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格子 QCD 数値計算を用いた QGP 相におけるクォークの探求

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. in the deconfined phase as the basic degrees of freedom of QCD will have many informations of the matter. property of quarks in this region.

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格子 QCD 数値計算を用いた QGP 相におけるクォークの探求

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  1. 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)

  2. Phase Diagram of QCD • in the deconfined phase • as the basic degrees of freedom of QCD • will have many informations of the matter property of quarks in this region T Lattice QCD Monte Carlo simulation = first principle calculation of QCD Tc hadron phase (confined phase) color superconductivity m 0

  3. Phase Diagram of QCD property of quarks in this region T Lattice QCD Monte Carlo simulation = 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 0

  4. 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

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

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

  7. m0/T=0.01 0.1 0.3 r+(w,p=0) 0.45 0.8 w/T Fermion Spectrum in QED & Yukawa Model Baym, Blaizot, Svetisky, ‘92 Yukawa model: 1-loop approx.: Spectral Function for g =1 , T =1 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

  8. Simulation Setup • vary bare quark mass m0 • for zero momentum p=0 • quenched approximation • clover improved Wilson • Landau gauge fixing • 2-pole approx. for r+(w,p=0) • wall source

  9. Simulation Setup • vary bare quark mass m0 • for zero momentum p=0 • quenched approximation • clover improved Wilson • Landau gauge fixing • 2-pole approx. for r+(w,p=0) • wall source

  10. Simulation Setup • vary bare quark mass m0 • for zero momentum p=0 • 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

  11. 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 ansatzworks quite well!! ( c 2/dof.~2 in corr. fit )

  12. m0 Dependence of C+(t ) 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.

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

  14. T = 3Tc 643x16 (b = 7.459) Spectral Function T=3Tc E2 E / T w = m0 pole of free quark E1 Z2 / (Z1+Z2) m0 / T • Limiting behaviors forare 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.

  15. T= 3Tc T=1.5Tc minimum of E1 Temperature Dependence E2 643x16 E / T 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.

  16. 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.

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

  18. 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.

  19. threshold 2mc Charm Quark & J/y charm quark T = 1.5Tc Preliminary • 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？

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

  21. 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

  22. 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。

  23. クォークの微視的理解 cf. M.K., Kunihiro, Nemoto, Mitsutani 数値解析の展望 • QGP中のメソン励起、熱力学量 • 有効模型の構成 • 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 展望 基礎理論（QCD） クォーク 有限温度多体系としての QGPの物性物理 観測量 重イオン衝突実験

  24. Choice of Source 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!

  25. Elliptic Flow v2 実空間 v2 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。

  26. Elliptic Flow v2 実空間 v2 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。 Recombination Modelの成功。 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。

  27. 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!

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

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