1. QCD 相転移における秩序変数 揺らぎとクォークスペクトル 根本幸雄 ( 名古屋大 ) with 北沢正清 ( 基研 ) 国広悌二 ( 基研 ) 小出知威 (Rio de Janeiro Federal U.)

2. Phase Diagram of QCD RHIC T  E Tc 2Tc chiral sym. broken (antiquark-quark condensate) confinement chiral sym. restored deconfinement quark-quark condensate FAIR compact stars fluctuations of PRD65,091504,2002 (KKKN) PRD70,056003,2004 (KKKN) PTP.114,117,2005 (KKKN) PLB631,157,2005 (KKN) ~170 MeV from Lattice QCD PLB633,269,2006 (KKN)

3. QGP from high T to low T strong coupling weak coupling HTL approximation Hadronic QGP GeV ~ Lattice QCD at finite T (current status) quenched approximation full QCD with heavy quark mass our approach model calculation massless quark limit (chiral limit) genuine phase transition dynamics ~ ~ weak coupling Mean field approx. exact chiral symmetry CSC from high  to low  CSC HDL appoximation Matsuura et al. 2004

4. Quark spectrum above T  CSC phase transition fluctuations of

5. NJL-like model (w/ diquark-correlation) (2-flavor,chiral limit)  ： SU(2) F Pauli matrices ： SU(3) C Gell-Mann matrices C :charge conjugation operator so as to reproduce Parameters: Klevansky(1992), T.M.Schwarz et al.(1999) 2SC is realized at low  and near T c. Nambu-Jona-Lasinio model 2nd order transition from Wigner-to-CSC, even in the finite current quark mass. Wigner phase

6. Description of fluctuations Linear response theory Response of quark plasma to the perturbation caused by an external pair field: A pair field is induced in the neighborhood of the external field: Linear response :Response function=Retarded Green function We use RPA:

7. Collective Modes Collective mode is an elementary excitation of the system induced spontaneously. For the infinitesimally small external field, is non-zero if the denominator of is zero. Dispersion relation of the collective mode Spectral function: Strength of the response of the system to the external field. In general, is complex.

8. Spectrum of diquark-fluctuations Dynamical Structure Factor T =1.1T c T =1.05T c for  = 400 MeV Peaks of the collective modes survive up to T=1.2 Tc. (cf. 1.005 Tc in Metal) Large fluctuations soft modes diffusion-like Pole position in the complex  plane

9. Quark self-energy (T-approximation) Spectral Function of quark quark Spectrum of a single-quark anti-quark  = 400 MeV  =0.01  =   (p)  [MeV] k [MeV] 40 80 0 -40 -80 400 320 480 0  kFkF kFkF Normal Super Disp. Rel.

10. stronger diquark coupling G C Stronger diquark couplings GCGC ×1.3×1.5  = 400 MeV  =0.01

11. Resonant Scattering G C =4.67GeV -2 Mixing between quarks and holes  k  n f (  ) kFkF

12. Quark spectrum above T  chiral phase transition fluctuations of

13. Recent topics near Tc T  E Tc 2Tc RHIC experiments robust collective flow good agreement with rel. hydro models almost perfect fluid (quenched) Lattice QCD charmonium states up to 1.6-2.0 Tc (Asakawa et al., Datta et al., Matsufuru et al. 2004) Strongly coupled plasma rather than weakly interacting gas

14. Description of fluctuations Linear response theory Response of quark plasma to the perturbation caused by an external pair field: A pair field is induced in the neighborhood of the external field: Linear response :Response function=Retarded Green function We use RPA:

15. Hatsuda, Kunihiro ( ’ 85) sharp peak in time-like region  -mode Spectral Function k  propagating mode T = 1.1Tc m = 0 T Tc Spectrum of quark-antiquark fluctuations

16. |p||p| Quark self-energy Spectral Function quark 3 peaks in also 3 peaks in |p||p| Spectrum of a single-quark

17. Resonant Scatterings of Quark for CHIRAL Fluctuations =++ … E E dispersion law Landau damping processes

18. p [MeV] p  [MeV]  + ( ,k)  - ( ,k) Resonant Scatterings of Quark for CHIRAL Fluctuations E E “quark hole”: annihilation mode of a thermally excited quark “antiquark hole”: annihilation mode of a thermally excited antiquark (Weldon, 1989) lead to quark-”antiquark hole” mixing cf: hot QCD (HTL approximation) (Klimov, 1981)

19.  1.4 Tc1.2 Tc 1.1 Tc 1.05 Tc Spectral Contour and Dispersion Relation  pp p p p p p p  + ( ,k)  - ( ,k)

20. Soft modes vs. massive scalar boson the collective (soft) modes above Tc propagating mode The widths are smaller as The soft modes can be approximately replaced by an elementary massive scalar boson. The interaction of a quark and the soft modes are expressed by that of a fermion (quark) and a massive scalar boson. Yukawa model at finite T

21. Fermion Spectrum in the Yukawa Theory quark + scalar boson ”  ” m q =0 m  >0 cf.) m q >0 m  =0 Baym, Blaizot, Svetitsky( ’ 92) One-loop Self-energy Parameters: g, m, T (on-shell renormalization for the T=0 part.)

22. The fermion (quark) spectral function g=1 T/m=0.8 T/m=1.2 T/m=1.6 ww w p pp

23. Imaginary part of  (a) (b)  Im  ( ,0) g=1 m=1 T=2 Parameters: g=1,m=1,T=2 for p=0 (a) (b)  k  E k E (a) (b) Two Landau damping processes make two peak structure of Im . Landau dampings: energy of scalar boson

24. Dispersion Relation Im  ( ,0) Parameters: g=1,m=1,T=2 Re  ( ,0)  There appear five dispersions for k=0. p 

25. Three-peak structure in the quark spectrum also appears. Two Landau damping processes form two peaks of the decay process. Summary of quark spectrum in Yukawa model From the analysis of the self-energy, we have found that Yukawa NJL near Tc Two resonant scatterings three peaks in the spectral function E w massive bosonic mode massless fermion

26. Summary 1 Around T c of the CSC and chiral phase transitions, existence of large fluctuations of the order parameters. They affect a single-quark spectrum CSC: mixing between a quark and a hole at the Fermi surface Chiral: mixing between a quark and an antiquark-hole, mixing between a antiquark and a quark-hole, CSC chiral

27. Summary 2 Similarity of the quark spectrum near chiral transition and the fermion spectrum in the Yukawa model. interaction of a massless fermion and a massive boson at finite temperature Fluctuations ofare propagating modes massive boson-like chiral Yukawa

28. Outlook finite quark mass effect (WIP) 2 nd order crossover explicit gluon degrees of freedom (WIP) effects of observables on the fluctuations The next talk (Mitsutani) with S.Yoshimoto and M.Harada. based on the Schwinger-Dyson approach improvement of approximation self-consistent T-approximation quark-antiquark loop (cf. Braaten, Pisarski, Yuan 1990) paraconductivity, dilepton production through