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Relativistic chiral mean field model for nuclear physics (II)

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Yukawa introduced pion as a mediator of nuclear interaction ... Numerical results 2 Chiral symmetry Nuclear matter Summary-2 NJL model provides the linear sigma model. – PowerPoint PPT presentation

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Title: Relativistic chiral mean field model for nuclear physics (II)


1
Relativistic chiral mean field model for nuclear
physics (II)
  • Hiroshi Toki
  • Research Center for Nuclear Physics
  • Osaka University

2
Pion is important !!
  • Yukawa introduced pion as a mediator of nuclear
    interaction (1934)
  • Meyer-Jensen introduced shell model for finite
    nuclei (1949)
  • Nambu-Jona-Lasinio introduced chiral symmetry and
    its breaking for mass and pion generation (1961)

3
Motivation for the second stage
  • Pion is important in nuclear physics.
  • Pion appears due to chiral symmetry.
  • Particles as nucleon, rho mesons,.. may change
    their properties in medium.
  • Chiral symmetry may be recovered partially in
    nucleus.
  • Unification of QCD physics and nuclear physics.

4
Spontaneous breaking of chiral symmetry
Hosaka
Potential energy surface of the vacuum
Yoichiro Nambu
Chiral order parameter
Quarks gluons
Confinement, Mass generation
Hadrons nuclei
5
Nobel prize (2008)
He was motivated by the BCS theory.
is the order parameter
is the order parameter
Chiral symmetry
Particle number
6
Nambu-Jona-Lasinio Lagrangian
Chiral transformation
Mean field approximation Hartree approximation
Fermion gets mass.
The chiral symmetry is spontaneously broken.
7
Chiral condensate is
The fermion mass is
m
G
Gc
The mass is similar to the pairing gap in the BCS
formalism. The mass generation mechanism for a
fermion.
8
The particle-hole excitation (pion channel) RPA
9
The pion mass is zero. Nambu-Goldstone mode has
a zero mass.
The nucleon gets mass by chiral
condensation. There appears a massless boson
pseudo-scalar meson.
All the masses of particles are zero at the
beginning, but they are generated
dynamically. Massless boson appears
(Nambu-Goldstone boson) with pseudo-scalar
quantum number.
10
Bosonization (Eguchi1974)
Fermion field is quark
Auxiliary fields
11
Nuclear physics with NJL model
Auxiliary fields
SU2 chiral transformation
Confinement
(Polyakov NJL Mode)
SU2c is done SU3c is not yet done.
12
Chiral sigma model
Pion is the Nambu boson of chiral symmetry
  • Linear Sigma Model Lagrangian

Polar coordinate
Weinberg transformation
13
Non-linear sigma model
N
r fp j
Lagrangian
Free parameters are and
(Two parameters)
14
Relativistic mean field model (standard)
Mean field approximation
Then take only the mean field part, which is just
a number.
The pion mean field is zero. Hence, the pion
contribution is zero in the standard mean field
approximation.
15
Relativistic mean field model (pion condensation)
Ogawa, Toki, et al. Brown, Migdal..
Since the pion has pseudo-scalar (0-) nature, the
parity and charge symmetry are broken.
Dirac equation
In finite nuclei, we have to project out spin and
isospin, which involves a complicated projection.
16
Relativistic Chiral Mean Field Model (powerful
method)
Wave function for mesons and nucleons
p
p
Mean field approximation for mesons.
h
h
Nucleons are moving in the mean field and
occasionally brought up to high momentum
states due to pion exchange interaction
Brueckner argument
17
Why 2p-2h states are necessary for pion
(tensor) interaction?
The spin flipped states are already occupied by
other nucleons.
Pauli forbidden
G.S.
Spin-saturated
18
Energy minimization with respect to meson and
nucleon fields
(Mean field equation)
Hartree-Fock
G-matrix component
19
Numerical results (1)
Ogawa Toki NP 2009
12C
Spin-spin
Pion
Tensor
Total
4He 12C 16O
Adjust binding energy and size
20
Numerical results 2
Individual contribution
Cumulative
O
C
O
The difference between 12C and 16O is 3 MeV/N.
P1/2
C
The difference comes from low pion spin states
(Jlt3). This is the Pauli blocking effect.
P3/2
S1/2
Pion tensor provides large attraction to 12C
Pion energy
21
Chiral symmetry
Ogawa Toki NP(2009)
Nucleon mass is reduced by 20 due to sigma.
N
Not 45 as discussed in RMF model.
We want to work out heavier nuclei for magic
number. Spin-orbit splitting should be worked out
systematically.
One half is from sigma meson and the other half
is from the pion.
22
Nuclear matter
Hu Ogawa Toki Phys. Rev. 2009
E/A
Total
Total
Pion
23
Deeply bound pionic atom
Predicted to exist
Toki Yamazaki, PL(1988)
Found by (d,3He) _at_ GSI
Itahashi, Hayano, Yamazaki.. Z. Phys.(1996),
PRL(2004)
Findings isovector s-wave
24
Suzuki, Hayano, Yamazaki.. PRL(2004)
Optical model analysis for the deeply bound state.
25
Summary-2
  • NJL model provides the linear sigma model.
  • Pion (tensor) is treated within the relativistic
    chiral mean field model.
  • JJ-magic is produced by pion.
  • Nucleon mass is reduced by 20
  • Deeply bound pionic atom seems to verify partial
    recovery of chiral symmetry.

26
Summary
  • Pion is important in Nuclear Physics.
  • Pion is a Goldstone-Nambu boson of chiral
    symmetry breaking.
  • By integrating out the quark field with
    confinement, we can get sigma model Lagrangian.
  • Relativistic chiral mean field model is able to
    work out the sigma model Lagrangian.
  • We have now a tool to unify the quark picture
    with the hadron picture and describe nucleus from
    quarks.

27
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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