Joint Lecture Groningen-Osaka

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Joint Lecture Groningen-Osaka
Spontaneous Breaking of Chiral Symmetry in
Hadron Physics 30 Sep 0900- CEST/1600- JST
Atsushi HOSAKA 07 Oct 0900- CEST/1600- JST
Nuclear Structure 21 Oct 0900- CEST/1600- JST
Nasser KALANTAR-NAYESTANAKI 28 Oct 0900-
CET/1700- JST Low-energy tests of the Standard
Model 25 Nov 0900- CET/1700- JST Rob
TIMMERMANS 02 Dec 0900- CET/1700- JST
Relativistic chiral mean field model description
of finite nuclei 09 Dec 0900- CET/1700- JST
Hiroshi TOKI 16 Dec 0900- CET/1700- JST
WRAP-UP/DISCUSSION
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Spontaneous Breaking of Chiral Symmetryin Hadron
Physics
What does spontaneous mean? What is the
breaking of Symmetry? What is chiral? What is
hadron? . . . .
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Contents
General discussions Aspects of symmetry and
of spontaneous breaking Concrete
examples NJL model for hadron physics
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What is symmetric andWhat is broken symmetry
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Symmetry
The key concept in the modern Physics
Example of translation
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Symmetry
The key concept in the modern Physics
Example of translation
Symmetric
Translation causes nothing
Uniform density
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Symmetry
The key concept in the modern Physics
Example of translation
Symmetric
Translation causes nothing
Uniform density
Less symmetric
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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
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Symmetry
Example of rotation
Symmetric
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Symmetry
Example of rotation
Symmetric
Rotation causes nothing
Spherical
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Symmetry
Example of rotation
Symmetric
Rotation causes nothing
Spherical
Less symmetric
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Symmetry
Example of rotation
Symmetric
Rotation causes nothing
Spherical
Less symmetric
Rotation changes the appearance
Deformed
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Symmetry
Example of rotation
Symmetric
Rotation causes nothing
Random
Less symmetric
Rotation changes the appearacnce
Ordered
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Spontaneous breaking
Symmetric
Simple Disordered
Less symmetric
Complex Ordered
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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
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Role of interaction
High temperature
Kinetic motion gt Interaction
Random
Like gas
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Role of interaction
High temperature
Kinetic motion gt Interaction
Random
Like gas

• Interaction breaks the symmetry
• gt Spontaneously broken

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Role of interaction
High temperature
Kinetic motion gt Interaction
Random
Like gas

• Interaction breaks the symmetry
• gt Spontaneously broken

Low temperature
Kinetic motion lt Interaction
Like solid
Ordered
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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)
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(3) Isospin invariance
Iso-spinor
Iso-vector
Internal symmetry Isospin (flavor),
chiral, color, .
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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
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Recover the broken symmetry
Symmetry transformation
Translation
Rotation
p
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Recover the broken symmetry
Symmetry transformation
Translation
Rotation
p
This does not require energy gt 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 gt pion
m? 0
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Quantum mechanics
Uncertainty principle
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Quantum mechanics
Uncertainty principle
p
Starts to move
Uncertainty principle Flctuations
Zeromode excitations
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Quantum mechanics
Uncertainty principle
p
Starts to move
Uncertainty principle Flctuations
Zeromode excitations
For small moment of inertia gt Easy to
fluctuate Symmetric states are realized in the
quantum world For large moment of inertia gt
hard to move Symmetry is left broken Classical
world
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Collective vs single particle motion
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Collective vs single particle motion
Nambu- Goldstone Boson Pion
In these motions, the shape does not change.
The objects move collectively (simultaneously)
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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 gt Motion of fewer particles
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Hadrons
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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 gt Nuclear
Physics mesons Many-body-dynamics
of quarks and gluson gt Hadron physics
Nucleons Mesons
Quarks
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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 gt Nuclear
Physics mesons Many-body-dynamics
of quarks and gluons Hadron Physics
Nucleons Mesons
Quarks
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Atoms
Many-electron system
Many-electron system gt Periodic table Ne 1,
2, 3. One dimensional plot
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Nuclei
Many-nucleon system (protons and neutrons)
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Nuclei
Many-nucleon system (protons and neutrons)
gt Nucleat chart Np 1, 2, 3.
Nn 1, 2, 3. gt Two-dimensional plot
Neutron number
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Hadrons
Many(?)-quark system (u, d, c, s, b, t)
Particle Data
Proton/neutron
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Particle Data Table
Mesons
Baryons
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Hadrons
Many(?)-quark system (u, d, c, s, b, t)
Particle Data
Proton/neutron
However
Why?
Mesons
Baryons
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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.
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1Birch and Swinnerton-Dyer Conjecture 2Hodge
Conjecture 3Navier-Stokes Equations 4P vs
NP 5Poincare Conjecture 6Riemann Hypothesis 7
Yang-Mills Theory gt 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.

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Tetraquark
Pentaquark
Exotic hadrons
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Spontaneous breaking of chiral (?) symmetry
Yoichiro Nambu
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Spontaneous breaking of chiral (?) symmetry
Potential energy surface of the vacuum
Yoichiro Nambu
Chiral order parameter
Quarks gluons
Confinement, Mass generation
Hadrons nuclei
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Dynamics of Spontaneous symmetry breakingin the
strongly interacting system
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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
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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
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Analogy with BCS
QED
Phonon exchange ee
Cooper pair
Order parameter
Gauge (local) symmetry Superconductivity
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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
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Superconductivity
Hadrons
Dirac mass
Majorana mass
Meissner effect
Exclusion of color electric field
Super
Normal
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Chiral symmetry
Hand
Left
Right
Chiral symmetry gt Left-hand world has a symmetry
(law) Right-hand
world has a symmetry (law)
If they mix, we say that chiral symmetry is broken
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Massless fermion
We can not pass the particle moving at the speed
of light
c
c c
Spin
Chirality remains unchanged
Spin
S-frame
S-frame
Right-handed
Right-handed
Right-left do not mixing Right and left can be
independent Isospin (internal) symmetry can be
introduced separately
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Massive fermion
v
v
Spin
Spin
Boost can change from right to left
Left-handed
Right-handed
The word chiral (handedness) comes from this
For massive particle, right and left mix gt
Chiral symmetry is broken
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Summary 1
Symmetry can be spontaneously broken by
interactions. Symmetry and broken phase can
change each other. (Temperature, density, ) In
the broken phase, symmetry is recovered by
the presence the Nambu-Goldstone mode. Zero
energy mode pion Collective, and single
particle modes are distinguished. The zero mode
(pions) governs the dynamics at low energy.
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Summary 2
Hadrons are made of quarks and gluons Baryons
qqq, mesons qq, others (exotics)?? Quark
properties changes drastically by the strong
interaction (nearly massless -gt massive) Chiral
symmetry is broken spontaneously Quark masses
are dynamically generated (by interaction) Pions
become massless (Nambu-Goldstone mode)
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Dynamics of L and R ltgt V and A
V R L, A R - L
Potential
Vacuum point
Only one
Infinitely many on -gt choose one
V
A
A
V
PionsNG boson appear
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Where and how pions appear
Quarks and gluons
Strong interaction dynamics
Quarks and mesons
Mass generation Constituent (quasi) quarks
Pions
p
p
p
q
q
q
q
q