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EoS in 2+1 flavor QCD with improved Wilson fermion

EoS in 2+1 flavor QCD with improved Wilson fermion. Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration. Nonperturbative Aspects of QCD at Finite Temperature and Density, Univ. of Tsukuba, Ibaraki, 8 - 9 Nov. 2010. /15. Quark Gluon Plasma in Lattice QCD.

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EoS in 2+1 flavor QCD with improved Wilson fermion

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  1. EoS in 2+1 flavor QCD with improved Wilson fermion Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration Nonperturbative Aspects of QCDat Finite Temperature and Density, Univ. of Tsukuba, Ibaraki, 8 - 9 Nov. 2010 T. Umeda (Hiroshima) /15

  2. Quark Gluon Plasma in Lattice QCD from the Phenix group web-site • Observables in Lattice QCD • Phase diagram in (T, μ, mud, ms) • Transition temperature • Equation of state ( ε/T4, p/T4,...) • Hadronic excitations • Transport coefficients • Finite chemical potential • etc... http://www.gsi.de/fair/experiments/ T. Umeda (Hiroshima) /15

  3. Choice of quark actions on the lattice • Most (T, μ≠0) studies done with staggerd-type quarks • less computational costs • a part of chiral sym. preserved ... •  Nf=2+1, almost physical quark mass, (μ≠0) • 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 Our aim is to calculate QCD EoSusing Wilson-type quarks with small lattice artifacts. T. Umeda (Hiroshima) /15

  4. fixed Nt approach fixed scale approach 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 Temperatures in each approach • Advantages • - Line of Constant Physics • - T=0 subtraction for renorm. • (spectrum study at T=0 ) • - fine “a” in whole T region • Disadvantages • - T resolution by integer Nt • - UV cutoff eff. at high T fine ~ coarse T. Umeda (Hiroshima) /15

  5. T-integration method to calculate the EOS We propose the T-integration method to calculate the EOS at fixed scales T.Umeda et al. (WHOT-QCD), Phys.Rev.D79 (2009) 051501(R) Our method is based on the trace anomaly (interaction measure), and the thermodynamic relation. T. Umeda (Hiroshima) /15

  6. Test in quenched QCD • Our results are roughly • consistent with previous results. • Our results deviate from the • fixed Nt=8 results [*] • at higher T ( aT~0.3 or higher ) • Trace anomaly is sensitive to • spatial volume at lower T • (below Tc). • V > (2fm)3 is ncessarry. ~ [*] G. Boyd et al., NPB469, 419 (1996) T. Umeda (Hiroshima) /15

  7. T=0 & T>0 configurations for Nf=2+1 QCD • 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 coupling parameters as T=0 simulation T. Umeda (Hiroshima) /15

  8. Formulation 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) /15

  9. Beta-functions from CP-PACS/JLQCD results Trace anomaly needs Beta-functions in Nf=2+1 QCD Direct fit method Phys. Rev. D64 (2001) 074510 fit β,κud,κs as functions of with fixed T. Umeda (Hiroshima) /15

  10. 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. 3 (β) x 5 (κud) x 2 (κs) = 30 data points χ2/dof=1.6 χ2/dof=2.1 χ2/dof=5.3 only statistical error T. Umeda (Hiroshima) /15

  11. Trace anomaly in Nf=2+1 QCD Nt config. (x 5MD traj.) SgSq(**) 56 1300(*) 980 16 1542 647 14 1448 647 12 1492 695 10 863 487 8 628 520 6 657 360 4 802 295 Preliminary (*) T=0 (Nt=56) by CP-PACS/JLQCD Sg calculated with 6500traj. (**) thermal. = 1000 traj. T. Umeda (Hiroshima) /15

  12. Trace anomaly in Nf=2+1 QCD WHOT-QCD Collaboration stout Preliminary S. Borsanyi et al., arXiv:1007.2580 HISQ HotQCD, arXiv:1005.1131 • peak height = 4~6 • in recent Staggered results • ( mq~ mqphys. ) T. Umeda (Hiroshima) /15

  13. Equation of State in Nf=2+1 QCD SB limit • T-integration • is performed by the trapezoidal • rule (straight line interpolation). • ε/T4 is calculated from • Large error in whole T region Preliminary T. Umeda (Hiroshima) /15

  14. Summary & outlook • We presented the status of WHOT-QCD “EoS” project. • First calculation of EoS with Wilson-type quarks in 2+1 flavor QCD • Small lattice artifacts • Guaranteed continuum limit • No flavor symmetry violations • No uncertainty in determination of a LCP • O(a) improvement with csw determined by SF method • Simulations on a fine lattice “a≃0.07fm” by Wilson-type quarks T. Umeda (Hiroshima) /15

  15. Summary & outlook • Equation of state • More statistics are needed in the lower temperature region • - Results at different scales (β=1.90 by CP-PACS/JLQCD) • - Techniques to suppress statistical error of EoS • Nf=2+1 QCD just at the physical point • the physical point (pion mass ~ 140MeV) by PACS-CS • β=1.90 is appropriate to control stat. error at lower T. • Odd Nt config. generation is necessary. • Finite density • Taylor expansion method to explore EOS at μ≠0 T. Umeda (Hiroshima) /15

  16. Quark mass dependence of Trace anomaly 0.05ms HotQCD PRD91,054504(2010) CP-PACS PRD64,074510 (2001) • peak height of the Trace anomaly •  small quark mass dependence • Our result seems to be reasonable ! • but small mq is necessary. 0.2ms HotQCD arXiv1005.1131 T. Umeda (Hiroshima)

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