joint lecture groningen-osaka spontaneous breaking of chiral symmetry in hadron physics 30 sep...
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Joint Lecture Groningen-Osaka Spontaneous Breaking of Chiral Symmetry in Hadron Physics30 Sep 09:00- CEST/16:00- JST Atsushi HOSAKA07 Oct 09:00- CEST/16:00- JST Nuclear Structure21 Oct 09:00- CEST/16:00- JST Nasser KALANTAR-NAYESTANAKI28 Oct 09:00- CET/17:00- JST Low-energy tests of the Standard Model25 Nov 09:00- CET/17:00- JST Rob TIMMERMANS02 Dec 09:00- CET/17:00- JST Relativistic chiral mean field model description of finite nuclei09 Dec 09:00- CET/17:00- JST Hiroshi TOKI16 Dec 09:00- CET/17:00- JST + WRAP-UP/DISCUSSION
Spontaneous Breaking of Chiral Symmetry
in Hadron Physics
• What does spontaneous mean? • What is the breaking of Symmetry? • What is chiral? • What is hadron? • . . . .
Contents
• General discussions Aspects of symmetry and of spontaneous breaking
• Concrete examples NJL model for hadron physics
SymmetryThe key concept in the modern Physics
SymmetricTranslation causes nothing
Example of translation
Uniform density
SymmetryThe key concept in the modern Physics
SymmetricTranslation causes nothing
Less symmetric
Example of translation
Uniform density
SymmetryThe key concept in the modern Physics
SymmetricTranslation causes nothing
Less symmetric
Example of translation
Uniform density
LocalizeClusterize
Translation changes the location of the cluster
Symmetry
SymmetricRotation causes nothing
Less symmetric Rotation changes the appearance
Example of rotation
Spherical
Deformed
SymmetricRotation causes nothing
Less symmetric Rotation changes the appearacnce
Symmetry
Example of rotation
Random
Ordered
Symmetric
Less symmetric
ComplexOrdered
Reality in our world
Symmetry is spontaneously broken(Dynamical: due to interactions)
Phase transition
Spontaneous breaking
SimpleDisordered
With Variety
Role of interaction
Random
Kinetic motion > Interaction
High temperature
Interaction breaks the symmetry=> Spontaneously broken
Like gas
Role of interaction
Random
Ordered
Kinetic motion > Interaction
Kinetic motion < Interaction
High temperature
Low temperature
Interaction breaks the symmetry=> Spontaneously broken
Like gas
Like solid
Examples of interaction(1) Translational invariance
H
rp1
2
2m1
rp2
2
2m2
v(rr1
rr2 )
r1
rr1
rR,
rr2
rr2
rRH is invariant under
This causes localization (clustering) of a two-particle system
(2) Rotational invariance
vT (
rr )
r1
rr
r2
rr
1
3
r1
r2 r2
r2 v(r)
This causes deformation of two-particle system (deuteron)
(3) Isospin invariance
N p
n
, , , 0 ~ (1, 2 , 3)
Iso-spinor Iso-vector
H gN †r N r
“Internal symmetry” Isospin (flavor), chiral, color, ….
Recover the broken symmetry
This does not mean the phase transition between them
There is a special way to recover the broken symmetry
Low T High T
Recover the broken symmetrySymmetry transformation
This does not require energy => Zero energy mode
Classical mechanics: No need to move an object on a flat/smooth surface
Field theory: Appearance of a massless particle => pion
W = Fs = 0
m = 0
pTranslation Rotation
Quantum mechanics
Starts to movepeipx
eimZeromode excitations
Uncertainty principleFlctuations
Uncertainty principle
Quantum mechanics
Starts to movepeipx
eim
For small moment of inertia => Easy to fluctuateSymmetric states are realized in the quantum world
For large moment of inertia => hard to moveSymmetry is left broken ~ Classical world
Zeromode excitations
Uncertainty principleFlctuations
Uncertainty principle
Collective vs single particle motion
In these motions, the shape does not change. The objects move collectively (simultaneously)
Nambu-GoldstoneBoson =Pion
Collective vs single particle motion
In these motions, the shape does not change. The objects move collectively (simultaneously)
Change in the shape requires more energy.Parts move => Motion of fewer particles
Nambu-GoldstoneBoson =Pion
Massive Modes=Massgeneration
Molecule
Atom
Nucleus
NucleonsMesons
Quarks
Electromagnetic interaction
Strong interaction
Many-body dynamics of electrons around atomic nuclei and/or ions
Many-body dynamics of nucleons => Nuclear Physics mesonsMany-body-dynamics of quarks and gluson => Hadron physics
Subatomic physics
Where to study?
Molecule
Atom
Nucleus
NucleonsMesons
Quarks
Electromagnetic interaction
Strong interaction
Many-body dynamics of electrons around atomic nuclei and/or ions
Many-body dynamics of nucleons => Nuclear Physics mesonsMany-body-dynamics of quarks and gluons Hadron Physics
Subatomic physics
Where to study?
Atoms
Many-electron system
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Many-electron system => Periodic tableNe = 1, 2, 3…. [One dimensional plot]
NucleiMany-nucleon system (protons and neutrons) => Nucleat chartNp = 1, 2, 3…. Nn = 1, 2, 3…. => [Two-dimensional plot]
Neutron number
Pro
ton
nu
mb
er
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MesonsBaryons
Particle Data Table
Hadrons
Many(?)-quark system (u, d, c, s, b, t)
Only qq and qqq?
Mesons Baryons
However
Particle DataProton/neutron
Why?
Problems of hadron physics
Clay Mathematics Institute, Millennium Problems
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.
http://www.claymath.org/millennium/
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1Birch and Swinnerton-Dyer Conjecture2Hodge Conjecture3Navier-Stokes Equations4P vs NP5Poincare Conjecture6Riemann Hypothesis7 Yang-Mills Theory => 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.
Spontaneous breaking of chiral () symmetry
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Yoichiro Nambu
Spontaneous breaking of chiral () symmetry
Quarks & gluons
Hadrons & nucleiConfinement, Mass generation
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Potential energy surface of the vacuum
Chiral order parameter
Yoichiro Nambu
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
Vacuum = Ground state is not empty
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
Particles are interacting with the vacuum
A particle
In the microscopic world
Analogy with BCS
Phonon exchange ee
QED
Cooper pairqq 0
Gauge (local) symmetry Superconductivity
Order parameter
Analogy with BCS
Phonon exchange ee
QED
Strong interaction qq
QCD
Cooper pairqq 0qq 0
Quark-antiquark pair
Gauge (local) symmetry Superconductivity
Flavor (global) symmetry Nambu-Goldstone boson
Order parameter
Superconductivity Hadrons
• Gap in energy spectrum • Mass of particles
E = 0Ground state
E = 0Vacuum
N
N*
• Meissner effect • Exclusion of color electric field
NormalSuper
Normal Super
Majorana mass
Dirac mass
Chiral symmetryHand
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Left Right
Chiral symmetry => Left-hand world has a symmetry (law) Right-hand world has a symmetry (law)If they mix, we say that chiral symmetry is broken
Massless fermion
c
Spin
c’ = c
Spin
S-frame S’-frame
Right-handed Right-handed
Right-left do not mixingRight and left can be independentIsospin (internal) symmetry can be introduced separately
We can not pass the particle moving at the speed of light
Chirality remains unchanged
Massive fermionv
Spin
v’
Spin
Right-handed Left-handed
For massive particle, right and left mix => Chiral symmetry is broken
The word chiral (handedness) comes from this
Boost can changefrom right to left
Summary 1Symmetry 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.
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 -> massive)
Chiral symmetry is broken spontaneously
Quark masses are dynamically generated (by interaction)
Pions become massless (Nambu-Goldstone mode)
Dynamics of L and R <=> V and A
V = R + L, A = R - L
Potential
V A
Vacuum pointOnly one Infinitely many on
-> choose one
V APions[NG boson] appear