Congratulation on the Establishment of KMI ! Wish a New Creative Era at KMI !!!

1. Congratulation on the Establishment of KMI ! Wish a New Creative Era at KMI !!!

2. Insights From Three Flavors to Three Families Based on Compositeness and Symmetry Yue-Liang Wu Kavli Institute for Theoretical Physics China（KITPC） State Key Laboratory of Theoretical Physics (SKLTP) Institute of Theoretical Physics, Chinese Academy of Sciences 2011.10.27-28

3. OUTLINE • Shoichi Sakata & Chinese Philosophy ‘兼听则明,偏信则暗’ • ‘Compositeness and Symmetry’ • Insight from Three Flavors to Three Families，Indirect and Direct CP Violation in kaon Meson Decays. • Dynamical Chiral Symmetry Breaking with Nonet Scalar Mesons as Composite Higgs Bosons and Predictions for Mass Spectra of Lowest Lying Mesons • Chiral Thermodynamic Model of QCD and QCD Phase Transition with Chiral Symmetry Restoration • Predictive Realistic Holographic AdS/QCD Model for the Mass Spectra of Resonance Mesons • SO(3) Gauge Family Model for Neutrino Mixing • Conclusions and Remarks

4. Shoichi Sakata & Chinese Philosophy Compositeness and Symmetry

5. 唐太宗贞观二年(628)，上问魏征曰： ‘人主何为而明，何为而暗？’ 对曰： ‘’ In Tang Dynasty (683) , the emperor (Li Shi-Ming) asked prime ministry (Wei Zheng) how he can become an enlightened rather than a benighted emperor, the prime ministry answered: “Listen to both sides and you will be enlightened; heed only one side you will be benighted” A Democratic Idea

6. “唐朝人魏徵说过：‘兼听则明，偏信则暗。’也懂得片面性不对。可是我们的同志看问题，往往带片面性，这样的人就往往碰钉子”“唐朝人魏徵说过：‘兼听则明，偏信则暗。’也懂得片面性不对。可是我们的同志看问题，往往带片面性，这样的人就往往碰钉子” “Everything has two sides：positive and negative” Since then ‘兼听则明,偏信则暗’ has become an idiom late on, it has been as the dialectics and philosophy Eg. “Contradiction Theory” by Chairman Mao Ze-Dong Particle-antiparticle, left-right, forward-backward (CPT) “One divides into two” Compositeness “Unity of opposites” Symmetry Shoichi Sakata

7. Concept of Compositeness Shoichi Sakata in 1955: The fundamental building blocks of all strongly interacting particles are the composite ones from the three known particles: the proton, the neutron and the lambda baryon,p, n, Λ Gell-Mann & Zweig in 1964: p, n, Λ three unknown flavors: u, d, s with the same isospin and flavor numbers but with fractional charges

8. In 1961, professor Shoichi Sakata published an article about “New Concept on Elementary Particles” in the Journal of the Physical Society of Japan. 1963年，《自然辩证法研究通讯》(dialectics of nature)杂志复刊，第一期就曾转载了坂田昌一的论文《基本粒子新概念》，这篇文章引起了毛泽东的很大兴趣。 That has had a big influence on study and development of Elementary Particle Physics in China , eg. : Straton Model based on the Compsiteness 1964年8月19日，毛泽东接见各国代表团，由于坂田在整个到会的科学家中间的学术地位是最高的，他成为与毛泽东第一个握手的科学家。当时毛泽东对坂田说了一句话：“你的文章写得很好，我读过了。” 1964年8月，九三学社副主席周培源（左二）陪同毛泽东接见参加科学讨论会的日本代表团团长坂田昌一

9. 新基本粒子观对话 书籍作者： 坂田昌一图书出版社：生活、读书、新知三联书店出版时间：1965-07 书籍作者： 坂田昌一图书出版社： 三联书店出版时间： 1973-04

10. 坂田昌一 物理学方法论论文集 核时代を超える 坂田昌一科学哲学论文集 书籍作者： 坂田昌一图书出版社： 知识出版社 书籍作者： 汤川秀树 朝永振一郎 坂田昌一图书出版社：岩波新书 • 书籍作者：坂田昌一图书出版社：商务印书馆出版时间：1966-05 • Methodology

11. Fumihiko Sakata 坐观天入峡，深幸雨中来。 大愧多诗笔，扁舟一酒杯。 虹桥横水断，云幔逐波开。 玉女方淋浴，慵妆傍镜台。 Prof. Shoichi Sakata visited China twice in 1956 and 1964, invited by the FundingPresident of CAS Mr. Mo-Ruo Guo (who is the famous Litterateur, Poet, Dramatist, Historian, Thinker, Calligrapher etc.). He had a handwriting to Prof. Sakata with his own poem and its first calligraphy. Looks like a jade woman taking a shower Science and peace New creation everyday Micro-universe of particles Turn round historical big wheels To Mr. Shoichi Sakata through the ages 科学与和平， 创造日日新。微观小宇宙， 力转大车轮。 坂田昌一先生 千古 郭沫若 When Prof. S. Sakata passed away in 1970, the CAS President Mr. Guo wrote a poem as a monumental writing with his calligraphy. 武夷山mountain

12. Insight From Three Flavors to Three Families Indirect and Direct CP violation in kaon Meson Decays 道生一、一生二、 二生三、三生万物 老子《道德经》，(B.C. 571)

13. CP Violation From 3 Flavors to 3 Families • Indirect CP violation was discovered in 1964 from kaon decays: K ππ, πππ, which only involves three flavors • The Question: CP violation is via weak-type interaction or superweak-type interaction (Wolfenstein 1964) • CP violation can occur in the weak interaction with three families of SM (Kobayashi-Maskawa 1973) • which has to be tested via the direct CP violation • ε’/ε = 0 (superweak hypothesis) • ε’/ε≠0 (weak interaction)

14. CP ViolationFrom 3 Flavors to 3 Families • CP violation may also happen via spontaneous symmetry breaking (SCPV) of scalar interaction (T.D. Lee, 1973) • Two Higgs Doublet Model (2HDM) with SCPV (Weinberg, Liu & Wolfenstein, Hall & Weinberg, …… Wolfenstein & YLW, 1994 PRL) (i) Induced Kobayashi-Maskawa CP-violating phase (ii) New sources of CP violation through the charged Higgs (iii) Induced superweak CP via FCNC through neutral Higgs (iV) CP violation via scalar-pseudoscalar Higgs mixing

15. Direct CP Violation & ΔI = ½ Rule in Kaon Decays Based on ChPT Direct CP violation arises from both nonzero relative weak and strong phases via the KM mechanism

16. Theoretical Prediction and Experimental Measurements Theoretical Prediction • ε′/ε＝（20±4±5）×10-4 (Y.L. Wu Phys. Rev. D64: 016001,2001) Experimental Results: • ε′/ε＝（20.7±2.8）×10-4 (KTeV Collab. Phys. Rev. D67: 012005,2003) • ε′/ε＝（14.7±2.2）×10-4 (NA48 Collab. Phys. Lett. B544: 97,2002)

17. Direct CP violation ’/ in kaon decays can be well explained by the KM CP-violating mechanism in SM S. Bertolini, Theory Status of ’/FrascatiPhys.Ser.28 275-290 (2002)

18. Consistency of Prediction The consistency of our theoretical prediction is strongly supported from a simultaneous prediction for the ΔI = ½ isospin selection rule of decay amplitudes (|A0/A2|= 22.5 (exp.) |A0/A2 |≈ 1.4(naïve fac.), differs by a factor 16 ) Theoretical Prediction Experimental Results

19. The chiral loop contribution of nonperturbative effects was found to be significant. It is important to keep quadratic terms proposed firstly by Bardeen,Buras & Gerard (1986)

20. Importance for matching ChPT with QCD Scale

21. Some Algebraic Relations of Chiral Operators Inputs and Theoretical Uncertainties

22. Dynamical Chiral Symmetry Breaking Scalar Mesons as Composite Higgs Bosons Mass Spectra of Lowest Lying Mesons

23. Symmetry & Quantum Field Theory • Symmetry has played an important role in elementary particle physics • All known basic forces of nature: electromagnetic, weak, strong & gravitational forces, are governed by U(1)_Y x SU(2)_L x SU(3)_c x SO(1,3) • Which has been found to be successfully described by quantum field theories (QFTs)

24. Why Quantum Field Theory So Successful Folk’s theorem by Weinberg: Any quantum theory that at sufficiently low energyand large distances looks Lorentz invariant and satisfies the cluster decomposition principle will also at sufficiently low energy look like a quantum field theory. • Indication:existence in any case a characterizing energy scale (CES) Mc • So that at sufficiently low energy gets meaning: E << Mc  QFTs

25. Why Quantum Field Theory So Successful Renormalization group by Wilson/Gell-Mann & Low Allow to deal with physical phenomena at any interesting energy scale by integrating out the physics at higher energy scales. Allow to define the renormalized theory at any interesting renormalization scale . • Implication:Existence of sliding energy scale(SES) μs which is not related to masses of particles. • Physical effects above the SES μs are integrated in the renormalized couplings and fields.

26. How to Avoid Divergence • QFTs cannot be defined by a straightforward perturbative expansion due to the presence of ultraviolet divergences. • Regularization: Modifying the behavior of field theory at very large momentum so Feynman diagrams become well-defined quantities • String/superstring: Underlying theory might not be a quantum theory of fields, it could be something else.

27. Regularization Schemes • Cut-off regularization Keeping divergent behavior, spoiling gauge symmetry & translational/rotational symmetries • Pauli-Villars regularization Modifying propagators, destroying non-abelian gauge symmetry • Dimensional regularization: analytic continuation in dimension • Gauge invariance, widely used for practical calculations • Gamma_5 problem: questionable to chiral theory • Dimension problem: unsuitable for super-symmetric theory • Divergent behavior: losing quadratic behavior (incorrect gap eq.) All the regularizations have their advantages and shortcomings

28. Criteria of Consistent Regularization (i)The regularization is rigorous: It can maintain the basic symmetry principles in the original theory, such as: gauge invariance, Lorentz invariance and translational invariance (ii)The regularization is general: It can be applied to both underlying renormalizable QFTs (such as QCD) and effective QFTs (like the gauged Nambu-Jona-Lasinio model and chiral perturbation theory).

29. Criteria of Consistent Regularization (iii)The regularization is also essential: It can lead to the well-defined Feynman diagrams with maintaining the initial divergent behavior of integrals, so that the regularized theory only needs to make an infinity-free renormalization. (iv)The regularization must be simple: It can provide practical calculations.

30. Symmetry-Preserving Loop Regularization (LORE) with String Mode Regulators • Yue-Liang Wu, SYMMETRY PRINCIPLE PRESERVING AND INFINITY FREE REGULARIZATION AND RENORMALIZATION OF QUANTUM FIELD THEORIES AND THE MASS GAP.Int.J.Mod.Phys.A18:2003, 5363-5420. • Yue-Liang Wu, SYMMETRY PRESERVING LOOP REGULARIZATION AND RENORMALIZATION OF QFTS.Mod.Phys.Lett.A19:2004, 2191-2204. • J.~W.~Cui and Y.~L.~Wu, Int. J. Mod. Phys. A 23, 2861 (2008) • J.~W.~Cui, Y.~Tang and Y.~L.~Wu, Phys. Rev. D 79, 125008 (2009) • Y.~L.~Ma and Y.~L.~Wu, Int. J. Mod. Phys. A21, 6383 (2006) • Y.~L.~Ma and Y.~L.~Wu, Phys. Lett. B 647, 427 (2007) • J.W. Cui, Y.L. Ma and Y.L. Wu, Phys.Rev. D 84, 025020 (2011) • Y.~B.~Dai and Y.~L.~Wu, Eur. Phys. J. C 39 (2004) S1 • Y.~Tang and Y.~L.~Wu, Commun. Theor. Phys. 54, 1040 (2010) • Y.~Tang and Y.~L.~Wu, arXiv:1012.0626 [hep-ph]. • D. Huang and Y.L. Wu, arXiv:1108.3603

31. Irreducible Loop Integrals (ILIs)

32. Loop Regularization (LORE) Method Simple Prescription: in ILIs, make the following replacement With the conditions So that

33. Gauge Invariant Consistency Conditions

34. Checking Consistency Condition

35. Checking Consistency Condition

36. Vacuum Polarization • Fermion-Loop Contributions

37. Gluonic Loop Contributions

38. Cut-Off & Dimensional Regularizations • Cut-off violates consistency conditions • DR satisfies consistency conditions • But quadratic behavior is suppressed with opposite sign  0 when m 0

39. Symmetry–preserving Loop Regularization (LORE) With String-mode Regulators • Choosing the regulator masses to have the string-mode Reggie trajectory behavior • Coefficients are completely determined • from the conditions

40. Explicit One Loop Feynman Integrals With Two intrinsic mass scales and play the roles of UV- and IR-cut offas well asCES and SES

41. Interesting Mathematical Identities which lead the functions to the following simple forms

42. Renormalization Constants of Non- Abelian gauge Theory and β Function of QCD in Loop Regularization Jian-Wei Cui & Yue-Liang Wu Int. J. Mod. Phys. A 23, 2861 (2008) • Lagrangian of gauge theory • Possible counter-terms

43. Ward-Takahaski-Slavnov-Taylor Identities Gauge Invariance Two-point Diagrams

44. Three-point Diagrams

45. Four-point Diagrams

46. Ward-Takahaski-Slavnov-Taylor Identities • Renormalization Constants • All satisfy Ward-Takahaski-Slavnov-Taylor identities

47. Renormalization β Function • Gauge Coupling Renormalization which reproduces the well-known QCD β function (GWP)

48. Supersymmetry in Loop Regularization J.W. Cui,Y.Tang,Y.L. Wu Phys.Rev.D79:125008,2009 Supersymmetry • Supersymmetry is a full symmetry of quantum theory • Supersymmetry should be Regularization-independent • Supersymmetry-preserving Regularization

49. Massless Wess-Zumino Model • Lagrangian • Ward identity • In momentum space

50. Check of Ward Identity Gamma matrix algebra in 4-dimension and translational invariance of integral momentum Loop regularization satisfies these conditions