of freedom
improvement of the flavor symmetry is
important
stout
high-T region
T>200MeV
for #flavors < 4
rooting trick
p4, asqtad, HISQ
quark degrees of freedom
quark dispersion relation
Lattice results on trace anomaly
(2+1)-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) , arXiv:0903.4379
lattice spacing from the heavy
quark potential :
arXiv:0903.4379
Pressure, energy density and speed of sound
Bazavov et al, (HotQCD Coll.) , arXiv:0903.4379
rapid rise in number of d.o.f at
T=185-195 MeV
For energy densities relevant
for RHIC the speed of sound is
smaller than the ideal gas value
about 10% deviation from the ideal gas limit
lattice discretization errors are small
The softest point corresponds to
Equation of State for physical quark masses
• Thermodynamics quantities are quark mass independent for T>200MeV
• The quark mass effect is also very small at low temperatures (T<170MeV) 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
QCD thermodynamics at non-zero chemical potential
Taylor expansion :
hadronic
quark
Fluctuation of conserved quantum
numbers at zero baryon density :
Physics at non-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
Isentropic EoS
radius of convergence,
critical end-point
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
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
Thermodynamics at high temperature
no constant non-perturbative term is
present in the entropy density
good agreement between lattice
and resummed perturbative (NLA)
calculations of the entropy
Rebhan, arXiv:hep-ph/0301130;
Blaizot et al, PRL 83 (99) 2906
The quark number susceptibilities
for T>300MeV agree
with resummed petrurbative
predictions
A. Rebhan, arXiv:hep-ph/0301130
Blaizot et al, PLB 523 (01) 143
and are in contrrast with
AdS/CFT expectations
Teaney, PRD 74 (06) 045025
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, arXiv:0903.2911
Hadron resonance gas (HRG) can be used as a reference at low temperatures
Cheng et al., arXiv:0811.1006
reasonable agreement with HRG for certain ratios at low T
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. arXiv:0909.xxxx
Baryon number fluctuations
discretization effects result in “effective shift” of T-scale
Strangeness fluctuations
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 s=0.95sSB at T=800MeV
Huovinen, P.P. arXiv:0909.xxxx
Speed of sound and elliptic flow
Huovinen, P.P. arXiv:0909.xxxx
softest point : cs2~0.15 @ ε~1GeV/fm3
significant enhancement of v2 compared to the Bag EoS
(see Huovinen, NPA761 (2005) 296 for similar results )
Deconfinement and chiral transition
stout : Budapest-Wuppertal Group, Aoki et al., PLB 643 (06) 46; arXiv:0903.4155
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
Deconfinement and chiral transition
stout : Budapest-Wuppertal Group, Aoki et al., PLB 643 (06) 46; arXiv:0903.4155
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 => significant discretization effects at T>200MeV
Deconfinement and chiral transition
stout : Budapest-Wuppertal Group, Aoki et al., PLB 643 (06) 46; arXiv:0903.4155
Strangeness fluctuations agree quite well with HRG for T<200MeV !
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 Nτ=6 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)
Summary and outlook
• Rapid increase in thermodynamic quantities at T=185-195 MeV for p4 and asqtad action
and Nτ=8 ; 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 Nτ=8 and
asqtad calculations with Nτ=12 should clarify this problem
Back-up:Results from improved staggered calculations at T=0
a=0.125fm, 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, arXiv:0903.4155v1 [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]
Backup: weak coupling results versus lattice data