1. Dilaton in Baryonic Matter
Hyun Kyu Lee
Hanyang University
M. Harada, T. Kuo, Y.Ma , C. Sasaki, W. Paeng, B.Y. Park and M. Rho
4th APCTP-WCU Focus Program, April 14-24, 2013,

2. Manifestations of symmetries of QCD in dense baryonic matter.
I. Introduction
Manifestations of symmetries of QCD
in dense baryonic matter.
1. Chiral symmetry
2. Scale symmetry
3. Hidden local symmetry
Density frontier
Temperature frontier

3. - Dilaton :
Higgs particle in hidden local
symmetry(HLS)
Phenomenology of dilaton for dense
baryonic matter :
Symmetry energy, Equation of state

4. II. Dilaton and chiral symmetry breaking
Linear sigma model
SU(2) x SU(2) symmetry
 SSB for masless pions
Explicit scale symmetry breaking :

5. A. - Degeneracy is removed  no SSB - Scale symmetry
- Approximate scale symmetry
- SSB
Scale symmetry breaking
 SSB of chiral symmetry

6. QCD Goldstone theorem for SSB Broken generators  Goldstone bosons
Massless  no scale
but decay constant, F  scale
Linear sigma model
Pion and massive sigma
decay constant
Nonlinear realization
pion and decay constant
QCD

7. Freund –Nambu model matter field dilaton
1.The mass of matter field comes from Va and is independent of tau and is arbitrary.
2.The mass of dilaton depends on tau, going to zero liniearly as tau  0.
vev does not depend on tau.
(approximate) SSB of scale symmetry:
only the mass of Goldstone boson(dilaton) must be small while all other fields can be arbitrary.
Freund & Nambu, 1968; B. Zumino, 1970

8. pion dynamics in nonlinear realization
QCD
- Running coupling constant
-Trace anomaly:
chiral singlet scalar

9. Dilaton-pion coupling
Scale symmetry breaking

10. III. Dilaton and Hidden local symmetry
Chiral symmetry breaking
Hidden symmetry

11. Spontaneous breaking of hidden local symmetry
Vector meson
Goldstone boson
Higgs mechanism

12. Dilaton: Higgs in hidden local symmetry

13. IV. Dilaton in dense hadronic matter
(1) Effective theory for hadronic matter
- hidden local symmetry (HLS)
Harada & Yamawaki(01)
Skyrmion on the lattice,
Skyrmion and hQCD, vetor meson
Dilaton limit and mean field
Talk by B.Y. Park, Y. Oh, Y.-L. Ma, W. Paeng, M. Rho

14. Dong, Kuo, HKL,Machleidt, Rho(12)
(2) Stiffer equation of state:
half skyrmion phase
Omega-nucleon coupling
Dong, Kuo, HKL,Machleidt, Rho(12)
EoS with new scaling
Mean field calculation is now in progress

15. 2. weak equilibrium: proton, neutron, electron, muon  Softer EoS
Neutron star with
1. charge neutrality
2. weak equilibrium: proton, neutron, electron, muon
 Softer EoS
Jaehyun Lee(2013) in preperation

16. PSR J
(1.97 ± 0.04)M⊙

17. astrophysical observation : PSR J1614-2230 : (1.97 ± 0.04)M⊙
V. Summary
Effective theory with chiral and scale symmetry.
- pion, vector meson, nucleon, dilaton
- vector mesons: hidden local symmetry (HLS)
- dilaton: Higgs in HLS
Dilaton  density dependence of hadronic natter
- skyrmion matter
- dialton limit , mean field approach
Stiffer symmetry energy and EoS for star matter
astrophysical observation : PSR J : (1.97 ± 0.04)M⊙
new RIB machines, advanced LIGO