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Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach

Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach. Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration. Lattice2012, Cairns, Australia, 25 June 2012. /13. QCD Thermodynamics with Wilson quarks.

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Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach

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  1. Thermodynamics in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration Lattice2012, Cairns, Australia, 25 June 2012 T. Umeda (Hiroshima) /13

  2. QCD Thermodynamics with Wilson quarks • Most (T, μ≠0) studies done with staggerd-type quarks • 4th-root trick to remove unphysical “tastes” •  non-locality “Validity is not guaranteed” • It is important to cross-check with • theoretically sound lattice quarks like Wilson-type quarks Aim of WHOT-QCD collaboration is finite T & μ calculations using Wilson-type quarks • Phys. Rev. D85 094508 (2012) [arXiv:1202.4719] • T. Umedaet al. (WHOT-QCD Collaboration) • PTEP in press [ arXiv: 1205.5347 (hep-lat) ] • S. Ejiri, K. Kanaya, T. Umeda for WHOT-QCD Collaboration T. Umeda (Hiroshima) /13

  3. Fixed scale approach to study QCD thermodynamics Temperature T=1/(Nta) is varied by Nt at fixed a a : lattice spacing Nt : lattice size in temporal direction • Advantages • - Line of Constant Physics • - T=0 subtraction for renorm. • (spectrum study at T=0 ) • - Lattice spacing at lower T • - Finite volume effects • Disadvantages • - T resolution due to integer Nt • - UV cutoff eff. at high T’s lattice spacing at fixed Nt • fixed • scale T. Umeda (Hiroshima) /13

  4. Lattice setup • T=0 simulation: on 283 x 56 by CP-PACS/JLQCDPhys. Rev. D78 (2008) 011502 • - RG-improved Iwasaki glue + NP-improved Wilson quarks • - β=2.05, κud=0.1356, κs=0.1351 • - V~(2 fm)3 , a~0.07 fm, • - configurations available on the ILDG/JLDG • T>0 simulations: on 323 x Nt (Nt=4, 6, ..., 14, 16) lattices • RHMC algorithm, same parameters as T=0 simulation T. Umeda (Hiroshima) /13

  5. Trace anomaly for Nf=2+1 improved Wilson quarks Phys. Rev. D73, 034501 CP-PACS/JLQCD Noise method ( #noise = 1 for each color & spin indices ) T. Umeda (Hiroshima) /13

  6. fit β,κud,κs as functions of Beta-functions from CP-PACS/JLQCD results Meson spectrum by CP-PACS/JLQCD Phys. Rev. D78 (2008) 011502. LCP scale 5 κud x 2 κs for each 3β = 30 data points Direct fit method T. Umeda (Hiroshima) /13

  7. Beta-functions from CP-PACS/JLQCD results fit β,κud,κs as functions of χ2/dof=1.1 χ2/dof=1.7 χ2/dof=1.6 with fixed systematic error  for scale dependence T. Umeda (Hiroshima) /13

  8. Equation of State in Nf=2+1 QCD • T-integration • is performed by Akima Spline • interpolation. • ε/T4 is calculated from • A systematic error • for beta-functions SB limit T. Umeda (Hiroshima) /13

  9. Polyakov loop in the fixed scale approach • Polyakov loop requires • T dependent renormalization c(T) : additive normalization factor of heavy quark free energy Fqq • matching of V(r) to Vstring(r) at r=1.5r0 • Cheng et al. PRD77(2008)014511 ( cm is a constant at all temperatures ) T. Umeda (Hiroshima) /13

  10. Renormalized Polyakov loop and Susceptibility • Roughly consistent with • the Staggered result • χL increases around T~200MeV • Similar behavior to Nf=0 case ( cm is a constant at all temperatures ) Nf=0 case T. Umeda (Hiroshima) /13

  11. Chiral condensate in the fixed scale approach Chiral condensate by the Wilson quarks requires additive & multiplicative renormalizations preliminary Renormalization factors are constants at all temperatures T. Umeda (Hiroshima) /13

  12. Chiral susceptibility in the fixed scale approach preliminary Renormalization factors are constants at all temperatures Peak positions in are identical to that in renormalized suscep. susceptibility peak around 200 MeV (?)  more statistics is needed T. Umeda (Hiroshima) /13

  13. Summary & outlook We presented the EOS, Polyakov loop, chiral condensate in Nf=2+1 QCD using improved Wilson quarks • Equation of state • first result in Nf=2+1 QCD with Wilson-type quarks • Thanks to the fixed scale approach, systematic errors • coming from lattice artifacts are well under control • Renormalizations are common at all temperatures • Nf=2+1 QCD just at the physical point • the physical point (pion mass ~ 140MeV) by PACS-CS • Finite density • Taylor expansion method to explore EOS at μ≠0 T. Umeda (Hiroshima) /13

  14. T. Umeda (Hiroshima)

  15. Renormalized Polyakov loop and Susceptibility Cheng et al.’s renormalization [PRD77(2008)014511] matching of V(r) to Vstring(r) at r=1.5r0 V(r) = A –α/r + σr Vstring(r) = cm -π/12r + σr Lren = exp(cm Nt/2)<L> T. Umeda (Hiroshima)

  16. Chiral condensate 3 Lattice2011 Borsanyi et al. T. Umeda (Hiroshima)

  17. Fixed scale approach to study QCD thermodynamics Temperature T=1/(Nta) is varied by Nt at fixed a a : lattice spacing Nt : lattice size in temporal direction • Advantages • - Line of Constant Physics • - T=0 subtraction for renorm. • (spectrum study at T=0 ) • - Lattice spacing at lower T • - Finite volume effects • Disadvantages • - T resolution • - High T region LCP’s in fixed Nt approach (Nf=2 Wilson quarks at Nt=4) T. Umeda (Hiroshima) /15

  18. Fixed scale approach to study QCD thermodynamics Temperature T=1/(Nta) is varied by Nt at fixed a a : lattice spacing Nt : lattice size in temporal direction • Advantages • - Line of Constant Physics • - T=0 subtraction for renorm. • (spectrum study at T=0 ) • - Lattice spacing at lower T • - Finite volume effects • Disadvantages • - T resolution • - High T region spatial volume at fixed Nt Ns for V=(4fm)3 T. Umeda (Hiroshima) /15

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