Congratulation on the Establishment of KMI !

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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 ????,????
• 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
???????(628),????? ??????,????? ??

• 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

• Since then ????,???? has become an idiom late
  on, it has been as the dialectics and philosophy
• Eg. Contradiction Theory by Chairman Mao Ze-Dong

???????????,????????????????????????,??????,??
????????
Everything has two sidespositive and negative
Particle-antiparticle, left-right,
forward-backward (CPT)
One divides into two
Compositeness
Unity of opposites
Symmetry
Shoichi Sakata
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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, ?
• Gell-Mann Zweig in 1964
• p, n, ? ? 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?,?????????(dialectics of
nature)????,??????????????????????,?????????????
???
That has had a big influence on study and
development of Elementary Particle Physics in
China , eg. Straton Model based on
the Compsiteness
1964?8?19?,??????????,????????????????????????,???
???????????????????????????????????,?????
1964?8?,??????????(??)??????????????????????????
9
????????
???? ?????????????????????????1965-07
???? ????????? ???????? 1973-04
10
???? ?????????
???????
???????????
???? ????????? ?????
???? ???? ????? ?????????????

• ??????????????????????1966-05
• Methodology

11

• 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 handwriting to Prof. Sakata with
  his own poem and its first calligraphy.

Fumihiko Sakata
?????,??????
?????,??????
?????,??????
?????,??????
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
When Prof. S. Sakata passed away in 1970, the
CAS President Mr. Guo wrote a poem as a
monumental writing with his calligraphy.
??? mountain
12
Insight From Three Flavors to
Three Families Indirect and Direct CP violation
in kaon Meson Decays
???????? ???????? ?????,(B.C.
571)
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CP Violation From 3 Flavors to 3
Families

• Indirect CP violation was discovered in 1964 from
  kaon decays K? p p, p p p, 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
• e/e 0 (superweak hypothesis)
• e/e ? 0 (weak interaction)

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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

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Direct CP Violation ?I ½ Rule in Kaon
Decays Based on ChPT

• Direct CP violation arises from both nonzero
  relative weak and strong phases via the KM
  mechanism

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Theoretical Prediction and Experimental
Measurements

• Theoretical Prediction
• e'/e(2045)10-4
• (Y.L. Wu Phys. Rev. D64 016001,2001)
• Experimental Results
• e'/e(20.72.8)10-4
• (KTeV Collab. Phys. Rev. D67 012005,2003)
• e'/e(14.72.2)10-4
• (NA48 Collab. Phys. Lett. B544 97,2002)

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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)
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Consistency of Prediction

• The consistency of our theoretical prediction is
  strongly supported from a simultaneous prediction
  for the ?I 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)

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Why Quantum Field Theory
So Successful

• Folks theorem by Weinberg
• Any quantum theory that at sufficiently low
  energy and 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 ltlt Mc ? QFTs

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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.

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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.

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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

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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.

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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.A182003, 5363-5420.
• Yue-Liang Wu, SYMMETRY PRESERVING LOOP
  REGULARIZATION AND RENORMALIZATION OF QFTS.
  Mod.Phys.Lett.A192004, 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, arXiv1012.0626 hep-ph.
• D. Huang and Y.L. Wu, arXiv1108.3603

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Irreducible Loop Integrals (ILIs)
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Loop Regularization (LORE) Method

• Simple Prescription
• in ILIs, make the following replacement
• With the conditions
• So that

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Gauge Invariant Consistency Conditions
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Checking Consistency Condition
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Checking Consistency Condition
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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

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Symmetrypreserving 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

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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
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Interesting Mathematical Identities
which lead the functions to the following
simple forms
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Renormalization Constants of Non- Abelian gauge
Theory and ß 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

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Renormalization ß Function

• Gauge Coupling Renormalization
• which reproduces the well-known QCD ß function
  (GWP)

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Supersymmetry in Loop Regularization
J.W. Cui, Y.Tang,Y.L. Wu Phys.Rev.D79125008,2009

• Supersymmetry
• Supersymmetry is a full symmetry of quantum
  theory
• Supersymmetry should be Regularization-independent
  
• Supersymmetry-preserving Regularization

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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
51
Massive Wess-Zumino Model

• Lagrangian
• Ward identity

52
Check of Ward Identity
Gamma matrix algebra in 4-dimension and
translational invariance of integral
momentum Loop regularization satisfies these
conditions
53
Triangle Anomaly

• Amplitudes
• Using the definition of gamma_5
• The trace of gamma matrices gets the most general
  and unique structure with symmetric Lorentz
  indices
• Y.L.Ma YLW

54
Anomaly of Axial Current

• Explicit calculation based on Loop Regularization
  with the most general and symmetric Lorentz
  structure
• Restore 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

55
Chiral Anomaly Based on Loop Regularization
Including the cross diagram, the final result is
Which leads to the well-known anomaly form
56
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
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Loop Regularization Merging With
Bjorken-Drells Circuit Analogy
The divergence arises from zero resistance ?
Short Circuit
which enables us to prove the validity of LORE
to all orders
58
Loop Regularization Merging With
Bjorken-Drells Circuit Analogy
59
Application to Two Loop Calculations
by LORE in ?4 Theory
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Log-running to coupling constant at two loop
level
Power-law running of mass at two loop level
62
Application to Two Loop Calculations
by LORE in ?4 Theory
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
63
Dynamically Generated Spontaneous
Chiral Symmetry Breaking In Chiral
Effective Field Theory
Importance of Quadratic Term by LORE method
64
QCD Lagrangian and Symmetry
Chiral limit Taking vanishing quark masses
mq? 0. QCD Lagrangian
has maximum global Chiral symmetry
65
QCD Lagrangian and Symmetry

• QCD Lagrangian with massive light quarks

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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
67
Dynamically Generated Spontaneous
Symmetry Breaking
68
Dynamically Generated Spontaneous
Symmetry Breaking
Quadratic Term by the LORE method
69
Composite Higgs Fields
70
Scalars as Partner of Pseudoscalars
The Lightest Composite Higgs Bosons
Scalar mesons
Pseudoscalar mesons
71
Mass Formula
Pseudoscalar mesons
72
Mass Formula
73
Predictions for Mass Spectra Mixings
74
Predictions
75
Chiral Thermodynamic Model QCD Phase
Transition with Chiral Symmetry Restoration
76
Consider two flavor without instanton effects
After integrating out quark fields
77
The propagator of quark fields
Applying the Schwinger Closed-Time-Path Green
Function (CTPGF) Formalism to the Quark
Propagators
Carrying out momentum integration by the LORE
method
78
Effective Lagrangian of Chiral Thermodynamic
Model (CTDM) of QCD at the lowest order with
Finite Temperature
Both log. quadratic integrals depend on
Temperature
79
Dynamically generated effective composite Higgs
potential of mesons in the CTDM of QCD at
finite temperature
Thermodynamic Gap Equation
80
Assumption The scale of NJL four quark
interaction due to NP QCD has the same
T-dependence as quark condensate
Critical temperature for Chiral Symmetry
Restoration at
T? Tc
Quadratic Term in the LORE method
81
Input Parameters
Output Predictions
Critical Temperature of chiral symmetry
restoration
82
Thermodynamic Behavior of Physical Quantities
Thermodynamic VEV
83
Thermodynamic Behavior of Physical Quantities
84
Chiral Symmetry Breaking
QCD Confinement in Predictive AdS/QCD
Models
85
Particle Theory Gravity Theory
String theory on

Most SUSY QCD SU(N)
N magnetic flux through S5
N colors
Radius of curvature
Duality
g2 N is small ? perturbation theory is easy
gravity is bad g2 N is large ? gravity
is good perturbation theory is hard
Strings made with gluons become fundamental
strings.
(J.M.)
86
Bottom-Up Approach
Hard-Wall AdS/QCD Model
Global SU(3)L x SU(3)R symmetry in QCD
SU(3)LXSU(3)R gauge symmetry in AdS5
5D Gauge fields AL and AR
4D Operators
4D Operators
5D Bulk fields Xij
Hard-Wall AdS/QCD Lagrangian
Mass term is determined by the scaling dimension
Xij has dimension? 3 and form p0, AL AR have
dimension ? 3 and form p1
87
Hard-Wall AdS/QCD with/without
Back-Reacted Effects

Quark masses
Quark condensate
just solve equations of motion!
Explicit chiral breaking
Spontaneous chiral breaking
Relevant in the UV
Relevant in the IR
88
Results from hard-wall AdS/QCD
J.P. Shock, F.Wu,YLW, Z.F. Xie, JHEP
0703064,2007
89
Soft-Wall AdS/QCD
Dilaton field
Solving equations of motion for vector field
Linear trajectory for mass spectra of vector
mesons
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Achievements Challenges

• Hard-wall AdS/QCD models contain the chiral
  symmetry breaking, the resulting mass spectra for
  the excited mesons are contrary to the
  experimental data.
• Soft-wall AdS/QCD models describe the linear
  confinement and desired mass spectra for the
  excited vector mesons, while the chiral symmetry
  breaking can't consistently be realized.
• How to naturally incorporate two important
  features into a single AdS/QCD model and obtain
  the consistent mass spectra.

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Realistic Predictive Holographic AdS/QCD
Deformed 5D Metric in IR Region Quartic
Interaction
Y.Q.Sui, YLWu, Z.F.Xie, Y.B.Yang,Phys.Rev.D810140
24,2010. arXiv0909.3887 Y-Q Sui, Y-L. Wu, Y-B
Yang, Phys.Rev.D83065030,2011 e-Print
arXiv1012.3518 L-X Cui, S Takeuchi, Y-L Wu, to
be pub. Phys. Rev. D. 2011 e-Print
arXiv1107.2738
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Minimal condition for the bulk vacuum
Chiral Symmetry Breaking UV IR boundary
conditions of the bulk vacuum
Linear Confinement Solutions for the dilaton
field at the UV IR boundary
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Various Modified Soft-wall AdS/QCD Models

• Some Exact Forms of bulk VEV in Models I, II,
  III

Two IR boundary conditions of the bulk VEV
Ia, IIa, IIIa
Ib, IIb, IIIb
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Behaviors of VEV Dilaton
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Determination of Model Parameters

• Two Energy Scales as Input Parameters

97
Fitted Parameters

• Without Quartic Interaction

Effective IR Cut-off Scale in Soft-Wall AdS/QCD
98
Fitted Parameters
With Quartic Interaction of bulk scalar
99
Solutions via Solving Equations of Motion

• Pseudoscalar Sector

Equation of Motion
100
Mass Spectra of Pseudoscalar Mesons
101
Mass Spectra of Pseudoscalar Mesons
102
Resonance States of Pseudoscalars
103
Solutions via Solving Equations of Motion
Scalar Sector
Equation of Motion
IR UV Boundary Condition
104
Mass Spectra of Scalar Mesons
105
Mass Spectra of Scalar Mesons
106
Resonance States of Scalars
107
Wave Functions of Resonance Scalars
108
Solutions via Solving Equations of Motion

• Vector Sector

Equation of Motion
IR UV Boundary Condition
109
Mass Spectra of Vector Mesons
110
Mass Spectra of Vector Mesons
111
Resonance States of Vectors
112
Wave Functions of Resonance Vectors
113
Solutions via Solving Equations of Motion

• Axial-vector Sector

Equation of Motion
IR UV Boundary Condition
114
Mass Spectra of Axial-vector Mesons
115
Mass Spectra of Axial-vector Mesons
116
Resonance States of Axial-vectors
117
Vector Coupling Pion Form Factor
118
Structure of Pion Form Factor
119
Predictive Thermodynamic AdS/QCD
QCD Phase Transition
120
Predictive AdS/QCD at Finite Temperature Quark
Number Susceptibility/QCD Phase Transition
121
Predictive AdS/QCD at Finite Temperature Quark
Number Susceptibility/QCD Phase Transition
Small Quark Mass, High Critical Temperature
122
Predictive AdS/QCD at Finite Temperature Quark
Number Susceptibility/QCD Phase Transition
Large QCD Scale, High Critical temperature
123
With the Same Input Parameters
Effects from Current Quark Mass
Effects from QCD Scale
124
QCD Critical Temperature Tc 170 MeV
Current Quark Mass has bigger effect than quark
condensate to critical temperature
125
SO(3) Gauge Family Model YLW
arXiv0708.0867, PRD D77113009 (2008)

• Why lepton sector is so different from quark
  sector ?
• Neutrinos are neutral fermions and can be
  Majorana!
• Majorana fermions have only real
  representations, they usually possess orthogonal
  symmetry
• Lagrangian for Yukawa Interactions with

126
Vacuum Structure

• With fixing gauge and following vacuum structure

127
Type-II like sea-saw mechanism

• For neutrinos
• For charged leptons

128
Small Mass and Large Mixing of Neutrinos

• Approximate global U(1) family symmetries
• Smallness of neutrino masses and charged lepton
  mixing
• Neutrino mixings could be large !!!

129
Nearly Tri-bimaximal neutrino mixings

• Neutrino and charged lepton mixings
• MNS Lepton mixing matrix

130
Numerical Results

• 4 Parameters / /
• Two inputs
• Neutrino masses with the given parameter

131
Taking Optimistic Predictions which may be
tested by the coming neutrino Experiments.
132
CONCLUSIONS REMARKS
Listen to both sides on
theory experiment you will become an
enlightened physicist !!!
The concepts of compositeness and symmetry have
led great progresses in particle physics
They will continue to deepen our understanding on
the origin of particles and the universe
133
THANKS
??!