国家自然科学基金委创新群体报告

Congratulation on the Establishment of KMI !
Wish a New Creative Era at KMI !!!
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
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

Shoichi Sakata & Chinese Philosophy
Compositeness and Symmetry
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
Since
then ‘兼听则明,偏信则暗’ has become an idiom
“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”
late
on, it has been as the dialectics and philosophy
Eg. “Contradiction Theory” by Chairman Mao Ze-Dong
“Everything has two sides：positive and negative”
Particle-antiparticle, left-right, forward-backward (CPT)
“One divides into two”
Compositeness
“Unity of opposites”
Symmetry Shoichi Sakata
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
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》
That has had a big influence
(dialectics of nature)杂志复刊，
on study and development
第一期就曾转载了坂田昌一的论文
of Elementary Particle
《基本粒子新概念》，这篇文章引起
Physics in China , eg. :
了毛泽东的很大兴趣。
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
1964年8月19日，毛泽东接见各国
Straton Model
代表团，由于坂田在整个到会的科
based on the Compsiteness
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。”
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


坂田昌一
物理学方法论论文集
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
核时代を超える
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 handwriting to Prof. Sakata with his
own poem and its first calligraphy.
科学与和平，
创造日日新。
微观小宇宙，
力转大车轮。
Fumihiko Sakata
坐大虹玉
观愧桥女
天
Looks多
like 横
a jade方
Science and peace
woman
入
诗taking
水 a淋
shower
笔，断，浴，
New creation峡，
everyday
深扁云慵
Micro-universe
of particles
坂田昌一先生幸
舟幔妆
千古
Turn round historical
big 逐
wheels
雨一
傍
To
Mr. Shoichi Sakata
中 through
酒 the
波 ages
镜
郭沫若
When Prof. S. Sakata passed away in 1970, the CAS
President Mr. Guo wrote a poem as a monumental 来。杯。
开。台。
writing with his calligraphy.
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、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 π π, π π π, 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
ε’/ε ≠ 0
(superweak hypothesis)
(weak interaction)
CP Violation
From 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
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
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)
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)
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
0.94
0.61
Re A0  3.10
4
4
Re A2  0.12  0.0210
4
4
10
Experimental Results
Re A0  3.3310
Re A2  0.1510
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 Operators




Q4  Q2  Q1

2

r
Q6   2  5 Q2  Q1


2
r
11
5 
2
2

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 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)
Why Quantum Field Theory
So Successful
Folk’s 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 << Mc  QFTs
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.
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.
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
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).
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.
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
Irreducible Loop Integrals (ILIs)
Loop Regularization (LORE) Method
Simple Prescription:
in ILIs, make the following replacement
With the conditions
So that
Gauge Invariant Consistency Conditions
Checking Consistency Condition
Checking Consistency Condition
Vacuum Polarization

Fermion-Loop Contributions
Gluonic Loop Contributions
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
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
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 Identities
which lead the functions to the following simple forms
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
Ward-Takahaski-Slavnov-Taylor Identities
Gauge Invariance
Two-point Diagrams
Three-point Diagrams
Four-point Diagrams
Ward-Takahaski-Slavnov-Taylor Identities

Renormalization Constants

All satisfy Ward-Takahaski-Slavnov-Taylor identities
Renormalization β Function

Gauge Coupling Renormalization
which reproduces the well-known QCD β function (GWP)
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 Regularizationindependent
Supersymmetry-preserving Regularization
Massless Wess-Zumino Model

Lagrangian

Ward identity

In momentum space
Check of Ward Identity
Gamma matrix algebra in 4-dimension and
translational invariance of integral momentum
Loop regularization satisfies these conditions
Massive Wess-Zumino Model

Lagrangian

Ward identity
Check of Ward Identity
Gamma matrix algebra in 4-dimension and
translational invariance of integral momentum
Loop regularization satisfies these conditions
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
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
Chiral Anomaly Based on Loop Regularization
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
Bjorken-Drell’s 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-Drell’s Circuit Analogy
Application to Two Loop Calculations
by LORE in ϕ^4 Theory
Log-running to coupling constant at two loop level
Power-law running of mass at two loop level
Application to Two Loop Calculations
by LORE in ϕ^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
Dynamically Generated
Spontaneous Chiral Symmetry Breaking
In Chiral Effective Field Theory
Importance of Quadratic Term by LORE method
QCD Lagrangian and Symmetry
Chiral limit: Taking vanishing quark masses mq→ 0.
QCD Lagrangian
(o)
QCD
L
1  
 qL  iD qL  qR  iD qR  G G
4
D     g s  / 2G
u 
 
q  d 
s 
 
qR , L
1
 (1   5 )q
2
has maximum global Chiral symmetry :
SUL (3)  SUR (3) U A (1) U B (1)
QCD Lagrangian and Symmetry

QCD Lagrangian with massive 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 LORE method
Composite Higgs Fields
Spont aneous
Symmet r y Br eaki ng
膺标介子作为
Gol dst one粒子
自发对称破缺
标量介子作为
Hi ggs粒子
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
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
Effective Lagrangian of Chiral Thermodynamic Model
(CTDM) of QCD at the lowest order with Finite Temperature
Both log. & quadratic integrals depend on Temperature
Dynamically generated effective composite Higgs potential
of mesons in the CTDM of QCD at finite temperature
Thermodynamic
Gap Equation
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
Input Parameters
Output Predictions
Critical Temperature of chiral symmetry restoration
Thermodynamic Behavior of Physical Quantities
Thermodynamic
VEV
Thermodynamic Behavior of Physical Quantities
Chiral Symmetry Breaking
&
QCD Confinement
in Predictive AdS/QCD Models
Particle Theory
Most SUSY QCD
SU(N)
N colors
Radius of curvature
Gravity Theory
=
String theory on
AdS5 x S 5
N = magnetic flux through S5

RS 5  RAdS5  g
2
YM

1/ 4
N
ls
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.)
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
4D Operators
5D Gauge fields AL and AR
4D Operators
5D Bulk fields Xij
Hard-Wall AdS/QCD Lagrangian
AL, AR, Xij
Mass term is determined by the scaling dimension
Xij has dimensionΔ= 3 and form p=0, AL & AR have dimension Δ= 3 and form p=1
Hard-Wall AdS/QCD
with/without Back-Reacted Effects
=
Quark masses
Quark condensate
Explicit chiral breaking
Relevant in the UV
Spontaneous chiral breaking
Relevant in the IR
just solve equations of motion!
Results from hard-wall AdS/QCD
J.P. Shock, F.Wu,YLW, Z.F. Xie, JHEP 0703:064,2007
Soft-Wall AdS/QCD
Dilaton field
Solving equations of motion for vector field
Linear trajectory for mass spectra of vector mesons
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.
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.D81:014024,2010. arXiv:0909.3887
Y-Q Sui, Y-L. Wu, Y-B Yang, Phys.Rev.D83:065030,2011 e-Print: arXiv:1012.3518
L-X Cui, S Takeuchi, Y-L Wu, to be pub. Phys. Rev. D. 2011 e-Print: arXiv:1107.2738
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
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:
Behaviors of
VEV & Dilaton
Determination of Model Parameters
Two Energy Scales as Input Parameters
Fitted Parameters
Without Quartic Interaction
Effective IR Cut-off Scale in Soft-Wall AdS/QCD
Fitted Parameters
With Quartic Interaction of bulk scalar
Solutions via Solving Equations of Motion
Pseudoscalar Sector
Equation of Motion
Mass Spectra of Pseudoscalar Mesons
Mass Spectra of Pseudoscalar Mesons
Resonance
States of
Pseudoscalars
Solutions via Solving Equations of Motion
Scalar Sector
Equation of Motion
IR & UV Boundary Condition
Mass Spectra of Scalar Mesons
Mass Spectra of Scalar Mesons
Resonance
States of
Scalars
Wave Functions of Resonance Scalars
Solutions via Solving Equations of Motion
Vector Sector
Equation of Motion
IR & UV Boundary Condition
Mass Spectra of Vector Mesons
Mass Spectra of Vector Mesons
Resonance
States of
Vectors
Wave Functions of Resonance Vectors
Solutions via Solving Equations of Motion

Axial-vector Sector
Equation of Motion
IR & UV Boundary Condition
Mass Spectra of Axial-vector Mesons
Mass Spectra of Axial-vector Mesons
Resonance
States of
Axial-vectors
Vector Coupling & Pion Form Factor
Structure of Pion Form Factor
Predictive Thermodynamic AdS/QCD
QCD Phase Transition
Predictive AdS/QCD at Finite Temperature &
Quark Number Susceptibility/QCD Phase Transition
Predictive AdS/QCD at Finite Temperature &
Quark Number Susceptibility/QCD Phase Transition
Small Quark Mass, High Critical Temperature
Predictive AdS/QCD at Finite Temperature &
Quark Number Susceptibility/QCD Phase Transition
Large QCD Scale, High Critical temperature
With the Same Input Parameters
Effects from Current Quark Mass
Effects from QCD Scale
QCD Critical
Temperature：
Tc ~ 170 MeV
Current Quark Mass
has bigger effect than
quark condensate to
critical temperature
SO(3) Gauge Family Model
YLW arXiv:0708.0867, PRD D77:113009 (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

Vacuum Structure
With fixing gauge and following vacuum structure:
Type-II like sea-saw mechanism


For neutrinos:
For charged leptons:
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 !!!
Nearly Tri-bimaximal neutrino mixings

Neutrino and charged lepton mixings:

MNS Lepton mixing matrix:
Numerical Results

4 Parameters:
Two inputs:

Neutrino masses with the given parameter

/
/
13
Taking
Optimistic Predictions
which may be tested by the coming neutrino
Experiments.
CONCLUSIONS & REMARKS
Listen to
The concepts of compositeness
both sides
and symmetry have led great
on
theory
&
progresses in particle physics
experiment
will our
They will continueyou
to deepen
understanding on the
origin
of
become an
particles and the universe
enlightened
physicist !!!
THANKS

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