Concluding Remarks

1. Concluding Remarks Teiji Kunihiro (Kyoto) Meson in Nucleus 2016, Jul.31-Aug.2, 2016 @YITP, Kyoto

2. A (formal) summary ４３Talkswere presented except for mine. Though in a rather tight schedule, Tte workshop consisted of interesting talks on Meson(hadron)innucleus from experimental and theoretical points of view with lively mutual discussions. This is a good aspect of this field asuuring the sound development of physics. Moreover, it has a significant advantage for educating and training students for making them as genuine experts of physics. (Oset @ banquet) Hadrons discussed include η/η’ ; axial anomaly & ChiSB Various vector/axial vector mesons; chiSB Heavy-quark hadrons; diquark correlations Pion; ChiSB (Anomalous enhancement of the s-wave pi-N int. coming from T-W int. ABC/possible dibaryons; K^-: K^-PP, K-^- in nucleus > the nature of Λ(1405) Various Exotics Various facilities/fancy detectors, Chiral dynamics, Lattics, hadron dynamics (eg. DCC)

3. Organizing committee: Please big hands to them (except me).

4. Personal Remarks

5. Introduction continued A condensed matter physics of vacuum (Y. Nambu; 1960): A change of vacuum may lead to a drastic change in excitation spectra on top of the new vacuum. Eg. Superconductor

6. Twenty years after the discovery of deeply boud pionic atom(1996); T.Tamazaki et al, ZPA (1996), As predicted by Hirenzaki, Toki and Yamazaki, (1991). @GSI ``Coulomb-assisted pionic Nuclei” The analyses of the data suggest that QCD vacuum may be effectively changed and chiral symmetry is partially restored even at sub-nuclear density. T.Yamazaki,S.Hirenzaki,R.S.Hayano and H.Toki, Phys.Rep.514(2012),1

7. How the absolute value to the quark condensate is expected to decrease in average in hot and/or dense hadronic matter, based on Hellmann-Feynman theorem.

8. Finite T q-bar q probes either the vacuume or pions that are thermallly excite.:The llatter gives a lositive number, and thus the absolute value of the averaged condensate decreases. Finite density In the n uclear medium, nucleons play the same role as the pions do in hot matter.

9. Cihiral symmetry; Axial anomaly, Effective Chiral models, At Finite T and density, Chiral transition, its precursory Phenomena, Soft modes of QCD CP, Baryon number susceptibility

10. Phenomena expected when chiral symm. Is (partially) restored. Chiral restoration implies that correlators in the positive/negative parity get degenerate. • Chiral symmetry in Baryon sector; parity doubling? What is the nature of N*(1535)? Ref. C. DeTar and T.K.Phys.Rev.D39,2805(1989) Axial anomaly: η’ in hot and dense matter Scalar-Pseudoscalar Axial vector-Vector

11. Karsch, Maezawa, Mukhrjee, Petereczky, In preparation ----------------------------------------------------------------------------------------------------------------------- Positive parityとnegative parity states が互いに「歩み寄る」（positive parityが より積極的） Dynamicalmasses?And/or@finiteρ At relatively low T and/or ρ, a decrease of the constituent quark masses might overwhelm the symm. restoration. T.K., Nucl. Phys. B351(1991)

12. 0 para sigma para pion Chiral Transition and the collective modes The low mass sigma in vacuum is now established: pi-pi scattering; Colangero, Gasser, Leutwyler(’06) and many others Full lattice QCD ; SCALAR collaboration (’03) q-qbar, tetra quark, glue balls, or their mixed st’s? M.Wakayamaetal（SCALARCollab.),PRD91(2015) c.f. The sigma as the Higgs particle in QCD ;a composite particle ; Higgs field Higgs particle (discovered @2012) with mass=125 GeV Is the Higgs a structureless elementary particle? Recent anomalous events in LHC?

13. :Screening masses a0  U1(A)  the softening of the  with increasing T and a_0 meson in the medium would be interesting to explore the effective restoration of U_A(1) symmetry.

14. The poles of the S matrix in the complex mass plane for the sigma meson channel: complied in Z. Xiao and H.Z. Zheng (2001) G.Colangero, J. Gasser and Leutwyler (2001) Softening ! See also, I. Caprini, G. Colangero and H. Leutwyler, PRL(2006); H. Leutwyler, hep-ph/0608218 ; M_sigma=441 – i 272 MeV

15. Issues with the low-mass  meson in QCD • In the constituent quark model; the mass in the 1.2 --- 1.6 GeV region. Some mechanism needed to down the mass; • (i) Color magnetic interaction between the di-quarks? (Jaffe; 1977) • (ii) The collectiveness of the scalar mode as the ps mode; a superposition of states. Chiral symmetry (NJL) • (iii) The - molecule as suggested in -  scatt.

16. Scalar Mesons as Tetraquarks (Jaffe(1977), Alford and Jaffe (2000))

17. QCD phse diagram with tetra-quark codensate as well as the q-qbar, and a possible crossover of the tetra-sigma and q-qbar sigma. N_f=2: AHeinz, S. Strueber, F. Giacosa and D.R. Rischke, PRD 79 (09),037502 c.f. For N_f>2, R.D. Pisarski and V.V. Skokov, arXiv:1606.04111[hep-ph] Quarknium-tetraquark mixing model D. Black, A.H. Fariborz and J. Schechter, PRD 61 (2000, 074001, and References cited in A. H。 Fariborz et al, PRD 91 (2015) 073013 Significance of the U(1)_A anomaly term for the coupling between the chiral (q-q-bqr) fieldand tetraquark field as known in the physics of colorsuperconductivity.

18. N_f=2 • Heinz, S. Strueber, F. Giacosa and D.R. Rischke, PRD 79 (09),037502 Condensates Masses Crossover from the tetera-dominated system to q-qbar system(chiral fluctuation). How about in nuclear medium? Mixing angle

19. η‘and Axial anomaly and ChiSB Demystified

20. model Effective Model; -invariant In the chiral limit, for simplicity. I.Vacuum： Ansatz: , i.e., If is invariant, but otherwise not.. for

21. 2. Meson spectra: Meson masses; (1) ps-mesons from the coefficients of NG- boson Octet Singlet Chiral condensate Anomaly term A change of the chiral condensate as well As the anomaly term affect the η’ mass! (2) scalar-mesons

22. Baryons and Chiral Symmetry

23. The masses: The axial charge Matrix of N and N*(1535) sector

24. Another role of the hot and/or dense medium for hadron physics ---- Filtering Effect of the medium -------

25. Hadron structure as suggested by Dynamical Coupled Channel Approach Talk by H. Kamano @ MENU2016

26. |H>=c_q|qqq>_B+∑c_i|M_iB_i> In dense and/or hot medium C_q(T,ρ) C_i(T,ρ) The dense and/or hot medium may play a role of a filter of the Hilbert space Describing hadrons, and may well reveal the structure of the hadrons: Eg. Compositeness or elementariness may change in the medium!

27. How about the role of Confinement/deconfinement in Hot and/or dense medium?

28. ・Magnetic field B induces isospin asymmetry due the different charges of u and d. EM field v.s. Chiral symm. Breaking ;eg. S. Klevansky,RMP (1992) and many many others. ・Hadron-`QGP’ transition at finite T is crossover! What is the physical picture of `hadrons’ around the crossover region? Swelled? Quarks/gluons are percolated? Super-multi quark hadrons? Tetraquarks or diquarks play significan roles? Implications to finite density systems? H-dibaryon matter in the intermediate stage? R. Tamagaki, PTP85 (1991) Hadron-quark transition at finite μalos crossover? Masuda, Hatsuda and Takatsuka, ApJ764(2013) The role of the vector interaction gVfor the crossover important? TK, PLB271 (1991), As well as the axial anomaly; Kitazawa et al,PTP108(2002); Hatsuda et a; PRL97 (2006)

29. Surely, There remain many things to do! Let’s meet again, here in Kyoto or somewhere else!

30. Back Ups

31. Atractive Coulom + Repulsive pi-N int. ``Coulomb-assisted pionic Nuclei” Localized around the surface of the nucleus,i.e., ``halo-type bound states” T.Yamazaki,S.Hirenzaki ,R.S.Hayano and H.Toki, Phys.Rep.514(2012),1

32. Deeply bound pionic atom/nuclei and in-medium chiral condensate • An enhanced repulsion due to Tomozawa-Weinberg term b1* as characterized by the reduced in-medium pion decay constant f* π : • s-wave optical potential for reads • which can be related to that of the chiral condensate directly as Kolomeitsev-Kaiser-Weise, PRL90 (2003) Jido,Hatsuda and TK, PLB670(2008) QCD vacuum may be effectively changed and chiral symmetry is partially restored even at density lower than the normal nuclear density in finite nuclei!

33. Nonperturbative nature of QCD vacuum Gell-Mann-Oakes-Renner using We have QCD sum rules for heavy-quark systems, ★　All the operators are given as normal product: the vev for the unpert. vacuum vanishes

34. What is a particle/the matter? According to modern QFT, a particle (consisting the matter) is an excited state of quantum fields. The ground state is the vacuum. ; the vacuum Def. The vacuum is defined through the annihilation operators of the Matter. The matter and the vacuum are inter-determined. The modern theory of the matter is automatically the theory of the vacuum. Determining what the matter is equivalent to determine the vacuum.

35. Example from condensed matter physics: normal metal Super conductor Particle number is not a good q. #. Gap ~ dispersion relation of a relativistic particle with the mass . change in elementary excitations change in the vacuum Particle number conservation c.f. Gauge invariance;

36. A dynamical Ciral Lagrangian with Axial Anomaly M. Kobayashi and T. Maskawa (’70), G. ‘t Hooft (’76) T.K. Soryushiron Kenkyu (1988), T.K. and T. Hatsuda, Phys. Lett. B (1988); Phys. Rep. 247 (1994) A presentation of Chiral Anomaly: Anomaly eq. of QCD Note: consistent with the instanton-induced interaction

37. The propagator and mixing angle diagonalize with a mixing matrix; (i) and ; flavor symmetric (ii) and realistic case and (iii) Chiral limit Level crossing by the anomaly!

38. Effective restoration of axial symmetry at finite temperature R. Pisarski and F. Wilczeck(1984) T. K. Phys. Lett. B (1989) tends to become Ideal mixing. T-independent g_D MeV NJL model with Kobayashi-Maskawa-’t Hooft term; T.K. and T.Hatsuda (1988)

39. Full QCD lattice calculation of the axial charges of N*(1535)/N*(1650) T.T.Takahashi and T.Kunihiro、PRD78(2008) Surprisingly, The lattice simulation with full QCD tells as that the axial charge of N*(1535) is vanishingly small!