Precursory Phenomena in Chiral Transition and Color Superconductivity

1. Precursory Phenomena in Chiral Transition and Color Superconductivity 国広　悌二（京大基研） 東大大学院特別講義2005年12月5-7日

2. QCD phase diagram Ｉ ＩＩＩ ＩＩ T RHIC QGP QCD CEP GSI,J-PARC cSB ? Various phases CSC CFL BCS-BEC? m  compact stars 0 H matter? superconducting phases meson condensation?

3. Color Superconductivity; diquark condensation [３]c×[３]c＝[３]c＋[６]c Dense Quark Matter: quark (fermion) system q q with attractive channel in one-gluon exchange interaction. Attractive! p Cooper instability at sufficiently low T Fermi surface -p SU(3)c gauge symmetry is broken! D~100MeV at moderate density mq~ 400MeV T confinement chiral symm. broken Color Superconductivity(CSC) m

4. (Dis)Appearance of CFL and Gapless phases in Charge- and Color-neutral System at T=0 Abuki, Kitazawa and T.K.; P.L.B615,102(‘05) strong coupling ｇ： gapless weak coupling

5. Various CSC phases in plane H .Abuki and T.K. hep-ph/0509172: The phase in the highest temperature is 2SC or g2SC.

6. 2. Precursory Phenomena of Color Superconductivity in Heated Quark Matter Ref. M. Kitazawa, T. Koide, T. K. and Y. Nemoto Phys. Rev. D70, 956003(2004); Prog. Theor. Phys. 114, 205(2005), M. Kitazawa, T.K. and Y. Nemoto, hep-ph/0505070 , Phys. Lett.B 631(2005),157

7. QCD phase diagram T QCD CEP QGP preformed pair fields? quark spectra modified? cSB ? CSC CFL m  0 H matter? meson condensation?

8. Pairing patterns of CSC a,b : color i,j : flavor for JP=0+ pairing attractive channel : color anti-symm. flavor anti-symm. m<Ms m>>Ms Two Flavor Superconductor (2SC) Color-Flavor Locked (CFL) r r u d d u s u d s u d s

9. The nature of diquark pairs in various coupling relevant tonewly born neutron stars or intermediate states in heavy-ion collisions (GSI, J-Parc) weak coupling strong coupling! D ~ 50-100MeV in electric SC Mean field approx. works well. D / EF ~ 0.0001 D / EF ~ 0.1-0.3 Very Short coherence length x. There exist large fluctuations of pair field even at T>0. invalidate MFA. cause precursory phenomena of CSC. Large pair fluctuations can

10. Collective Modes in CSC Response Function of Pair Field Linear Response external field: expectation value of induced pair field: Retarded Green function Fourier transformation with Matsubara formalism RPA approx.: with

11. After analytic continuation to real time, Equivalent with the gap equation (Thouless criterion)

12. (Kitazawa, Koide, Nemoto and T.K., PRD 65, 091504(2002)) Precursory Mode in CSC Spectral function of the pair field at T>0 at k=0 ε→０ （Ｔ→ＴＣ） As T is lowered toward TC, The peak of r becomes sharp. (Soft mode) Pole behavior The peak survives up toelectric SC：

13. The pair fluctuation as the soft mode; --- movement of the pole of the precursory mode--- diffusion-mode like

14. How does the soft mode affect the quark spectra? ---- formation of pseudogap ----

15. T-matrix Approximationfor Quark Propagator Soft mode Density of States N(w):

16. 1-Particle Spectral Function • = 400 MeV e=0.01 quasi-particle peak of anti-particle, w = -k-m quasi-particle peak, w =w-(k)~ k-m position of peaks k kF=400MeV k w Fermi energy quasi-particle peaks at w =w-(k)~ k-m and w =-k-m. 0 -m =-400MeV w Quasi-particle peak has a depression around the Fermi energy due to resonant scattering. : on-shell : the soft mode

17. Density of states of quarks in heated quark matter m = 400 MeV Pseudogap structure appears in N(w). N(w)/104 The pseudogap survives up to e ~ 0.05 ( 5% above TC ). w Fermi energy

18. Density of States in Superconductor Quasi-particle energy: Density of States: The gap on the Fermi surface becomes smaller as T is increased, and it closes at Tc.

19. Pseudogap :Anomalous depression of the density of state near the Fermi surface in the normal phase. Conceptual phase diagram of HTSC cuprates Renner et al.(‘96) The origin of the pseudogap in HTSC is still controversial.

20. stronger diquark coupling GC ×1.3 ×1.5 Diquark Coupling Dependence m= 400 MeV e=0.01 GC

21. Resonance Scattering of Quarks GC=4.67GeV-2 Mixing between quarks and holes w k (M.Kitazawa, Y. Nemoto, T.K. Phys. Lett.B631 (2005),157)

22. Summary of this section There may exist a wide T region where the precursory soft mode of CSC has a large strength. The soft mode induces thepseudogap, Typical Non-Fermi liquid behavior resonant scattering Future problems: effects of the soft mode on . H-I coll. & proto neutron stars anomalous lepton pair production eg.1) collective mode: (w,k) (M.Kitazawa and T.K in progress.) ; cooling of newly born stars eg.2)

23. 3. Precursory Hadronic Mode and Single Quark Spectrum aboveChiral Phase Transition

24. Fermions at finite T • free massless quark at T=0 / quark and antiquark • quark at finite T (massless) several solutions several solutions

25. T Tc QGP m CSC hadron Quarks at very high T (T>>>Tc) • 1-loop (g<<1) + HTL approx. thermal masses dispersion relations plasmino plasmino

26. quark distribution anti-q distribution particle(q)-like anti-quark like Plasmino excitation

27. QCD phase diagram and quasi-particles precursory hadronic modes? free quark spectrum? T QCD CEP QGP cSB ? CSC CFL m  0 H matter? meson condensation?

28. RHIC experiments robust collective flow • good agreement with rel. hydro models • almost perfect liquid (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 Interest in the particle picture in QGP T 2Tc fluctuationeffects fluctuation effects QGP Tc E Hadron CSC m

29. The spectral function of the degenerate hadronic ``para-pion” and the ``para-sigma” at T>Tc for the chiral transition: Tc=164 MeV response function in RPA ... spectral function Hatsuda and T.K,1985 1.2Tc sharp peak in time-like region w k T. Hatsuda and T.K. (1985) , they become elementary modes with small width! M.Kitazawa, Y.Nemoto and T.K. (05)

30. Chiral Transition and the collective modes 0 para sigma para pion c.f. Higgs particle in WSH model ; Higgs field Higgs particle

31. How does the soft mode affect a single quark spectrum near Tc? Y. Nemoto, M. Kitazawa ,T. K. hep-ph/0510167;Phys.Lett. B, in press.

32. Model • low-energy effective theory of QCD 4-Fermi type interaction (Nambu-Jona-Lasinio with 2-flavor) t：SU(2) Pauli matrices chiral limit finite : future work • Chiral phase transition takes place at Tc=193.5 MeV(2nd order). • Self-energy of a quark (above Tc) T->Tc, may be well described with a Yukawa coupling. + … = + + scalar and pseudoscalar parts : imaginary time real time

33. Formulation (Self-energy) ... = 1- Quark self-energy:

34. Formulation (Spectral Function) Spectral function: quark antiquark

35. for free quarks, Spectral Function of Quark Quark self-energy Spectral Function quark antiquark 3 peaks in also 3 peaks in |p| |p|

36. E E Resonant Scatterings of Quark for CHIRAL Fluctuations = + + … fluctuations of almost elementary boson at dispersion law

37. E 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) lead to quark-”antiquark hole” mixing w [MeV] the ‘mass’ of the elementary modes cf: hot QCD (HTL approximation) r-(w,k) r+(w,k) (Klimov, 1981) quark p p[MeV] plasmino

38. T Tc QGP m CSC hadron Quarks at very high T (T>>>Tc) • 1-loop (g<<1) + HTL approx. thermal masses dispersion relations

39. T Tc QGP m CSC hadron Quarks at very high T (T>>>Tc) • 1-loop (g<<1) + HTL approx. thermal masses dispersion relations

40. T Tc QGP m CSC hadron Quarks at very high T (T>>>Tc) • 1-loop (g<<1) + HTL approx. thermal masses spectral function of the space-like region dispersion relations 0 10 0 p/mf w/mf -10 10

41. Difference between CSC and CHIRAL above CSC phase: One resonant scattering fluctuations of the order parameter ~ diffusion-like above chiral transition: Two resonant scatterings fluctuations of the order parameter ~ propagating-like

42. 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

43. Level Repulsions For massless gauge field,

44. Spectral function of the quarks

45. Finite dependence; asymmetry between and particle(q)-like anti-quark like particle-like states suppressed

46. Summary of the second part • We have investigated how the fluctuations of affect the quark spectrum in symmetry-restored phase near Tc. • Near (above) Tc, the quark spectrum at long-frequency and low momentum is strongly modified by the fluctuation of the chiral condensate, . • The many-peak structure of the spectral function can be understood in terms of two resonant scatterings at small w and p of a quark and an antiquark off the fluctuation mode. • This feature near Tc is model-independent if the fluctuation of is dominant over the other degrees offreedom. can be reproduced by a Yukawa theory with the boson being a scalar/pseudoscalar or vector/axial vector one Future (Kitazawa, Nemoto and T.K.,in preparation) • finite quark mass effects. (2nd order crossover) • finite coupling with density fluctuation; CEP?

47. Summary of the Talk QCD phasediagram 2.precursory hadronic modes? T strongly modified quark spectra QCD CEP 1. preformed pair fields? quark spectra modified? QGP `QGP’ itself seems surprisingly rich in physics! cSB ? CSC Condensed matter physics of strongly coupled Quark-Gluon systems will constitute a new field of fundamental physics. CFL m  0 H matter?

48. Back Upps

49. Calculated phase diagram

50. BCS-BEC transition in QM Y.Nishida and H. Abuki, hep-ph/0504083