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

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 T (Quark Gluon Plasma phase)QGP 2Tc chiral sym. restoreddeconfinement fluctuations of PLB633,269,2006 (KKN) RHIC Tc PRD65,091504,2002 (KKKN) FAIR fluctuations of E ~170 MeV PRD70,056003,2004 (KKKN) PTP.114,117,2005 (KKKN) from Lattice QCD Hadronic phase PLB631,157,2005 (KKN) chiral sym. broken (antiquark-quark condensate)confinement (Color SuperConducting phase)CSC quark-quark condensate m compact stars

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

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

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

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 In general, is complex. Spectral function: Strength of the response of the system to the external field.

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

9. 80 w =w+(p) 40 w [MeV] 0 -40 -80 400 480 320 k [MeV] Spectrum of a single-quark Quark self-energy (T-approximation) Spectral Function of quark Super Normal w quark anti-quark 0 kF kF m= 400 MeV e=0.01 Disp. Rel.

10. stronger diquark coupling GC ×1.3 Stronger diquark couplings m= 400 MeV e=0.01 GC ×1.5

11. Resonant Scattering GC=4.67GeV-2 Mixing between quarks and holes w kF k nf (w) w

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

13. 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 Recent topics near Tc T 2Tc QGP Tc E Hadron CSC m

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

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

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

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

19. Spectral Contour and Dispersion Relation w w r-(w,k) r-(w,k) r+ (w,k) r+ (w,k) 1.1 Tc 1.05 Tc p p p p r+ (w,k) r-(w,k) r-(w,k) r+ (w,k) 1.2 Tc 1.4 Tc p p p p

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 expressedby that of a fermion (quark) and a massive scalar boson. Yukawa model at finite T

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

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

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

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

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

26. Summary 1 Around Tcof 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 of are propagating modes massive boson-like Yukawa chiral

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