F. Karsch and M.K., Phys. Lett. B, in press. RCNP, 30, Oct., 2007 格子QCD数値計算を用いた QGP相におけるクォークの探求 北沢正清 F. Karsch and M.K., Phys. Lett. B, in press. (arXiv:0708.0299)

Phase Diagram of QCD Lattice QCD Monte Carlo simulation T property of quarks in this region = first principle calculation of QCD Tc in the deconfined phase as the basic degrees of freedom of QCD will have many informations of the matter hadron phase (confined phase) color superconductivity m

Phase Diagram of QCD Lattice QCD Monte Carlo simulation T property of quarks in this region = first principle calculation of QCD Tc Boyd, Gupta, Karsch, NPB 385,481(’92). Petreczky, et al., NPPS106,513(’02). Hamada, et al., hep-ph/0610010. hadron phase (confined phase) color superconductivity m

Quarks at Extremely High T Hard Thermal Loop approx. ( p, w, mq<<T ) 1-loop (g<<1) Klimov ’82, Weldon ’83 Braaten, Pisarski ’89 Gauge independent spectrum w / mT “plasmino” 2 collective excitations having a “thermal mass” The plasmino mode has a minimum at finite p. p / mT

Decomposition of Quark Propagator HTL ( high T limit ) Free quark with mass m p / mT w / mT p / m w / m

Quark Spectrum as a function of m0 Quark propagator in hot medium at T >>Tc - as a function of bare scalar mass m0 m0 << gT w m0 >> gT We know two gauge-independent limits: m0 mT -mT r+(w,p=0) How is the interpolating behavior? How does the plasmino excitation emerge as m00 ?

Fermion Spectrum in QED & Yukawa Model Baym, Blaizot, Svetisky, ‘92 Yukawa model: 1-loop approx.: Spectral Function for g =1 , T =1 m0/T=0.01 0.8 0.45 0.3 0.1 r+(w,p=0) w/T thermal mass mT=gT/4 single peak at m0 Plasmino peak disappears as m0 /T becomes larger. cf.) massless fermion + massive boson M.K., Kunihiro, Nemoto,’06

Simulation Setup vary bare quark mass m0 for zero momentum p=0 T b Lattice size 1.5Tc 6.64 483x12 6.87 643x16, 483x16 3Tc 7.19 7.45 quenched approximation clover improved Wilson Landau gauge fixing 2-pole approx. for r+(w,p=0) wall source

Simulation Setup vary bare quark mass m0 for zero momentum p=0 T b Lattice size 1.5Tc 6.64 483x12 6.87 643x16, 483x16 3Tc 7.19 7.45 quenched approximation clover improved Wilson Landau gauge fixing 2-pole approx. for r+(w,p=0) wall source

Simulation Setup vary bare quark mass m0 for zero momentum p=0 T b Lattice size 1.5Tc 6.64 483x12 6.87 643x16, 483x16 3Tc 7.19 7.45 quenched approximation clover improved Wilson Landau gauge fixing 2-pole approx. for r+(w,p=0) wall source 4-parameter fit E1, E2, Z1, Z2

Correlation Function 643x16, b = 7.459, k = 0.1337, 51confs. Fitting result t /T We neglect 4 points near the source from the fit. 2-pole ansatz works quite well!! ( c 2/dof.~2 in corr. fit )

m0 Dependence of C+(t ) m0: small k = 0.134 k = 0.132 m0: large kc=0.13390 m0: small k = 0.134 k = 0.132 m0: large k = 0.130 t /T Shape of C+(t) changes from chiral symmetric to single pole structures.

Spectral Function T = 3Tc 643x16 (b = 7.459) T=3Tc E2 E / T E1 w = m0 pole of free quark Z2 / (Z1+Z2) m0 / T w E1 -E2 Z1 Z2 w E1 -E2 Z1 Z2

Spectral Function T = 3Tc 643x16 (b = 7.459) T=3Tc E2 E / T E1 w = m0 pole of free quark Z2 / (Z1+Z2) m0 / T Limiting behaviors for are as expected. Chiral symmetry of quark propagator restores around m0=0. Quarks in the chiral limit have a thermal mass! E2>E1 : qualitatively different from the 1-loop result.

Temperature Dependence 643x16 T = 3Tc T =1.5Tc E / T E1 minimum of E1 Z2 / (Z1+Z2) m0 / T mT /T is insensitive to T. The slope of E2 and minimum of E1 is much clearer at lower T.

Lattice Spacing Dependence T=3Tc E2 643x16 (b = 7.459) 483x12 (b = 7.192) E / T E1 same physical volume with different a. m0 / T No lattice spacing dependence within statistical error.

Spatial Volume Dependence T=3Tc E2 643x16 (b = 7.459) 483x16 E / T E1 same lattice spacing with different aspect ratio. m0 / T Excitation spectra have clear volume dependence even for Ns /Nt =4.

Extrapolation of Thermal Mass Extrapolation of thermal mass to infinite spatial volume limit: T=1.5Tc mT /T = 0.800(15) mT = 322(6)MeV mT /T 1.5Tc 3Tc T=3Tc 643x16 483x16 mT /T = 0.771(18) mT = 625(15)MeV Small T dependence of mT/T, while it decreases slightly with increasing T. Simulation with much larger volume is desireble.

Preliminary Charm Quark & J/y charm quark T = 1.5Tc threshold 2mc Z2/(Z1+Z2)は十分小さい 　　　c-quarkは、free quarkに近い粒子描像を持つ。 J/y粒子は閾値2mcより高いエネルギーを持つ？

Preliminary!!! Finite Momentum In the chiral limit, E1 E / T E2 p / T E2<E1 for finite momentum.

Effect of Dynamical Quarks Quark propagator in quench approximation: In full QCD,  screen gluon field  suppress mT?  meson loop  will have strong effect if mesonic excitations exist massless fermion + massive boson  3 peaks in quark spectrum! M.K., Kunihiro, Nemoto, ‘06

まとめ 臨界温度付近のQGP相におけるクォークは、熱質量および plasminoを伴った崩壊幅の小さい準粒子として振る舞っている。 格子QCDはクォークの解析に適している。 lightクォークは、ゲージ場の媒質効果により温度程度の熱質量を獲得する。 Heavyクォーク極限ではplasminoの寄与は無視でき、自由粒子のそれへ漸近する。 比 mT/T の温度依存性は、今回調べた温度領域で非常に小さい。 Puzzles : 1-loop とは定性的に異なる振る舞い。 強い空間体積依存性。

展望 クォークの微視的理解 基礎理論（QCD） QGP中のメソン励起、熱力学量 有効模型の構成 クォーク 有限温度多体系としての cf. M.K., Kunihiro, Nemoto, Mitsutani 基礎理論（QCD） QGP中のメソン励起、熱力学量 有効模型の構成 クォーク 有限温度多体系としての QGPの物性物理 体積効果：Karsch et al., 1283x16, 　　 LQGP collaboration, in progress full QCD 有限運動量 ゲージ依存性、 T~Tc & T >>Tc グルオンのpole mass 数値解析の展望 観測量 重イオン衝突実験

Choice of Source Wall source, instead of point source point: wall : t What’s the source? Wall source, instead of point source point: wall : point t same (or, less) numerical cost quite effective to reduce noise!! wall t the larger spatial volume, the more effective!

Elliptic Flow v2 v2 実空間 pT空間 v2 >0 v2 <0 RHICエネルギーではv2>0。 反応平面 pT空間 v2 >0 v2 <0 RHICエネルギーではv2>0。 完全流体模型が低pTでよく成り立つ。 非常に小さい粘性係数h 短い平均自由行程 strongly coupled QGP (sQGP) v2が飽和する pTは粒子により異なる。

Elliptic Flow v2 v2 実空間 pT空間 v2 >0 v2 <0 クォーク数によるscalingが 反応平面 pT空間 v2 >0 v2 <0 クォーク数によるscalingが 非常に良く成り立っている。 　　　　　　　　　　　　　　　Nonaka, et al. RHICエネルギーではv2>0。 完全流体模型が低pTでよく成り立つ。 非常に小さい粘性係数h Recombination Modelの成功。 短い平均自由行程 strongly coupled QGP (sQGP) v2が飽和する pTは粒子により異なる。

Quark Propagator in Quenched Lattice quenched approx. Configurations are distributed with a weight exp(-SG). fermion matrix: in continuum Wilson fermion: We can calculate quark propagator with various m0 for a given set of gauge(-fixed) configuration!

Dirac Structure of Quark Propagator in stand. repr. even odd Chiral symmetric  Ss=0  S+ is an even function.