TQFT 2010 T. Umeda (Hiroshima) 1 Equation of State in 2+1 Equation of State in 2+1 flavor QCD flavor QCD with with improved Wilson quarks improved Wilson quarks Takashi Umeda (Hiroshima Univ.) Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration for WHOT-QCD Collaboration TQFT 2010, YITP, Kyoto, 30 Aug. 2010 TQFT 2010, YITP, Kyoto, 30 Aug. 2010 /15
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TQFT 2010T. Umeda (Hiroshima)1 Equation of State in 2+1 flavor QCD with improved Wilson quarks Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration.
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TQFT 2010 T. Umeda (Hiroshima) 1
Equation of State in 2+1 flavor Equation of State in 2+1 flavor QCD QCD with improved Wilson with improved Wilson quarksquarks
for WHOT-QCD Collaborationfor WHOT-QCD Collaboration
TQFT 2010, YITP, Kyoto, 30 Aug. 2010TQFT 2010, YITP, Kyoto, 30 Aug. 2010
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TQFT 2010 2
Quark Gluon Plasma in Lattice QCD
from the Phenix group web-site
Observables in Lattice QCDObservables in Lattice QCD
Phase diagram in (T, Phase diagram in (T, μμ, m, mudud, m, mss))
Transition temperatureTransition temperature
Equation of state ( ε/TEquation of state ( ε/T44, p/T, p/T44,...),...)
Hadronic excitationsHadronic excitations
Transport coefficientsTransport coefficients
Finite chemical potentialFinite chemical potential
etc...etc...http://www.gsi.de/fair/experiments/
T. Umeda (Hiroshima) /15
TQFT 2010 T. Umeda (Hiroshima) 3
Choice of quark actions on the lattice
Most (T, μ≠0) studies done with staggerd-type quarksMost (T, μ≠0) studies done with staggerd-type quarks less computational costsless computational costs a part of chiral sym. preserved ...a part of chiral sym. preserved ...
NNff=2+1, almost physical quark mass, (μ≠0)=2+1, almost physical quark mass, (μ≠0)
4th-root trick to remove unphysical “tastes”4th-root trick to remove unphysical “tastes”
non-locality “universality is not guaranteed”non-locality “universality is not guaranteed”
It is important to cross-check with It is important to cross-check with
theoretically sound lattice quarks like Wilson-type quarkstheoretically sound lattice quarks like Wilson-type quarks
Our aim is to investigateOur aim is to investigate
QCD Thermodynamics with Wilson-type quarksQCD Thermodynamics with Wilson-type quarks
WHOT-QCD CollaborationWHOT-QCD Collaboration
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TQFT 2010 T. Umeda (Hiroshima) 4
Fixed scale approach to study QCD thermodynamics
Temperature Temperature T=1/(NT=1/(Ntta)a) is varied by is varied by NNtt at fixed at fixed aa
AdvantagesAdvantages
- Line of Constant Physics- Line of Constant Physics
- T=0 subtraction for renorm.- T=0 subtraction for renorm.
(spectrum study at T=0 )(spectrum study at T=0 )
- larger 1/a in whole T region- larger 1/a in whole T region
DisadvantagesDisadvantages
- T resolution by integer N- T resolution by integer Ntt
- coding for odd N- coding for odd Ntt
- Integration method- Integration method
is not applicableis not applicable
a : lattice spacinga : lattice spacingNNtt : lattice size in temporal direction : lattice size in temporal direction
Temperatures in each approachTemperatures in each approach
fixed Nfixed N tt a
pproach approach
fixed scale approachfixed scale approach
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TQFT 2010 T. Umeda (Hiroshima) 5
T-integration method to calculate the EOS
We propose a new method (“We propose a new method (“T-integration methodT-integration method”) ”)
to calculate the EOS at fixed scalesto calculate the EOS at fixed scales
Our method is based on Our method is based on the trace anomaly (interaction measure),the trace anomaly (interaction measure),
and and the thermodynamic relation.the thermodynamic relation.
T.Umeda et al. (WHOT-QCD), Phys.Rev.D79 (2009) 051501(R)T.Umeda et al. (WHOT-QCD), Phys.Rev.D79 (2009) 051501(R)
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TQFT 2010 T. Umeda (Hiroshima) 6
Test in quenched QCD
Our results are roughlyOur results are roughly consistent with previous results. consistent with previous results.
Our results deviate from the Our results deviate from the fixed Nfixed Ntt=8 results [*] =8 results [*] at higher T ( aT~0.3 or higher )at higher T ( aT~0.3 or higher )
Trace anomaly is sensitive toTrace anomaly is sensitive to spatial volume at lower Tspatial volume at lower T (below T(below Tcc).). V > (2fm)V > (2fm)33 is ncessarry. is ncessarry.
~~
[*] [*] G. Boyd et al., NPB469, 419 (1996) G. Boyd et al., NPB469, 419 (1996)
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TQFT 2010 T. Umeda (Hiroshima) 7
T=0 & T>0 configurations for Nf=2+1 QCD
T=0 simulation: on 28T=0 simulation: on 2833 x 56 x 56 by CP-PACS/JLQCDby CP-PACS/JLQCD Phys. Rev. D78 (2008) 011502Phys. Rev. D78 (2008) 011502
- - RG-improved Iwasaki glue + NP-improved Wilson quarksRG-improved Iwasaki glue + NP-improved Wilson quarks