Transcript Petreczky

QCD thermodynamic on the lattice and the
hadron resonance gas
Péter Petreczky
Physics Department and RIKEN-BNL
• Thermodynamics at high temperaure : EoS, fluctuations
BI-RBC, MILC, HotQCD : p4, asqtad, Nτ=4, 6 and 8
Quark Gluon Gas
• Thermodynamics at low temperatures and the Hadron Resonance Gas (HRG)
• Parametrization of the EoS based on lattice+HRG and its effect on flow
Winter Workshop on Nuclear Dynamics, Ocho Rios, Jamaica, January 2-9, 2010
Thermodynamics at high temperature
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
Deviations from ideal gas limit at T=800MeV is only 5-10%
The cutoff effects (estimated from Nτ=6 and Nτ=8) are about 5%
similar results for HISQ and stout actions, see talks by Bazavov and Fodor
Lattice results for physical quark masses
Lattice calculations at the physical quark mass and Nτ=8, Cheng et al, arXiv:0911.2215
• Thermodynamics quantities are quark mass independent for T>200MeV
• The quark mass effect is small at low temperature and is similar to cutoff effects dominate
• Lattice results are significantly below the Hadron Resonance Gas
Improved staggered calculations at finite temperature
low T region
T<200 MeV
cutoff effects are different in :
a>0.125fm
hadronic degrees of freedom
improvement of the flavor symmetry is
important
stout
high-T region
T>200MeV
a<0.125fm
quark degrees of freedom
quark dispersion relation
for #flavors < 4
rooting trick
p4, asqtad, HISQ
Quark mass and lattice spacing dependence of hadron masses
Hadron specturm has been calculated with improved staggered (asqtad) quarks for several
values of quark masses and a=0.18, 0.15, 0.12, 0.09 and 0.06 fm
Fit lattice results with:
For range of the lattice spacing used in T>0 calculations cutoff effects on the hadron
mass could be as large as 15-20%
Huovinen, P.P. arXiv:0912.2541
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:0912.2541
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 or s=0.90sSB at T=800MeV
fit the lattice data
Huovinen, P.P. arXiv:0912.2541
EoS parametrization
Huovinen, P.P. arXiv:0912.2541
• EoS is never softer than HRG EoS
• Large transition region : 170MeV < T < 220MeV,where the system is neither hadronic
nor partonic
EoS and hydrodynamic flow
The sensitivity of flow to EoS is studied in ideal hydrodynamics
Au+Au, √s =200 GeV, b=7 fm
Huovinen, P.P. arXiv:0912.2541
Momentum anisotropy:
• εp is sensitive to EoS, though the difference between different lattice
parameterization is small
• About half of the momentum anisotropy is produced in the partonic state,
half in the transition region and only negligible fraction in hadronic stage (T < 170 MeV)
EoS and hydrodynamic flow
Huovinen, P.P. arXiv:0912.2541
pT –differential v2 is not sensitive to EoS, but the spectra are
adjusting the freezout temperature to reproduce the spectra gives
significantly larger proton v2 compared to the EoS with 1st order transition (EoSQ)
(see Huovinen, NPA761 (2005) 296 for similar results )
Within ideal hydrodynamics it is not possible to describe both the proton spectrum and v2,
i.e. ideal hydrodynamics does not work !
Summary and outlook
•
In the high T region cutoff effects are under control and thermodynamics can be
understood in terms of quark gluon gas
•
In the low temperature region (T<200MeV) there are potentially large cutoff effects
which are responsible for significant discrepancy between HRG model and lattice results
•
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 that be used in hydrodynamic modeling.
•
Significant effect on the proton elliptic flow was observed in ideal hydro
compared to bag model type EoS
=> ideal hydrodynamic model does not work if realistic EoS are used !
Comparison of EoS
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]