Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach
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Transcript of Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach
Lattice 2012 T. Umeda (Hiroshima) 1
Thermodynamics in 2+1 flavor QCD Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the with improved Wilson quarks by the fixed scale approachfixed scale approach
Takashi Umeda (Hiroshima Univ.)Takashi Umeda (Hiroshima Univ.)
for WHOT-QCD Collaborationfor WHOT-QCD Collaboration
Lattice2012, Cairns, Australia, 25 June 2012Lattice2012, Cairns, Australia, 25 June 2012
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QCD Thermodynamics with Wilson quarks
Most (T, μ≠0) studies done with staggerd-type quarksMost (T, μ≠0) studies done with staggerd-type quarks
4th-root trick to remove unphysical “tastes”4th-root trick to remove unphysical “tastes”
non-locality “Validity is not guaranteed”non-locality “Validity 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
Aim of WHOT-QCD collaboration is Aim of WHOT-QCD collaboration is
finite T & μ calculations using finite T & μ calculations using Wilson-type quarksWilson-type quarks
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Phys. Rev. D85 094508 (2012) [arXiv:1202.4719]Phys. Rev. D85 094508 (2012) [arXiv:1202.4719] T. UmedaT. Umeda et al. (WHOT-QCD Collaboration) et al. (WHOT-QCD Collaboration) PTEP in press [ arXiv: 1205.5347 (hep-lat) ]PTEP in press [ arXiv: 1205.5347 (hep-lat) ] S. Ejiri, K. Kanaya, T. Umeda for WHOT-QCD CollaborationS. Ejiri, K. Kanaya, T. Umeda for WHOT-QCD Collaboration
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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
a : lattice spacinga : lattice spacingNNtt : lattice size in temporal direction : lattice size in temporal direction
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lattice spacing at fixed Nlattice spacing at fixed Ntt 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 )
- Lattice spacing at lower T- Lattice spacing at lower T
- Finite volume effects- Finite volume effects
DisadvantagesDisadvantages
- T resolution due to integer N- T resolution due to integer Ntt
- UV cutoff eff. at high T’s- UV cutoff eff. at high T’s
fixed fixed scale scale
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Lattice setup
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
- β=2.05, κ- β=2.05, κudud=0.1356, κ=0.1356, κss=0.1351=0.1351
- V~(2 fm)- V~(2 fm)33 , a~0.07 fm, , a~0.07 fm,
- configurations available on the - configurations available on the ILDG/JLDGILDG/JLDG
T>0 simulations: on 32T>0 simulations: on 3233 x N x Ntt (N (Ntt=4, 6, ..., 14, 16) lattices=4, 6, ..., 14, 16) lattices
RHMC algorithm, same parameters as T=0 simulationRHMC algorithm, same parameters as T=0 simulation
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Trace anomaly for Nf=2+1 improved Wilson quarks
Noise methodNoise method ( #noise = 1 for each color & spin indices ) ( #noise = 1 for each color & spin indices )
Phys. Rev. D73, 034501Phys. Rev. D73, 034501CP-PACS/JLQCDCP-PACS/JLQCD
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Beta-functions from CP-PACS/JLQCD results
Meson spectrum by CP-PACS/JLQCD Meson spectrum by CP-PACS/JLQCD Phys. Rev. D78 (2008) 011502Phys. Rev. D78 (2008) 011502. .
5 κ5 κudud x 2 κ x 2 κss for each 3 for each 3 β = 30 data pointsβ = 30 data points
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fit fit ββ,,κκudud,,κκss as functions of as functions of
LCPLCPscalescaleDirect fit method Direct fit method
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Beta-functions from CP-PACS/JLQCD results
χχ22/dof=1.6/dof=1.6
χχ22/dof=1.1/dof=1.1 χχ22/dof=1.7/dof=1.7
fit fit ββ,,κκudud,,κκss as functions of as functions of
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systematic error systematic error for scale dependencefor scale dependence
with fixed with fixed
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Equation of State in Nf=2+1 QCD
T-integrationT-integration
is performed by Akima Splineis performed by Akima Spline interpolation. interpolation.
ε/Tε/T44 is calculated from is calculated from
A systematic error A systematic error for beta-functionsfor beta-functions
SB limitSB limit
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Polyakov loop in the fixed scale approach
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Polyakov loop requiresPolyakov loop requires T dependent renormalizationT dependent renormalization
c(T) : additive normalization factorc(T) : additive normalization factor of heavy quark free energy Fof heavy quark free energy Fqqqq
matching of V(r) to Vmatching of V(r) to Vstringstring(r) at r=1.5r(r) at r=1.5r00
Cheng et al. PRD77(2008)014511Cheng et al. PRD77(2008)014511
( c( cmm is a constant at all temperatures ) is a constant at all temperatures )
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Renormalized Polyakov loop and Susceptibility
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NNff=0 case=0 case
( c( cmm is a constant at all temperatures ) is a constant at all temperatures ) Roughly consistent with Roughly consistent with
the Staggered resultthe Staggered result χχLL increases around T~200MeV increases around T~200MeV
Similar behavior to NSimilar behavior to Nff=0 case=0 case
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Chiral condensate in the fixed scale approach
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Renormalization factorsRenormalization factors
are constants at all temperaturesare constants at all temperatures
preliminarypreliminary
Chiral condensate by the Wilson quarks requiresChiral condensate by the Wilson quarks requires
additive & multiplicative renormalizationsadditive & multiplicative renormalizations
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Chiral susceptibility in the fixed scale approach
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Peak positions in are Peak positions in are
identical to that in renormalized suscep.identical to that in renormalized suscep.
susceptibility peak around 200 MeV (?)susceptibility peak around 200 MeV (?)
more statistics is neededmore statistics is needed
preliminarypreliminary
Renormalization factorsRenormalization factors
are constants at all temperaturesare constants at all temperatures
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Summary & outlook
Equation of stateEquation of state
first result in Nfirst result in Nff=2+1 QCD with Wilson-type quarks =2+1 QCD with Wilson-type quarks
Thanks to the fixed scale approach, systematic errors Thanks to the fixed scale approach, systematic errors coming from lattice artifacts are well under controlcoming from lattice artifacts are well under control
Renormalizations are common at all temperaturesRenormalizations are common at all temperatures
NNff=2+1 QCD just at the physical point=2+1 QCD just at the physical point
the physical point (pion mass ~ 140MeV) by PACS-CSthe physical point (pion mass ~ 140MeV) by PACS-CS
Finite densityFinite density
Taylor expansion method to explore EOS at Taylor expansion method to explore EOS at μμ≠≠00
We presented the EOS, Polyakov loop, chiral condensateWe presented the EOS, Polyakov loop, chiral condensate in Nin Nff=2+1 QCD using improved Wilson quarks=2+1 QCD using improved Wilson quarks
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Renormalized Polyakov loop and Susceptibility
Cheng et al.’s renormalization Cheng et al.’s renormalization [PRD77(2008)014511][PRD77(2008)014511]
matching of V(r) to Vmatching of V(r) to Vstringstring(r) at r=1.5r(r) at r=1.5r00
V(r) = A –α/r + σrV(r) = A –α/r + σr
VVstringstring(r) = c(r) = cm m -π/12r + σr-π/12r + σr
LLrenren = exp(c = exp(cmm N Ntt/2)<L>/2)<L>
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Chiral condensate 3
Lattice2011 Borsanyi et al.Lattice2011 Borsanyi et al.
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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 )
- Lattice spacing at lower T- Lattice spacing at lower T
- Finite volume effects- Finite volume effects
DisadvantagesDisadvantages
- T resolution- T resolution
- High T region - High T region
a : lattice spacinga : lattice spacingNNtt : lattice size in temporal direction : lattice size in temporal direction
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LCP’s in fixed NLCP’s in fixed Ntt approach approach (N(Nff=2 Wilson quarks at N=2 Wilson quarks at Ntt=4)=4)
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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
a : lattice spacinga : lattice spacingNNtt : lattice size in temporal direction : lattice size in temporal direction
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spatial volume at fixed Nspatial volume at fixed Ntt
NNss for V=(4fm) for V=(4fm)33
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 )
- Lattice spacing at lower T- Lattice spacing at lower T
- Finite volume effects- Finite volume effects
DisadvantagesDisadvantages
- T resolution- T resolution
- High T region - High T region