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Masakiyo Kitazawa (Osaka Univ.)

BNL, Apr., 25, 2008. Spectral Properties of Quarks at Finite Temperature in Quenched Lattice QCD. Masakiyo Kitazawa (Osaka Univ.). with Frithjof Karsch. F. Karsch and MK, PL B658 ,45 (2007) [arXiv:0708.0299]; in preparation. Why Quarks ? .

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Masakiyo Kitazawa (Osaka Univ.)

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  1. BNL, Apr., 25, 2008 Spectral Properties of Quarks at Finite Temperature in Quenched Lattice QCD Masakiyo Kitazawa (Osaka Univ.) with Frithjof Karsch F. Karsch and MK, PLB658,45 (2007) [arXiv:0708.0299]; in preparation.

  2. Why Quarks ? The quark may beone of the basic d.o.f. of the QGP. — success of the recombination model — fluctuations in full lattice QCD It is a gauge dependent quantity. — but, poles should be gauge independent The quarks at high T have collective natures. Exploring the quark spectral function as functions of — bare quark mass — temperature (above and below Tc) — momentum

  3. Quarks at Extremely High T Klimov ’82, Weldon ’83 Braaten, Pisarski ’89 • Hard Thermal Loop approx. ( p, w, mq<<T ) • 1-loop (g<<1) • Gauge invariant spectrum • 2 collective excitations • having a “thermal mass” ~ gT w / mT “plasmino” • width ~g2T • The plasmino mode has • a minimum at finite p. p / mT

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

  5. Bare quark mass dependence at zero momentum for T=3Tc

  6. We know two gauge-invariant 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. m/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 MK, Kunihiro, Nemoto,’06

  8. Simulation Setup • quenched approximation • clover improved Wilson • Landau gauge fixing • 2-pole approx. for r+(w,p=0) • wall source configurations generated byBielefeld collaboration

  9. 2-pole structure may be a good assumption for r+(w). Z2 Z1 4-parameter fit E1, E2, Z1, Z2 w -E2 E1 Correlator and Spectral Function dynamical information observable in lattice

  10. 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!

  11. Dirac Structure of r(t) in stand. repr. correlator in imag. time symmetric anti-symm. quark propagator p=0 even odd Chiral symmetric  rs=0  r+ is an even function.

  12. 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 correlated fit)

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

  14. Spectral Function T = 3Tc 643x16 (b = 7.459) T=3Tc E2 E / T w = m0 pole of free quark E1 Z2 / (Z1+Z2) m0 / T • Limiting behaviors forare as expected. • Quark propagator approaches the chiral symmetric one near m0=0. • E2>E1 : qualitatively different from the 1-loop result.

  15. 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.

  16. 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.

  17. Temperature Dependence

  18. minimum of E1 Temperature Dependence 643x16 E2 T= 3Tc E / T E1 T= 1.5Tc T= 1.25Tc 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. 1-loop result might be realized for high T.

  19. Extrapolation of Thermal Mass Extrapolation of thermal mass to infinite spatial volume limit: T=1.25Tc mT/T = 0.816(20) mT = 274(8)MeV 483x16 mT/T T=1.5Tc mT/T = 0.800(15) mT = 322(6)MeV 643x16 T=3Tc 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 desirable.

  20. threshold 2mc Charm Quark k from Datta et al. PRD69,094507(2004). T=1.5Tc mc preliminary • Charm quark is free-quark like, rather than HTL. • The J/y peak in MEMseems to exist above 2mc.

  21. Quark correlator below Tc • is convex upward. • inconsistent with positive r (w). • does not approach the chiral • sym. one in the chiral limit. Below Tc for 483x16 lattices T/Tc= 3, 1.5, 1.25, 0.9, 0.55.

  22. Momentum Dependence

  23. p=0 m=0 Finite Momentum • Spectral function in each channel • is positive definite!

  24. HTL(1-loop) Pole Structure for p>0 • 2-pole approx. works • well again. • E2<E1; consistent with the HTL result. • E1 approaches the light cone for large momentum.

  25. Summary We analyzed the quark spectral function at finite T in lattice QCD. Above Tc, The quark degrees of freedom have a simple quasi-particle picture similar to that in the high T limit even near Tc. — Light quarks have the plasmino and thermal mass. — The ratio mT/T is insensitive to T near Tc. Below Tc, The pole approximation fails completely. Future Work gauge dependence / volume dependence / full QCD / gluon propagator / …

  26. 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

  27. Beyond the Chiral Limit 643x16, T=3Tc T=3Tc E2 E / T E1 Z2 / (Z1+Z2) m0 / T , -m0 / T • Inversion routine converges down to m0/T~-0.2 for 643x16, T=3Tc. • Propagator has a symmetric properties for positive and negative mass.

  28. A quark and a thermally- excited anti-quark annihilate and produce a gluon. = w / mT The quark turns into the “anti-quark hole”. What is the Plasmino? A quark is scattered by a gluon. =

  29. m0 Dependence of C+(t ) kc=0.13390 in vacuum 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.

  30. 0.1337 0.1340 0.1339 m0 Dependence of C+(t ) kc=0.13390 in vacuum 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.

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