1. ｢第５回 J-PARC における高エネルギーハドロン物理｣ J-PARC に活きる南部先生のアイデア 1.Introdution 2.Stability of hadronic matter 3. Chiral symmetry in vacuum & in medium 4. No summary T. Hatsuda (Univ. of Tokyo) KEK, Jan. 8, 2009 plan ○ Y. Nambu, “Broken Symmetry”, Selected Papers of Y. Nambu, World Scientific (1995). ○ Y. Nambu, “Spontaneus symmetry breaking in particle physics: a case of cross fertilization”, Nobel Lecture (Dec. 8, 2008) pp.1-25. ○ T. Hatsuda & T. Kunihiro, “QCD phenomenology based on a chiral effective lagrangian”, Phys. Rep. Vol. 247 (1994) pp.221-367. ○ R. Hayano & T. Hatsuda, “Hadron properties in the nuclear medium”, Rev. Mod. Phys. (2009) [arXiv:0812.1702 [nucl-ex] ] references

2. String ？ r << 10 -4 [fm] Nuclei r ～ 10 [fm] r ～ 1 [fm] Hadron Y. Nambu at INPC2007 1.Repulsive core in nuclear force: “Possible existence of a heavy neutral meson”, Phys. Rev. 106 (1957) 1366. 2.Dynamical breaking of chiral symmetry (with G. Jona-Lasinio): “Dynamical model of elementary particles based on an analogy with superconductivity I, II”, Phys. Rev. 122 (1961) 345, ibid. 124 (1961) 246. 3.Quantum chromodynamics: “A systematics of hadrons in subnuclear physics”, in Preludes in Theoretical Physics (North-Holland, Amsterdam, 1966). 4.String theory: “Duality and hadrodynamics”, note prepared for the Copenhagen High Energy Symposium, Aug. 1970. Subatomic structure of matter

3. Phys. Rev. 106 (1957) 1366 ω-meson NN,YN and YY interactions in lattice QCD (Aoki, Ishii, Nemura & Hatsuda, 2008) YN and YY interactions at J-PARC Structure of neutron stars after 50 years powered by QCD Repulsive core in nuclear force

4. Origin of the fermion mass These ideas are relevant in QCD and are dual relevant Nambu’s fermion/boson = quark/pion Skyrme’s fermion/boson = nucleon/pion dual bosonized Nambu = Skyrme Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (’61) 345 1.massless fermion ⇒ massive fermion + massless composite boson 2.massless boson ⇒ massive topological fermion + massless boson T.H.R. Skyrme, Proc. Roy. Soc. Lond. A260 (’61) 127 Two revolutionary ideas proposed in 1961

5. Y. Nambu, Nobel Lecture (Dec.8, 2008), page 22/25

6. Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25

7. One-page summary of NJL

8. massless Dirac sea massive Dirac sea -M “Cooper” instability ・ Dynamical mass ・ Vacuum energy M g g c

9. [QCD] ・ most attractive channels : scalar & pseudo-scalar ・ running coupling : large at low energies ⇒ NJL mechanism is expected to take place SuperconductivityStrong interaction Microscopic theory (relevant symmetry) electron + phonon (global gauge symmetry) quark + gluon (global chiral symmetry) Effective theory for fermions BCS model for electrons e ↑ (x) & e ↓ (x) NJL model for quarks q L (x) & q R (x) Effective theory for soft modes Ginzburg-Landau theory for Cooper pair Δ(x) Chiral perturbation theory for pion π(x) What about QCD ?

10. Y. Nambu, Nobel Lecture (Dec.8, 2008), page 21/25

11. NJL+KMT vs. Exp. data taken from Hatsuda & Kunihiro, Phys.Rep. 247 (1994).

12. 100G 100P 10P 1P 100T 10T 1T 10G 1990 1995 2000 2005 2010 2015 Keisoku Growth in Supercomputer peak performance (year) (Flops) Doubling time = 1.2 years Adapted from Wikimedia Commons

13. Gell-Mann-Oakes-Renner (GOR) formula (1968) 0 Lattice QCD calculation by JLQCD+TWQCD Collaborations, arXiv:0810.0085 [hep-lat] Di Vecchia-Veneziano formula (1980) Dim.3 chiral condensate (Nambu condensate) in the QCD vacuum

14. Dynamical quark-mass in the QCD vacuum Lattice QCD calculation in Landau gauge, 20 3 x64, a=0.125fm, MILC config. P. O. Bowman et al., Phys. Rev. D71 (2005) 054507 M (0) ~ 300-400 MeV

15. σ （６００） Spectral evidence of DBCS in QCD Nambu condensate “Higgs” in QCD Nambu-Goldstone boson

16. (Theoretical) Nambu condensate in the QCD medium Lattice QCD, (2+1)-flavor Cheng et al., PRD 77 (2008) Finite Temperature Nuclear chiral perturbation Kaiser et al., PRC 77 (2008) Finite Baryon Density

17. Experimental determination of in-medium Nambu condensate from deeply bound pionic atom Experimental determination of in-medium Nambu condensate from deeply bound pionic atom  Toki, Hirenzaki, Yamazaki & Hayano, NP A501 (1989) 653 Suzuki et al., PRL 92 (2004) 72302 Jido, Hatsuda & Kunihiro, PL B670 (2008) 109 Hayano & Hatsuda, Rev. Mod. Phys. (2009)

18. What about other mesons (ρ, ω, φ, σ, η, η’ …) ? ・ Many models proposed (BR scaling, HLS, Bag, ….) ・ None of them are exact except for spectral sum rules from OPE e.g. Weinberg-type sum rules Hatsuda, Koike & Lee. Nucl. Phys. B394 (1993) 221 Kapusta & Shuryak, Phys. Rev. D49 (1994) 4694 Dim.6 chiral condensate

19. ALEPH Collaboration, Phys. Rep. 421 (2005) 191 V & A spectral functions in the QCD vacuum fromτ-decay at LEP-1 ρ V (s)/s ρ A (s)/s [ρ V (s)-ρ A (s)] /s Precision measurement at KEKB ?

20. Dim.6 chiral condensate Messages 1.DBCS is best seen in the spectral difference: -, -, etc 2.Spectral difference in different channels ⇔ different chiral condensates 3.“Origin of hadron mass = Nambu condensate” : true for the pion (GOR) BUT ， ρ, ω, N, … could be massive even if chiral restoration takes place “Origin of hadron mass = Nambu condensate” ? Theretically, we need further logical step Experimentally, precision measurement of SPF at J-PARC

21. Spectral sum at finite T on the lattice (π, σ, δ) π σ δ

22. Color Superfluid Chiral Superfluid ～ 1 GeV ～ 0.2 GeV Quark-Gluon Plasma “Phase” diagram of QCD Q ～ 1 GeV RHIC/LHC Neutron star J-PARC

23. J-PARC に活きる南部先生のアイデア J-PARC に活きる南部先生のアイデア nucleon quark ｢物質安定性の起源と質量の起源」 ｢物質安定性の起源と質量の起源」 J-PARC as a QCD machine J-PARC as a QCD machine