1、Congratulation on the Establishment of KMI ! Wish a New Creative Era at KMI !,Yue-Liang WuKavli Institute for Theoretical Physics China（KITPC）State Key Laboratory of Theoretical Physics (SKLTP)Institute of Theoretical Physics, Chinese Academy of Sciences2011.10.27-28,Insights From Three Flavors to T
2、hree FamiliesBased on Compositeness and Symmetry,OUTLINE,Shoichi Sakata & Chinese Philosophy 兼听则明,偏信则暗 Compositeness and SymmetryInsight 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
3、 Higgs Bosons and Predictions for Mass Spectra of Lowest Lying MesonsChiral Thermodynamic Model of QCD and QCD Phase Transition with Chiral Symmetry Restoration Predictive Realistic Holographic AdS/QCD Model for the Mass Spectra of Resonance MesonsSO(3) Gauge Family Model for Neutrino MixingConclusi
4、ons and Remarks,Shoichi Sakata & Chinese Philosophy Compositeness and Symmetry,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 enligh
5、tened; heed only one side you will be benighted”,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： ,A Democratic Idea,Since then 兼听则明,偏信则暗 has become an idiom late on, it has been as the dialectics and philosophyEg. “Contradiction Theory” by Chairman Mao Ze-Dong,“Everything has two sides：positive and negative”,“On
6、e divides into two”,“Unity of opposites”,Compositeness,Symmetry,Particle-antiparticle, left-right, forward-backward (CPT),Shoichi Sakata,“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”,Concept of Compositeness,Shoichi Sakata in 1955: The fundamental building blocks of all strongly interact
7、ing particles are the composite ones from the three known particles: the proton, the neutron and the lambda baryon, p, n, Gell-Mann & Zweig in 1964: p, n, three unknown flavors: u, d, s with the same isospin and flavor numbers but with fractional charges,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
8、田昌一,1963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。,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。”,In 1961, professor Shoichi Sakata published an article about “New Concept on Elementary Particles” in the Journal of th
9、e Physical Society of Japan.,That has had a big influence on study and development of Elementary Particle Physics in China , eg. : Straton Model based on the Compsiteness,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,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：坂田昌一图书出版社：
10、商务印书馆出版时间：1966-05Methodology,坂田昌一物理学方法论论文集,核时代超,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,Prof. Shoichi Sakata visited China twice in 1956 and 1964, invited by the Funding President of CAS Mr. Mo-Ruo Guo (who is the famous Litterateur, Poet, Dramatist, Historian, Thinker, Calligrapher etc.). He had a handwriti
11、ng to Prof. Sakata with his own poem and its first calligraphy.,When Prof. S. Sakata passed away in 1970, the CAS President Mr. Guo wrote a poem as a monumental writing with his calligraphy.,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,Fumihiko Sakata,大愧多诗笔，扁舟一酒杯。,坐观天入峡，深幸雨中来。,玉女方淋浴，慵妆傍镜台。,虹桥横水断，云幔逐波开。
12、,Looks like a jade woman taking a shower,Science and peaceNew creation everydayMicro-universe of particlesTurn round historical big wheelsTo Mr. Shoichi Sakata through the ages,武夷山 mountain,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
13、、三生万物 老子道德经，(B.C. 571),CP Violation From 3 Flavors to 3 Families,Indirect CP violation was discovered in 1964 from kaon decays: K , , which only involves three flavorsThe Question: CP violation is via weak-type interaction or superweak-type interaction (Wolfenstein 1964)CP violation can occur in the
14、 weak interaction with three families of SM (Kobayashi-Maskawa 1973) which has to be tested via the direct CP violation / = 0 (superweak hypothesis) / 0 (weak interaction),CP violation may also happen via spontaneous symmetry breaking (SCPV) of scalar interaction (T.D. Lee, 1973) Two Higgs Doublet M
15、odel (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-pseudos
16、calar Higgs mixing,CP ViolationFrom 3 Flavors to 3 Families,Direct CP Violation & I = Rule in Kaon Decays Based on ChPT,Direct CP violation arises from both nonzero relative weak and strong phases via the KM mechanism,Theoretical Prediction and Experimental Measurements,Theoretical Prediction /（2045
17、）10-4 (Y.L. Wu Phys. Rev. D64: 016001,2001)Experimental Results:/（20.72.8）10-4 (KTeV Collab. Phys. Rev. D67: 012005,2003)/（14.72.2）10-4 (NA48 Collab. Phys. Lett. B544: 97,2002),S. Bertolini, Theory Status of / FrascatiPhys.Ser.28 275-290 (2002),Direct CP violation / in kaon decays can be well explai
18、ned by the KM CP-violating mechanism in SM,Consistency of Prediction,The consistency of our theoretical prediction is strongly supported from a simultaneous prediction for the I = isospin selection rule of decay amplitudes (|A0/A2|= 22.5 (exp.) |A0/A2 | 1.4 (nave fac.), differs by a factor 16 ) Theo
19、retical Prediction,Experimental Results,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),Importance for matching ChPT with QCD Scale,Some Algebraic Relations of Chiral Operat
20、ors,Inputs and Theoretical Uncertainties,Dynamical Chiral Symmetry Breaking Scalar Mesons as Composite Higgs Bosons Mass Spectra of Lowest Lying Mesons,Symmetry & Quantum Field Theory,Symmetry has played an important role in elementary particle physicsAll known basic forces of nature: electromagneti
21、c, 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),Why Quantum Field Theory So Successful,Folks theorem by Weinberg: Any quantum theory that at sufficiently low energy and larg
22、e 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) McSo that at sufficiently low energy gets meaning: E Mc QFTs,Why Quantum F
23、ield 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: Exis
24、tence of sliding energy scale(SES) s which is not related to masses of particles.Physical effects above the SES s are integrated in the renormalized couplings and fields.,How to Avoid Divergence,QFTs cannot be defined by a straightforward perturbative expansion due to the presence of ultraviolet div
25、ergences. Regularization: Modifying the behavior of field theory at very large momentum so Feynman diagrams become well-defined quantitiesString/superstring: Underlying theory might not be a quantum theory of fields, it could be something else.,Regularization Schemes,Cut-off regularization Keeping d
26、ivergent behavior, spoiling gauge symmetry & translational/rotational symmetriesPauli-Villars regularization Modifying propagators, destroying non-abelian gauge symmetryDimensional regularization: analytic continuation in dimensionGauge invariance, widely used for practical calculationsGamma_5 probl
27、em: questionable to chiral theoryDimension problem: unsuitable for super-symmetric theoryDivergent behavior: losing quadratic behavior (incorrect gap eq.) All the regularizations have their advantages and shortcomings,Criteria of Consistent Regularization,(i) The regularization is rigorous: It can m
28、aintain 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 mo
29、del and chiral perturbation theory).,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 ren
30、ormalization.(iv) The regularization must be simple: It can provide practical calculations.,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 MA
31、SS 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
32、. 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.
33、 Wu, arXiv:1108.3603,Irreducible Loop Integrals (ILIs),Loop Regularization (LORE) Method,Simple Prescription: in ILIs, make the following replacementWith the conditionsSo that,Gauge Invariant Consistency Conditions,Checking Consistency Condition,Checking Consistency Condition,Vacuum Polarization,Fer
34、mion-Loop Contributions,Gluonic Loop Contributions,Cut-Off & Dimensional Regularizations,Cut-off violates consistency conditionsDR satisfies consistency conditionsBut quadratic behavior is suppressed with opposite sign 0 when m 0,Symmetrypreserving Loop Regularization (LORE) With String-mode Regulat
35、ors,Choosing the regulator masses to have the string-mode Reggie trajectory behaviorCoefficients are completely determinedfrom the conditions,Explicit One Loop Feynman Integrals,With,Two intrinsic mass scales and play the roles of UV- and IR-cut off as well as CES and SES,Interesting Mathematical Id
36、entities,which lead the functions to the following simple forms,Renormalization Constants of Non- Abelian gauge Theory and Function of QCD in Loop Regularization,Lagrangian of gauge theoryPossible counter-terms,Jian-Wei Cui & Yue-Liang Wu Int. J. Mod. Phys. A 23, 2861 (2008),Ward-Takahaski-Slavnov-T
37、aylor Identities,Gauge Invariance,Two-point Diagrams,Three-point Diagrams,Four-point Diagrams,Ward-Takahaski-Slavnov-Taylor Identities,Renormalization ConstantsAll satisfy Ward-Takahaski-Slavnov-Taylor identities,Renormalization Function,Gauge Coupling Renormalizationwhich reproduces the well-known
38、QCD function (GWP),Supersymmetry in Loop Regularization,SupersymmetrySupersymmetry is a full symmetry of quantum theorySupersymmetry should be Regularization-independent Supersymmetry-preserving Regularization,J.W. Cui, Y.Tang,Y.L. Wu Phys.Rev.D79:125008,2009,Massless Wess-Zumino Model,LagrangianWar
39、d identityIn momentum space,Check of Ward Identity,Gamma matrix algebra in 4-dimension and translational invariance of integral momentumLoop regularization satisfies these conditions,Massive Wess-Zumino Model,LagrangianWard identity,Check of Ward Identity,Gamma matrix algebra in 4-dimension and tran
40、slational invariance of integral momentumLoop regularization satisfies these conditions,Triangle Anomaly,AmplitudesUsing the definition of gamma_5The trace of gamma matrices gets the most general and unique structure with symmetric Lorentz indices Y.L.Ma & YLW,Anomaly of Axial Current,Explicit calcu
41、lation based on Loop Regularization with the most general and symmetric Lorentz structureRestore the original theory in the limit which shows that vector currents are automatically conserved, only the axial-vector Ward identity is violated by quantum corrections,Chiral Anomaly Based on Loop Regulari
42、zation,Including the cross diagram, the final result is,Which leads to the well-known anomaly form,Anomaly Based on Various Regularizations,Using the most general and symmetric trace formula for gamma matrices with gamma_5. In unit,Loop Regularization (LORE) Method,Loop Regularization Merging With B
43、jorken-Drells Circuit Analogy,The divergence arises from zero resistance Short Circuit,which enables us to prove the validity of LORE to all orders,Loop Regularization Merging With Bjorken-Drells Circuit Analogy,Application to Two Loop Calculations by LORE in 4 Theory,Power-law running of mass at tw
44、o loop level,Log-running to coupling constant at two loop level,One loop contribution with quadratic term to the scalar mass by the LORE method,Two loop contribution with quadratic term to the scalar mass by the LORE method,Application to Two Loop Calculations by LORE in 4 Theory,Dynamically Generat
45、ed Spontaneous Chiral Symmetry Breaking In Chiral Effective Field Theory,Importance of Quadratic Term by LORE method,Chiral limit: Taking vanishing quark masses mq 0. QCD Lagrangian,has maximum global Chiral symmetry :,QCD Lagrangian and Symmetry,QCD Lagrangian and Symmetry,QCD Lagrangian with massi
46、ve light quarks,Effective Lagrangian Based on Loop Regularization,Y.B. Dai and Y-L. Wu, Euro. Phys. J. C 39 s1 (2004),After integrating out quark fields by the LORE method,Dynamically Generated Spontaneous Symmetry Breaking,Dynamically Generated Spontaneous Symmetry Breaking,Quadratic Term by the LO
47、RE method,Composite Higgs Fields,Scalars as Partner of Pseudoscalars & The Lightest Composite Higgs Bosons,Scalar mesons:,Pseudoscalar mesons :,Mass Formula,Pseudoscalar mesons :,Mass Formula,Predictions for Mass Spectra & Mixings,Predictions,Chiral Thermodynamic Model & QCD Phase Transition with Chiral Symmetry Restoration,Consider two flavor without instanton effects,After integrating out quark fields,
