JPS2010springT. Umeda (Hiroshima)1 ウィルソンクォークを用いた N f =2+1 QCD の熱力学量の研究 Takashi Umeda (Hiroshima Univ.) for WHOT-QCD Collaboration JPS meeting, Okayama Univ., Okayama, March 2010 /14

JPS2010springT. Umeda (Hiroshima)2 Motivation /14 QCD Thermodynamics on the lattice QCD Thermodynamics on the lattice Phase diagram in (T, μ, m ud, m s ) Phase diagram in (T, μ, m ud, m s ) Transition temperature Transition temperature Equation of state ( e, p, s,...) Equation of state ( e, p, s,...) Heavy quarkonium Heavy quarkonium Transport coefficients (shear/bulk viscosity) Transport coefficients (shear/bulk viscosity) Finite chemical potential Finite chemical potential etc... etc... These are important to study - Quark Gluon Plasma in Heavy Ion Collision exp. - Early universe - Neutron star - etc... quantitative studies qualitative studies

JPS2010springT. Umeda (Hiroshima)3 QCD Thermodynamics on the lattice /14 Most studies done with staggerd-type quarks less computational costs less computational costs a part of chiral sym. preserved... a part of chiral sym. preserved...  N f =2+1, almost physical quark mass, μ ≠0  N f =2+1, almost physical quark mass, μ ≠0 4th-root trick to remove unphysical “tastes” 4th-root trick to remove unphysical “tastes”  non-locality “universality is not guaranteed”  non-locality “universality is not guaranteed” It is important to cross-check with theoretically sound lattice quarks Our aim is to investigate QCD Thermodynamics with Wilson-type quarks QCD Thermodynamics with Wilson-type quarks

JPS2010springT. Umeda (Hiroshima)4 Improved staggered (p4fat vs asqtad) /14 Y.Aoki et al., JHEP06 (2009) 088 chiral susceptibility renormalized chiral condensate (In Sect.4: conclusions, outlooks) As a final remark we have to mention that the staggered formalism used in this work and all other large scale thermodynamics studies may suffer from theoretical problems. To date it is not proven that the staggered formalism with 2+1 flavors really describes QCD in the continuum limit. Therefore it is desirable to also study QCD thermodynamics with a theoretically firmly established (e.g. Wilson type) fermion discretization.

JPS2010springT. Umeda (Hiroshima)5 Conventional approach to study QCD thermodynamics /14 safe region ? integral method needs low T (p=0) (3fm/a) 3 = fixed N t approach Temperature T=1/(N t a) is varied by a at fixed N t Disadvantages Disadvantages - Line of Constant Physics - Line of Constant Physics - T=0 subtraction for renorm. - T=0 subtraction for renorm. - small 1/a at low T region - small 1/a at low T region Advantages Advantages - T resolution by integer N t - T resolution by integer N t - program for odd N t - program for odd N t - (1/a) vs T at high T - (1/a) vs T at high T

JPS2010springT. Umeda (Hiroshima)6 Fixed scale approach to study QCD thermodynamics /14 Temperature T=1/(N t a) is varied by N t at fixed a safe region ? integral method needs low T (p=0) (3fm/a) 3 = fixed scale approach Advantages Advantages - 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 ) - larger 1/a at whole T region - larger 1/a at whole T region Disadvantages Disadvantages - T resolution by integer N t - T resolution by integer N t - program for odd N t - program for odd N t - (1/a) vs T at high T - (1/a) vs T at high T

JPS2010springT. Umeda (Hiroshima)7 T-integration method to calculate the EOS /14 We propose a new method (“T-integration method”) to calculate the EOS at fixed scales Our method is based on the trace anomaly (interaction measure), and the thermodynamic relation. T.Umeda et al. (WHOT-QCD), Phys.Rev.D79 (2009) (R)

JPS2010springT. Umeda (Hiroshima)8 Pressure & Energy density in quenched QCD /14 Integration Integration is performed with the cubic is performed with the cubic spline of (e-3p)/T 4 spline of (e-3p)/T 4 Cubic spline vs trapezoidal inte. Cubic spline vs trapezoidal inte. yields small difference ~ 1σ yields small difference ~ 1σ Our results are roughly Our results are roughly consistent with previous results. consistent with previous results. Unlike the fixed N τ approach, Unlike the fixed N τ approach, scale/temp. is not constant. scale/temp. is not constant.  Lattice artifacts increase  Lattice artifacts increase as temperature increases. as temperature increases.

JPS2010springT. Umeda (Hiroshima)9 T=0 & T>0 configurations for N f =2+1 QCD /14 Basic T=0 simulation: Basic T=0 simulation: CP-PACS / JLQCD Collab. N f =2+1 study Phys. Rev. D78 (2008) CP-PACS / JLQCD Collab. N f =2+1 study Phys. Rev. D78 (2008) RG-improved Iwasaki glue + NP clover-improved Wilson quarks - (2 fm) 3 lattice, a=0.07, 0.1, 0.12 fm - configurations available on the ILDG T>0 simulations: on 32 3 x N t (N t =4, 6,..., 14, 16) lattices T>0 simulations: on 32 3 x N t (N t =4, 6,..., 14, 16) lattices Nt’s correspond to T~170—700MeV Nt’s correspond to T~170—700MeV

JPS2010springT. Umeda (Hiroshima)10 Beta-functions from CP-PACS/JLQCD results /14 Beta-functions to calculate the EOS of Nf=2+1 QCD Nf=2+1 QCD  β, κ ud, κ s  β, κ ud, κ s e.g. m ρ, e.g. m ρ, m π /m ρ, m π /m ρ, m ηss /m φ m ηss /m φ Inverse matrix method Phys. Rev. D64 (2001) Phys. Rev. D64 (2001) (1) Collect T=0 lattice results of #param. observables (2) Fit them as functions of coupling param. (3) Determine LCP’s (4) Invert the coupling param. dependence of observables along a LCP. in case of Nf=2

JPS2010springT. Umeda (Hiroshima)11 Beta-functions from CP-PACS/JLQCD results /14 Direct fit method Phys. Rev. D64 (2001) fit β,κ ud,κ s as functions of χ 2 /dof~5 χ 2 /dof~2

JPS2010springT. Umeda (Hiroshima)12 First trial calculations on these configurations /14 gluon contribution to the trace anomaly (cf.1) peak height ~ 7 (KS N f =2+1 N t =8) (cf.2) peak height ~ 13 (Wilson N f =2 N t =4) gluon ~ 45, quark ~ -32 gluon ~ 45, quark ~ -32 Preliminary !

JPS2010springT. Umeda (Hiroshima)13 Heavy quark free energy at T>T c /14 Temp. insensitivity of F 1 (r,T) Temp. insensitivity of F 1 (r,T) at short distances Q’s are screened at T>Tc Q’s are screened at T>Tc at long distances - HQ free energy in the color singlet channel Fixed scale approach : equal renormalization for all T  no T-dependent adjustments needed for the constant term in F 1 (r,T) ( 2 x single quark free energy ) T=0 data by CP-PACS/JLQCD

JPS2010springT. Umeda (Hiroshima)14 Perspectives /14 Beta functions Beta functions More work needed More work needed Reweighting method to directly calculated beta functions Reweighting method to directly calculated beta functions at the simulation point ? at the simulation point ? Equation of state Equation of state Fermion part measurement Fermion part measurement Nf=2+1 QCD just at the physical point Nf=2+1 QCD just at the physical point the physical point (pion mass ~ 140MeV) the physical point (pion mass ~ 140MeV) with N f =2+1 Wilson quarks (PACS-CS) with N f =2+1 Wilson quarks (PACS-CS) Finite density Finite density We can combine our approach with the Taylor expansion method, We can combine our approach with the Taylor expansion method, to explore EOS at μ ≠0 to explore EOS at μ ≠0

JPS2010springT. Umeda (Hiroshima)15 /13 Thank you for your attention !!!