Lattice 2012T. Umeda (Hiroshima)1 Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by...

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


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


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


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


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 )


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


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


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


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>


Chiral condensate 3

Lattice2011 Borsanyi et al.Lattice2011 Borsanyi et al.




AdvantagesAdvantages







- T resolution- T resolution

- High T region - High T region


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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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spatial volume at fixed Nspatial volume at fixed Ntt

NNss for V=(4fm) for V=(4fm)33

AdvantagesAdvantages







- T resolution- T resolution

- High T region - High T region

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