1. Quarks Quarks in the Quark-Gluon Plasma Masakiyo Kitazawa (Osaka Univ.) Tokyo Univ., Sep. 27, 2007 Lattice Study of F. Karsch and M.K., arXiv:0708.0299

2. QGP Phase near T c QGP Phase near T c RHIC experiments Lattice simulations strong collective behavior  perfect fluid? critical temperature energy density charmonium spectra Asakawa, Hatsuda, PRL92,012001 (’04). Datta, Karsch, Petreczky, PRD69,094507 (’04). Umeda, Nomura Matsufuru, EPJC39S1,9 (‘05). M. Cheng, et al., PRD74,054507 (’06). Y. Aoki, et al., PLB643,46 (’06).

3. Why Quark ? Why Quark ? Because there are quarks. in the deconfined phase as the basic degrees of freedom of QCD will have many informations of the matter

4. Why Quark ? Why Quark ? Bowman et al. Because there are quarks. Study of property of quark in lattice Z(p)Z(p) M(p)M(p) in the deconfined phase as the basic degrees of freedom of QCD will have many informations of the matter vacuum finite T Bowman, Heller, Williams, Zhang, Coad, Leinweber, Furui, Nakajima, … Boyd, Gupta, Karsch NPB 385,481(’92). Petreczky, Karsch, Laermann, Stickan, Wetzorke, NPPS106,513(’02). Hamada, Kouno, Nakamura, Saito, Yahiro, hep-ph/0610010. : a paper and 2 proceedings.

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

6. Decomposition of Quark Propagator Decomposition of Quark Propagator Free quark with mass mHTL ( high T limit )

7. p / m  / m Decomposition of Quark Propagator Decomposition of Quark Propagator Free quark with mass mHTL ( high T limit ) p / m T  / m T

8. Quark Spectrum as a function of m 0 Quark Spectrum as a function of m 0 Quark propagator in hot medium at T >>T c - as a function of bare scalar mass m 0 How is the interpolating behavior? How does the plasmino excitation emerge as m 0  0 ? m 0 << gT  m 0 >> gT  We know two gauge-independent limits: m0m0 mTmT -m T +(,p=0)+(,p=0) +(,p=0)+(,p=0)

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

10. Quark Propagator in Quenched Lattice Quark Propagator in Quenched Lattice quenched approx. Configurations are distributed with a weight exp(  S G ). fermion matrix: Wilson fermion: in continuum We can calculate quark propagator with various m 0 for a given set of gauge(-fixed) configuration!

11. Correlator and Spectral Function Correlator and Spectral Function  E1E1 E2E2 Z1Z1 Z2Z2 observable in lattice dynamical information 2-pole structure may be a good assumption for  + (  ). 4-parameter fit E 1, E 2, Z 1, Z 2

12. Simulation Setup Simulation Setup quenched approximation clover improved Wilson Landau gauge fixing T  NN Lattice size 1.5T c 6.641248 3 x12, 36 3 x12 6.871664 3 x16, 48 3 x16 3Tc3Tc 7.191248 3 x12, 36 3 x12 7.451664 3 x16, 48 3 x16 configurations generated by Bielefeld collaboration vary bare quark mass m 0 see only zero momentum p=0 2-pole approx. for  + ( ,p=0) wall source

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

14. Exercise 1 : Dirac Structure of C (   ) Exercise 1 : Dirac Structure of C (   ) quark propagator in stand. repr. p=0p=0 even odd correlator in imag. time symmetric anti-symm. Chiral symmetric  S s =0  S + is an even function.

15. Exercise 2 : C (   ) and   (   ) Exercise 2 : C (   ) and   (   )  E0 log C(  ) 01  log C(  ) 01   EE 0

16. Exercise 2 : C (   ) and   (   ) Exercise 2 : C (   ) and   (   ) E0 log C(  ) 01  log C(  ) 01   E0 EE 

17. Correlation Function Correlation Function We neglect 4 points near the source from the fit. 2-pole ansatz works quite well!! (  2 /dof.~2 in correlated fit) 64 3 x16,  = 7.459,  = 0.1337, 51confs.  /T Fitting result  /T

18. m 0 Dependence of C + (  ) m 0 Dependence of C + (  )  = 0.134  = 0.132  = 0.130  /T Shape of C + (  ) changes from chiral symmetric to single pole structures.  c =0.13390 in vacuum m 0 : small m 0 : large

19. m 0 Dependence of C + (  ) m 0 Dependence of C + (  )  = 0.134  = 0.132  = 0.130  /T Shape of C + (  ) changes from chiral symmetric to single pole structures. m 0 : small m 0 : large  c =0.13390 in vacuum 0.1337 0.1340 0.1339

20. Spectral Function Spectral Function  E1E1 E2E2 Z1Z1 Z2Z2  E1E1 E2E2 Z1Z1 Z2Z2 T = 3T c 64 3 x16 (  = 7.459) E2E2 E1E1  = m 0 pole of free quark m 0 / T E / T Z 2 / (Z 1 +Z 2 ) T=3T c

21. Spectral Function Spectral Function T = 3T c 64 3 x16 (  = 7.459) E2E2 E1E1  = m 0 pole of free quark m 0 / T E / T Z 2 / (Z 1 +Z 2 ) Limiting behaviors for are as expected. Chiral symmetry of quark propagator restores around m 0 =0. E 2 >E 1 : qualitatively different from the 1-loop result. T=3T c

22. Temperature Dependence Temperature Dependence m T /T is insensitive to T. The slope of E 2 and minimum of E 1 is much clearer at lower T. T = 3T c T =1.5T c minimum of E 1 E2E2 E1E1 m 0 / T E / T Z 2 / (Z 1 +Z 2 ) 1-loop result might be realized for high T. 64 3 x16

23. Lattice Spacing Dependence Lattice Spacing Dependence 64 3 x16 (  = 7.459) 48 3 x12 (  = 7.192) E / T E2E2 E1E1 m 0 / T same physical volume with different a. No lattice spacing dependence within statistical error. T=3T c

24. Spatial Volume Dependence Spatial Volume Dependence E2E2 E1E1 m 0 / T E / T T=3T c 64 3 x16 (  = 7.459) 48 3 x16 (  = 7.459) same lattice spacing with different aspect ratio. Excitation spectra have clear volume dependence even for N  /N  =4.

25. Extrapolation of Thermal Mass Extrapolation of Thermal Mass Extrapolation of thermal mass to infinite spatial volume limit: Small T dependence of m T /T, while it decreases slightly with increasing T. Simulation with much smaller N  /N  is desireble. 3Tc3Tc 1.5T c m T /T 64 3 x16 48 3 x16 T=1.5T c T=3T c m T /T = 0.800(15) m T = 322(6)MeV m T /T = 0.771(18) m T = 625(15)MeV

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

27. Summary Summary Excitations of quark degrees of freedom near but above T c have a simple excitation spectrum having a plasmino mode and m T ! Thermal gluon field gives rise to the thermal mass in the light quark spectra. The plasmino mode disappears for heavy quarks. The ratio m T /T is insensitive to T near T c. Future Work Future Work finite momentum / gauge dependence / T~T c & T >>T c full QCD / gluon propagator / … Lattice simulation can successfully analyze it. different behavior from 1-loop result. strong spatial volume dependence of thermal mass. Puzzles :