1. Shigehiro Yasui Tokyo Institute of Technology
Charm nuclei and
related topics
Shigehiro Yasui
Tokyo Institute of Technology
ExHIC Mar. 2016

2. Nucleus + Strangeness 1. Hadron-nucleon interaction
1. Multi-flavor nucleus
Nucleus + Strangeness
1. Hadron-nucleon interaction
2. Hadron in medium
3. Nuclear structure
Impurity physics

3. ??? Nucleus + Charm 1. Hadron-nucleon interaction 2. Hadron in medium
1. Multi-flavor nucleus
Nucleus + Charm
Mass hierarchy (mc>>ΛQCD)
~1.2 GeV ~0.2 GeV
1. Hadron-nucleon interaction
???
2. Hadron in medium
3. Nuclear structure
Impurity physics

4. Charm nucleus mass spectroscopy
1. Multi-flavor nucleus
Charm nucleus mass spectroscopy
D, D*
- Binding energy
- Dispersion relation
- Spectral function
- Reaction
- Restoration of χSB
- Nuclear structure
- etc. q c
Nucleus

5. Charm/bottom “light” nuclei
1. Multi-flavor nucleus
Charm/bottom “light” nuclei
M. Bayer, C. W. Xiao, T. Hyodo, A. Dote, M. Oka, E. Oset, Phys. Rev. C86, (2012)
DNN
D(*)NN
BNN
Y. Yamaguchi, S.Y., A. Hosaka, Nucl. Phys. A927, 110 (2014)
A. Yokota, E. Hiyama, M. Oka,
Pog. Ther. Exp. Phys. 2013, 113D01
J/ψNN
ηc N N
Λc N N
S. Maeda, M. Oka, A. Yokota, E. Hiyama, Y-R. Liu, Pog. Ther. Exp. Phys. 2016, 023D02

6. Repulsive? or Attractive?
1. Multi-flavor nucleus
D (B) meson in nuclear matter
Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction), ...
Binding energy [MeV]
Hadron dynamics
Quark-meson coupling model
QCD rum rule
Mean field
WT-type coupling
π exchange
~ a few ten MeV
Repulsive? or Attractive?
[26]
-50 MeV [27]
+30 MeV [28]
-66 MeV [29]
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7. D (B) meson in nuclear matter
1. Multi-flavor nucleus
D (B) meson in nuclear matter
Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction), ...
Heavy quark symmetry
DN ⇄ D*N
Hadronic model
C. Garcia-Recio, J. Nieves, L. L. Salcedo,
L. Tolos, Phys. Rev. C 85, (2012)

8. π meson exchange between D (D*) and N
1. Multi-flavor nucleus
D (B) meson in nuclear matter
Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction), ...
Heavy quark symmetry
DN ⇄ D*N
Hadronic model
S. Y. , K. Sudoh, Phys Rev. C87, (2013)
π meson exchange between D (D*) and N
D, B
D*, B* ρ0 ρ0

9. D (B) meson in nuclear matter
1. Multi-flavor nucleus
D (B) meson in nuclear matter
Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction), ...
QCD sum rule
K. Suzuki, P. Gubler, M. Oka, arXiv: [hep-ph]
Cf. Quark confinement picture
A. Park. P. Gubler, M. Harada, S. H. Lee, C. Nonaka, W. Park, arXiv: [nucl-th]

10. D (B) meson in nuclear matter
1. Multi-flavor nucleus
D (B) meson in nuclear matter
Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction), ...
PNJL model
D. Blaschkem P. Costa, Y-L. Kalinovsky, Phys. Rev. D85, (2012)

11. Charm nucleus mass spectroscopy
1. Multi-flavor nucleus
Charm nucleus mass spectroscopy
D, D*
- Binding energy
- Dispersion relation
- Spectral function
- Reaction
- Restoration of χSB
- Nuclear structure
- etc. q c
Nucleus
Kondo effect “heavy impurity” physics
(This should be applicable in general cases...)

12. Mean-field approach to Kondo effect
Contents
1. Multi-flavor nucleus
2. Kondo effect
2.1 What’s Kondo effect?
2.2 Kondo effect in atomic nuclei (mean-field + RPA)
3. Conclusion
Mean-field approach to Kondo effect
bulk systems
finite systems
F. Takano, T. Ogawa, Prog. Theor. Phys. 35, 343 (1966)
A. Yoshimori, A. Sakurai, Suppl. Prog. Theor. Phys. 46, 162 (1970)
M. Eto, Y. V. Narazov, Phys. Rev. B 64, (2001)
This work

13. 2. Kondo effect
Jun Kondo
(1930-)

14. 2.1 What’s Kondo effect?
Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964))
Impurity atom with spin ½
with Ta・Ta interaction
electron T2
(classical)
metal
Log T/TK
(quantum)
T1, ..., Tn^2-1: generators of SU(n)
(n=2 for spin ½)
TK: Kondo temperature
“Kondo bound state”
impurity
spin
electron
spin

15. (particle-hole creation)
2.1 What’s Kondo effect?
impurity
fermion
Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964))
Heavy impurity 1
Fermi surface
(degenerate state) 2
Loop effect
(particle-hole creation) 3
Non-Abelian int.
(SU(n) symmetry)

16. 2.1 What’s Kondo effect?
Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964))
Scattering amplitude at tree and one-loop levels
electron l k +
k, l, i, j=↑, ↓ in SU(n) (n=2 for spin ½)
T1, ..., Tn^2-1: generators of SU(n)
impurity atom j i
(Ta)kl(Ta)ij interaction
electron
E: energy from Fermi surface l k l k j i j i
hole
Log E divergence for infrared limit (E→0) for any small coupling
→ Logarithmic divergence in resistance of electron

17. “Isospin Kondo effect” “Color (QCD) Kondo effect”
2.1 What’s Kondo effect?
Application to nuclear/quark matter
NJL-type: S.Y., K.Sudoh, Phys. Rev. C88, (2013)
QCD: K. Hattori, K. Itakura, S. Ozaki, S. Y., Phys. Rev. D92, (2015)
the ground state?
What’s
nucleon
u,d,s quark
D, B meson
c, b quark
(τa)kl(τa)ij interaction
(λa)kl(λa)ij interaction
“Isospin Kondo effect”
“Color (QCD) Kondo effect”
① nuclear matter
② nucleon-hole loop
③ isospin SU(2) symmetry
① quark matter
② quark-hole loop
③ color SU(3) symmetry
Cf. “Magnetic catalysis QCD Kondo effect”
S. Ozaki, K. Itakura, Y. Kuramoto, arXiv:1509:06966 [hep-ph]

18. the ground state? What’s
2.1 What’s Kondo effect?
Application to nuclear/quark matter
NJL-type: S.Y., K.Sudoh, Phys. Rev. C88, (2013)
QCD: K. Hattori, K. Itakura, S. Ozaki, S. Y., Phys. Rev. D92, (2015)
the ground state?
What’s
nucleon
u,d,s quark
D, B meson
c, b quark
(τa)kl(τa)ij interaction
(λa)kl(λa)ij interaction
“Isospin Kondo effect”
“Color (QCD) Kondo effect”
① nuclear matter
② nucleon-hole loop
③ isospin SU(2) symmetry
① quark matter
② quark-hole loop
③ color SU(3) symmetry
What’s about in finite size nuclei?
S. Yasui, arXiv: [hep-ph
Cf. “Magnetic catalysis QCD Kondo effect”
S. Ozaki, K. Itakura, Y. Kuramoto, arXiv:1509:06966 [hep-ph]

19. ? 2.2 Kondo effect in atomic nuclei Simple model for atomic nucleus
-shell model-like picture- ・ ? 2S 1D
isospin-exchange 1P 1S
D sector
D meson
nucleon sector
↑/↓ for proton/neutron
Schematic figure of the nucleon energy-levels
in harmonic oscillator potential/Woods-Saxon potential
Ansatz:
1. Single-particle motion of nucleon
2. Isospin-exchange in residual interaction

20. Purpose: the ground state energy?
2.2 Kondo effect in atomic nuclei
Simple model for atomic nucleus
-shell model-like picture-
k = 1 2 3 N
nucleon sector
↑/↓ for proton/neutron
D sector εk HK
cf. This method can be extended to multi-shells, à la Lipkin model.
Kinetic term
ckσ: annihilation operator for nucleon in level k and isospin σ=↑/↓
T+, T-, T3: isospin operator for D meson
Cf. π-exchange interaction: S.Y. and K.Sudoh, Phys. Rev. D80, (2009)
Kondo (isospin-exchange) interaction
D meson
Purpose: the ground state energy?

21. 2.2 Kondo effect in atomic nuclei
Exact solution
Simple case: εk=ε ε
k = 1 2 3 N
Ex. nucleon # = 1
with
singlet w.f.
linear algebraic equation
solution !! ε
ε-3Ng/2 : “Kondo bound state”
(superposed state of nucleons and D meson)
k’ = 1 2 3 N

22. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
k = 1 2 3 N
nucleon sector
↑/↓ for proton/neutron
D sector εk HK
cf. This method can be extended to multi-shells à la Lipkin model.
Kinetic term
ckσ: annihilation operator for nucleon in level k and isospin σ=↑/↓
T+, T-, T3: isospin operator for D meson
Cf. π-exchange interaction: S.Y. and K.Sudoh, Phys. Rev. D80, (2009)
Kondo (isospin-exchange) interaction

23. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Step 1. Introduce auxiliary fermion fields fσ (SU(2))
auxiliary fermion # constraint
fermion # 0, 2
fermion # 1
physical space
How does it work?
Step 2. Introduce Lagrange multiplier λ
Step 3. Apply mean-field (Δ) approx.
“gap”
isosinglet
Step 4. Variation by λ and Δ

24. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Step 1. Introduce auxiliary fermion fields fσ (SU(2))
auxiliary fermion # constraint
fermion # 0, 2
fermion # 1
physical space
Step 2. Introduce Lagrange multiplier λ
Step 3. Apply mean-field (Δ) approx.
“gap”
isosinglet
Step 4. Variation by λ and Δ

25. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Simple case: εk=ε ε
k = 1 2 3 N
Step 3
Matrix
Basis N↑ N↑ D↑ N↓ N↓ D↓
Attraction by
N-D mixing (Δ) ↓
New ground state N↑ D↑ N↓ D↓ N↑ D↑ N↓ D↓
Diagonalization
(next page)

26. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Simple case: εk=ε ε
k = 1 2 3 N
Step 3
Diagonalized matrix
lowest energy (↑)
lowest energy (↓)
New basis
Linear combination of
(coherent) nucleon and D meson

27. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Simple case: εk=ε ε
k = 1 2 3 N
Step 3
Diagonalized matrix
lowest energy (↑)
lowest energy (↓)
Step 4
Variation by
“Kondo bound state”
Binding energy (MF): Ng
different form exact solution 3Ng/2?

28. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Simple case: εk=ε ε
k = 1 2 3 N
① Mean-value of auxiliary fermion number
Impurity particle number is one in average.

29. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Simple case: εk=ε ε
k = 1 2 3 N
② Fluctuation effect (random-phase approx.: RPA)
zero-point energy in H.O. potential
Binding energy (MF+RPA): 1.378Ng
close to exact solution 3Ng/2=1.5Ng!!

30. Mean-field (+RPA) approach
2.2 Kondo effect in atomic nuclei
What’s about more general cases?
Mean-field (+RPA) approach
Simple case: εk=ε
ε+δε
③ Violation of isospin symmetry (application) ε
k = 1 2 3 N
ε↑=ε, ε↓=ε+δε Δ
Δ=0 at δε=4Ng δε
4Ng
critical
EMF-ε
EMF=ε at δε=4Ng δε
4Ng
critical
-Ng

31. Nuclear system with D meson x Isospin-dependent interaction
3. Conclusion
1. We study the ground state of charm nucleus
(D meson) with isospin Kondo effect.
Nuclear system with D meson
x Isospin-dependent interaction
= “Kondo bound state”
2. We apply the mean-field + RPA approach
to the ground state in a simple model in success.
3. This method can be applied to realistic nuclear
structure with charm/bottom hadron.
Future works:
1. Application to realistic D meson-nucleon interaction.
2. Effect by nuclear shell effects/collective modes.
3. Observables for experiments.
4. etc.

32. References HQS doublet/singlet in exotic hadrons and nuclei
S.Y., K.Sudoh, Y.Yamaguchi, S.Ohkoda, A.Hosaka, T.Hyodo, Phys. Lett. B727, 185 (2013)
Y.Yamaguchi, S.Ohkoda, T.Hyodo, A.Hosaka, S.Y., Phys. Rev. D91, (2015)
D(*)N, D(*)NN hadronic molecules
S.Y., K.Sudoh, Phys. Rev. D80, (2009)
Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D84, (2011)
Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D85, (2013)
Y.Yamaguchi, S.Y., A.Hosaka, Nucl. Phys. A927, 110 (2014)
D(*) in nuclear matter and Kondo effects
S.Y., K.Sudoh, Phys. Rev. C87, (2013)
S.Y., K.Sudoh, Phys. Rev. C88, (2013)
NLO in 1/mQ expansion for D(*) in nuclear matter
S.Y., K.Sudoh, Phys. Rev. C89, (2014)
D(*)N hadronic molecules
Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D87, (2013)