Bulk and Spectral Observables in Lattice QCDTetsuo Hatsuda () Univ. Tokyo Three Major Tools to study Early Universe

[1] Introduction -- lattice approach to hot QCD

[2] Bulk properties of hot QCD

-- equation of state (precision) -- order of the thermal transition (precision) -- critical temperature (precison) -- critical point at finite density (exploratory)

[3] Spectral properties of hot QCD

-- heavy probes (exploratory) -- light probes (exploratory)

[4] SummaryContents

T Introduction

Lattice QCD

Lattice thermodynamics Full QCD

To collect 1000 indep. gauge conf.On 243x40, a=0.08 fm lattice (T=0)Clark, hep-lat/0610048.

Bulk Properties of Hot QCD

Energy density in full QCD (Nf=2+1)MILC Coll., hep-lat/061001O(a2) improved actionNs/Nt=2, inexact R-algorithm.

Order of the transition in full QCD (Nf=2+1)

Pseudo critical temperature Tpc

MILC Coll., hep-lat/0405029169(12)(4)(5) MeVAsqtad, Nt=4,6,8, Ns/Nt=2, r_1=0.317(7) fm

RBC-Bielefeld Coll., hep-lat/0608013192(7)(4) MeVP4fat3, Nt=4,6 Ns/Nt=2-4, r_0=0.469(7) fm

Wuppertal-Budapest Coll., hep-lat/0609068 151(3)(3) MeV + 9 MeVstout, Nt=6,8,10, Ns/Nt=4, F_K scale

WHOT-QCD Coll., preliminary 175(4)(2) MeV (Nf=2, Nt=6, Polyakov-loop sus.)clover, Nt=4, 6, Ns/Nt=3-4, m_V scaleWilson fermionStaggered fermionTpc (a 0) in full QCD (Nf=2+1) from cm/T2

Tpc on the lattice from chain rule

Critical point Cf. Asakawa & Yazaki, NPA504 (1989) 668 Klimt, Lutz & Weise, PLB249 (90) 386

Charmonium wave functionquenched QCD)

Charmonium spectra in quenched QCDh

Charmonium spectra in full QCD (Nf=2)

Datta, Karsch, Wissel, Petreczky & Wetzorke, [hep-lat/0409147]

Aarts, Allton, Foley, Hands & Kim, [hep-lat/0610061]g J/Y moving in the plasma in quenched QCD

quenched, a = 0.02 fmDatta, Jakovac, Karsch & Petreczky, [hep-lat/0603002]Bottomonium spectra in quenched QCD

Asakawa, Nakahara & Hatsuda, [hep-lat/0208059] mud

Hot QCD -- a paradigm --

Summary2. Progress in bulk thermodynamics Equation of state, Pseudo-critical temperature, Susceptibilities precision science3. Progress in spectral analysis elementary excitations in QGP still exploratory4. Progress in finite density many attempts, no conclusion yet

Back up slides

Scale of each phase

Symmetry of each phase (case for small mud with ms=)

Ginzburg-Landau Potential (3-flavor, chiral limit)Symmetry: Chiral modes: Diquark modes:

GSU(3)LSU(3)R B# A#SU(3)C 3 3* 0 2/3 1 3 1 2/3 -2/3 3 1 3 2/3 2/3 3

Ginzburg-Landau Potential (3-flavor, chiral limit)

= U(1)A breaking terms = Yamamoto, Tachibana, Baym & Hatsuda, hep-ph/0605018

Examples in full lattice QCD

QGP for g > 100 GeV )

QCD is non-perturbative even at T = Non-Abelian magnetic problem

Karsch, hep-lat/0608003

Wuppertal-Budapest Coll., hep-lat/0510084 stout, Ccond/Cnt correction by hand Ns/Nt=3

Heavy probes of QGP

Singlet free energy in full QCD (Nf=2+1)RBC-Bielefeld Coll., hep-lat/0610041163x4, p4fat3 action, mud/ms=0.1

Casimir scaling in full QCD (Nf=2)WHOT-QCD Coll., (Maezawa et al.,)In preparation

quark - anti-quark channelquark-quark channelCasimir scaling in full QCD (Nf=2)WHOT-QCD Coll., (Maezawa et al.,)In preparation