Joint Lecture Groningen-Osaka

1. Joint Lecture Groningen-Osaka Spontaneous Breaking of Chiral Symmetry in Hadron Physics 30 Sep 09:00- CEST/16:00- JST Atsushi HOSAKA 07 Oct 09:00- CEST/16:00- JST Nuclear Structure 21 Oct 09:00- CEST/16:00- JST Nasser KALANTAR-NAYESTANAKI 28 Oct 09:00- CET/17:00- JST Low-energy tests of the Standard Model 25 Nov 09:00- CET/17:00- JST Rob TIMMERMANS 02 Dec 09:00- CET/17:00- JST Relativistic chiral mean field model description offinite nuclei 09 Dec 09:00- CET/17:00- JST Hiroshi TOKI 16 Dec 09:00- CET/17:00- JST + WRAP-UP/DISCUSSION

2. Spontaneous Breaking of Chiral Symmetryin Hadron Physics • What does spontaneous mean? • What is the breaking of Symmetry? • What is chiral? • What is hadron? • . . . .

3. Contents • General discussions Aspects of symmetry and of spontaneous breaking • Concrete examples NJL model for hadron physics

4. What is symmetric andWhat is broken symmetry

5. Symmetry The key concept in the modern Physics Example of translation

6. Symmetry The key concept in the modern Physics Example of translation Symmetric Translation causes nothing Uniform density

7. Symmetry The key concept in the modern Physics Example of translation Symmetric Translation causes nothing Uniform density Less symmetric

8. Symmetry The key concept in the modern Physics Example of translation Symmetric Translation causes nothing Uniform density Less symmetric Translation changes the location of the cluster Localize Clusterize

9. Symmetry Example of rotation Symmetric

10. Symmetry Example of rotation Symmetric Rotation causes nothing Spherical

11. Symmetry Example of rotation Symmetric Rotation causes nothing Spherical Less symmetric

12. Symmetry Example of rotation Symmetric Rotation causes nothing Spherical Less symmetric Rotation changes the appearance Deformed

13. Symmetry Example of rotation Symmetric Rotation causes nothing Random Less symmetric Rotation changes the appearacnce Ordered

14. Spontaneous breaking Symmetric Simple Disordered Less symmetric Complex Ordered

15. Spontaneous breaking Symmetric Simple Disordered Symmetry is spontaneously broken (Dynamical: due to interactions) Phase transition Reality in our world Less symmetric Complex Ordered With Variety

16. Role of interaction High temperature Kinetic motion > Interaction Random Like gas

17. Role of interaction High temperature Kinetic motion > Interaction Random Like gas Interaction breaks the symmetry => Spontaneously broken

18. Role of interaction High temperature Kinetic motion > Interaction Random Like gas Interaction breaks the symmetry => Spontaneously broken Low temperature Kinetic motion < Interaction Like solid Ordered

19. Examples of interaction (1) Translational invariance H is invariant under This causes localization (clustering) of a two-particle system (2) Rotational invariance This causes deformation of two-particle system (deuteron)

20. (3) Isospin invariance Iso-spinor Iso-vector “Internal symmetry” Isospin (flavor), chiral, color, ….

21. Recover the broken symmetry Low T High T This does not mean the phase transition between them There is a special way to recover the broken symmetry

22. Recover the broken symmetry Symmetry transformation Translation Rotation p

23. Recover the broken symmetry Symmetry transformation Translation Rotation p This does not require energy => Zero energy mode Classical mechanics: No need to move an object on a flat/smooth surface W = Fs = 0 Field theory: Appearance of a massless particle => pion m = 0

24. Quantum mechanics Uncertainty principle

25. Quantum mechanics Uncertainty principle p Starts to move Uncertainty principle Flctuations Zeromode excitations

26. Quantum mechanics Uncertainty principle p Starts to move Uncertainty principle Flctuations Zeromode excitations For small moment of inertia => Easy to fluctuate Symmetric states are realized in the quantumworld For large moment of inertia => hard to move Symmetry is left broken ~ Classical world

27. Collective vs single particle motion

28. Collective vs single particle motion Nambu- Goldstone Boson = Pion In these motions, the shape does not change. The objects move collectively (simultaneously)

29. Collective vs single particle motion Nambu- Goldstone Boson = Pion In these motions, the shape does not change. The objects move collectively (simultaneously) Massive Modes= Mass generation Change in the shape requires more energy. Parts move => Motion of fewer particles

30. Hadrons

31. Where to study? Electromagnetic interaction Molecule Many-body dynamics of electrons around atomic nuclei and/or ions Atom Subatomic physics Strong interaction Nucleus Many-body dynamics of nucleons => Nuclear Physics mesons Many-body-dynamics of quarks and gluson => Hadron physics Nucleons Mesons Quarks

32. Where to study? Electromagnetic interaction Molecule Many-body dynamics of electrons around atomic nuclei and/or ions Atom Subatomic physics Strong interaction Nucleus Many-body dynamics of nucleons => Nuclear Physics mesons Many-body-dynamics of quarks and gluons Hadron Physics Nucleons Mesons Quarks

33. Atoms Many-electron system Many-electron system => Periodic table Ne = 1, 2, 3….[One dimensional plot]

34. Nuclei Many-nucleon system (protons and neutrons)

35. Proton number Nuclei Many-nucleon system (protons and neutrons) => Nucleat chart Np = 1, 2, 3…. Nn = 1, 2, 3…. => [Two-dimensional plot] Neutron number

36. Hadrons Many(?)-quark system (u, d, c, s, b, t) Particle Data Proton/neutron

37. Particle Data Table Mesons Baryons

38. Only qq and qqq? Hadrons Many(?)-quark system (u, d, c, s, b, t) Particle Data Proton/neutron However Why? Mesons Baryons

39. Problems of hadron physics Clay Mathematics Institute, Millennium Problems http://www.claymath.org/millennium/ Millennium Problems In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven Prize Problems. The Scientific Advisory Board of CMI selected these problems, focusing on important classic questions that have resisted solution over the years. The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each. During the Millennium Meeting held on May 24, 2000 at the Collège de France, Timothy Gowers presented a lecture entitled The Importance of Mathematics, aimed for the general public, while John Tate and Michael Atiyah spoke on the problems. The CMI invited specialists to formulate each problem.

40. １Birch and Swinnerton-Dyer Conjecture ２Hodge Conjecture ３Navier-Stokes Equations ４P vs NP ５Poincare Conjecture ６Riemann Hypothesis ７ Yang-Mills Theory => QCD A. Jaffe and E. Witten • It must have a “mass gap,” that is, there must be some strictly positive constant ∆ such that every excitation of the vacuum has energy at least ∆. • It must have “quark confinement,” that is, even though the theory is described in terms of elementary fields, such as the quarks, that transform non-trivially under S U (3), the physical particle states – such as the proton, neutron, and pion – are S U (3)-invariant. • It must have “chiral symmetry breaking,” which means that the vacuum is potentially invari- ant (in the limit that the quark bare masses vanish) only under a certain subgroup of the full symmetry group that acts on the quark fields.

41. Whereqqqq, qqqqq and more ? Tetraquark Pentaquark Exotic hadrons

42. Spontaneous breaking of chiral () symmetry Yoichiro Nambu

43. Spontaneous breaking of chiral () symmetry Potential energy surface of the vacuum Yoichiro Nambu Chiral order parameter Quarks & gluons Confinement, Mass generation Hadrons & nuclei

44. Dynamics of Spontaneous symmetry breakingin the strongly interacting system

45. Tasks of Physics • Find the ultimate law of everything • Reconstruct phenomena from the law They are not independent due to the presence of interactions We are on the vacuum. Particles are the excitations of the vacuum. Complicated system Physics is to find the properties of the vacuum and its excitations in the presence of interactions

46. A particle In the microscopic world Vacuum = Ground state is not empty Particles are interacting with the vacuum A simply looking system can be more complicated due to the interaction and change its properties drastically. E.G. from quarks to Hadrons with mass generation

47. Analogy with BCS QED Phonon exchange ee Cooper pair Order parameter Gauge (local) symmetry Superconductivity

48. Analogy with BCS QED QCD Phonon exchange ee Strong interaction qq Quark-antiquark pair Cooper pair Order parameter Gauge (local) symmetry Superconductivity Flavor (global) symmetry Nambu-Goldstone boson

49. • Mass of particles • Gap in energy spectrum N* N M D E =0 Ground state E =0 Vacuum Normal Super Superconductivity Hadrons Dirac mass Majorana mass • Meissner effect • Exclusion of color electric field Super Normal

50. Chiral symmetry Hand Left Right Chiral symmetry => Left-hand world has a symmetry (law) Right-hand world has a symmetry (law) If they mix, we say that chiral symmetry is broken