Nf21 QCD Takashi Umeda Hiroshima Univ for WHOTQCD

ウィルソンクォークを用いた Nf=2+1 QCD の状態方程式の研究 Takashi Umeda (Hiroshima Univ. ) for WHOT-QCD Collaboration JPS meeting, Kyushu-koudai, Fukuoka, 13 Sep. 2010 JPS autumn 2010 T. Umeda (Hiroshima) 1 /12

Quark Gluon Plasma in Lattice QCD from the Phenix group web-site Observables in Lattice QCD http: //www. gsi. de/fair/experiments/ JPS autumn 2010 n Phase diagram in (T, μ, mud, ms) n Transition temperature n Equation of state ( ε/T 4, p/T 4, . . . ) n Hadronic excitations n Transport coefficients n Finite chemical potential n etc. . . T. Umeda (Hiroshima) 2 /12

Choice of quark actions on the lattice Most (T, μ≠ 0) studies done with staggerd-type quarks n less computational costs n a part of chiral sym. preserved. . . Nf=2+1, almost physical quark mass, (μ≠ 0) n 4 th-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 investigate QCD Thermodynamics with Wilson-type quarks WHOT-QCD Collaboration JPS autumn 2010 T. Umeda (Hiroshima) 3 /12

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 fine ~ coarse JPS autumn 2010 ed fix n Advantages - Line of Constant Physics - T=0 subtraction for renorm. (spectrum study at T=0 ) - larger 1/a in whole T region n Disadvantages - T resolution by integer Nt - UV cutoff eff. at high T h ac fixedroscale approach p p a Nt T. Umeda (Hiroshima) 4 /12

T=0 & T>0 configurations for Nf=2+1 QCD n T=0 simulation: on 283 x 56 by CP-PACS/JLQCD Phys. Rev. D 78 (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 n T>0 simulations: on 323 x Nt (Nt=4, 6, . . . , 14, 16) lattices RHMC algorithm, same parameters as T=0 simulation JPS autumn 2010 T. Umeda (Hiroshima) 5 /12

Formulation for Nf=2+1 improved Wilson quarks Phys. Rev. D 73, 034501 CP-PACS/JLQCD Noise method ( #noise = 1 for each color & spin indices ) JPS autumn 2010 T. Umeda (Hiroshima) 6 /12

Beta-functions from CP-PACS/JLQCD results Trace anomaly needs Beta-functions in Nf=2+1 QCD Direct fit method Phys. Rev. D 64 (2001) 074510 fit β, κud, κs as functions of with fixed JPS autumn 2010 T. Umeda (Hiroshima) 7 /12

Beta-functions from CP-PACS/JLQCD results Meson spectrum by CP-PACS/JLQCD Phys. Rev. D 78 (2008) 011502. 3 (β) x 5 (κud) x 2 (κs) = 30 data points fit β, κud, κs as functions of χ2/dof=5. 3 χ2/dof=1. 6 χ2/dof=2. 1 only statistical error JPS autumn 2010 T. Umeda (Hiroshima) 8 /12

Trace anomaly in Nf=2+1 QCD Preliminary Nt 56 16 14 12 10 8 6 4 JPS autumn 2010 T. Umeda (Hiroshima) config. (x Sg 1300(*) 1542 1448 1492 863 628 657 802 5 MD traj. ) Sq (**) 980 647 695 487 520 360 295 (*) T=0 (Nt=56) by CP-PACS/JLQCD Sg calculated with 6500 traj. (**) thermal. = 1000 traj. 9 /12

Trace anomaly in Nf=2+1 QCD WHOT-QCD Collaboration stout S. Borsanyi et al. , ar. Xiv: 1007. 2580 Preliminary HISQ peak height = 4~6 in recent Staggered results ( mq ~ mqphys. ) JPS autumn 2010 T. Umeda (Hiroshima) Hot. QCD, ar. Xiv: 1005. 1131 n 10 /12

Equation of State in Nf=2+1 QCD Preliminary SB limit n T-integration is performed by the trapezoidal rule (straight line interpolation). n n JPS autumn 2010 T. Umeda (Hiroshima) ε/T 4 is calculated from Large error in whole T region 11 /12

Summary & outlook We presented the EOS in Nf=2+1 QCD using improve Wilson quarks n Equation of state More statistics are needed in the lower temperature region Results at different scales (β=1. 90 by CP-PACS/JLQCD) n Nf=2+1 QCD just at the physical point (pion mass ~ 140 Me. V) by PACS-CS β=1. 90 is appropriate to control stat. error at lower T. Odd Nt config. generation is necessary. n Finite density Taylor expansion method to explore EOS at μ≠ 0 JPS autumn 2010 T. Umeda (Hiroshima) 12 /12

T-integration method to calculate the EOS We propose a new method (“T-integration method”) to calculate the EOS at fixed scales T. Umeda et al. (WHOT-QCD), Phys. Rev. D 79 (2009) 051501(R) Our method is based on the trace anomaly (interaction measure), and thermodynamic relation. JPS autumn 2010 T. Umeda (Hiroshima) 13

Test in quenched QCD n Our results are roughly consistent with previous results. n Our results deviate from the fixed Nt=8 results [*] at higher T ( a. T~0. 3 or higher ) n Trace anomaly is sensitive to ~ spatial volume at lower T (below Tc). V > (2 fm)3 is ncessarry. [*] G. Boyd et al. , NPB 469, 419 (1996) JPS autumn 2010 T. Umeda (Hiroshima) 14

Quark mass dependence of Trace anomaly 0. 05 ms Hot. QCD PRD 91, 054504(2010) 0. 2 ms CP-PACS PRD 64, 074510 (2001) n peak height of the Trace anomaly small quark mass dependence n Our result seems to be reasonable ! but small mq is necessary. Hot. QCD ar. Xiv 1005. 1131 JPS autumn 2010 T. Umeda (Hiroshima) 15