1. Recent progress in few-body physics and structure of hypernuclei
E. Hiyama (RIKEN)

2. The major goal of hypernuclear physics
1) To understand baryon-baryon interactions
Fundamental and important for the study
of nuclear physics
To understand the baryon-baryon interaction, two-body scattering experiment is most useful.
Total number of
Nucleon (N) -Nucleon (N) data: 4, 000
YN and YY potential models so far proposed
(ex. Nijmegen,
Julich, Kyoto-Niigata) have large ambiguity.
・ Total number of differential cross section
Hyperon (Y) -Nucleon (N) data: 40
・ NO YY scattering data

3. Therefore, as a substitute for the 2-body
limited YN and non-existent YY scattering data,
the systematic investigation of the
structure of light hypernuclei is essential.

4. Hypernuclear g-ray data since 1998 (figure by H.Tamura)
・Millener (p-shell model), 　・ Hiyama (few-body)

5. 4H 4He Charge symmetry breaking (2) ΛN－ΣN coupling In S= -1 sector,
what are important to study YN interaction?
Charge symmetry breaking
(2) ΛN－ΣN coupling
J-PARC : Day-1 experiment
　　　　　E13
Jlab E05-115, Mainz n n n p Λ p Λ p 4H
4He Λ Λ

6. Non-strangeness nucleiΔ
Nucleon can be converted into Δ.
However, since mass difference between
nucleon and Δ is large, then probability
of Δ in nucleus is not large. N N
On the other hand, the mass difference
between Λ and Σ is much smaller, then
Λ　can be converted into Σ particle
easily. Δ
300MeV
In non-strangeness nuclei, nucleon can be converted into Delta. However, since mass difference between nucleon and Delta is large, then, probability of Delta in nucleus is not large. On the other hand, the mass difference between Lambda and Sigma is smaller, then, there is significant probability of Sigma in Lambda hypernuclei. N Λ Σ N
80MeV Σ Λ N Λ

7. Interesting Issues for the ΛN-ΣN particle conversion
in hypernuclei
How large is the mixing probability of the Σ particle in the
hypernuclei?
(2) How important is the ΛＮーΣＮ coupling in the binding
energy of the Λ hypernuclei?
(3) How much contribution of CSB effect do we have in
light hypernuclei?

8. Exp. 4H 4He In S= -1 sector 3He+Λ 3H+Λ 0 MeV 0 MeV -1.00 -1.24 1+ 1+
-2.04
-2.39 0+
0.35 MeV 0+ n n p n Λ Λ p n Λ p 4H Λ
4He p Λ Λ

9. 4He 4H 4He 4H p n n n Λ Λ p p However, Λ particle has no charge. n p n+ + Λ Λ
So, charge symmetry breaking effect is considered to come from interaction between Sigma and nucleon.Then, in order to CSB effect, these Σ coupling effect should be taken into account. p Σ- p Σ- p n + + + + n p n n n p n n + + Σ0 n Σ0 p Σ+ n Σ+ p

10. Σ In order to explain the energy difference, 0.35 MeV, N N N N + N Λ N
・E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto,
Phys. Rev. C65, (R) (2001).
・A. Nogga, H. Kamada and W. Gloeckle,
Phys. Rev. Lett. 88, (2002)
・H. Nemura. Y. Akaishi and Y. Suzuki,
Phys. Rev. Lett.89, (2002).
Coulomb potentials between charged particles (p, Σ±) are included.

11. 4H 4He 3He+Λ 3H+Λ + 0 MeV 0 MeV -1.00 -1.24 1+ 1+ (Exp: 0.24 MeV)
(cal: MeV(NSC97e))
-2.04 0+
-2.39
(Exp: 0.35 MeV) 0+
(cal MeV(NSC97e)) n n p n Λ p Λ p
Among these calculation, Nogga and his collaborators investigated the charge symmetry breaking effect by sophisticated 4-body calculation using modern realistic YN and NN interactions. These are results using Nijmegen soft core ’97e model. The calculated energy difference in the ground state is 0.07 MeV. And this value in the excited state is MeV. Both of energy difference in the ground state and the excited state are inconsistent with the data. At the present, there exist no YN interaction to reproduce the charge symmetry breaking effect. 4H
・A. Nogga, H. Kamada and W. Gloeckle,
Phys. Rev. Lett. 88, (2002)
4He Λ Λ
・E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto,
Phys. Rev. C65, (R) (2001).
・H. Nemura. Y. Akaishi and Y. Suzuki,
Phys. Rev. Lett.89, (2002). N N N N + Σ N Λ N

12. 4H 4He 3H+Λ 3He+Λ There exist NO YN interaction to reproduce the data.
0 MeV
3H+Λ
0 MeV
3He+Λ
-1.00
-1.24 1+ 1+
(Exp: 0.24 MeV)
(cal: MeV(NSC97e))
-2.04 0+
-2.39
(Exp: 0.35 MeV) 0+
(cal MeV(NSC97e)) n n p n Λ p Λ p 4H
4He Λ Λ
There exist NO YN interaction to reproduce the data.
For the study of CSB interaction, it was highly requested to perform
the experiment of A=4 hypernuclei again.

13. Exp. 4H 4He In S= -1 sector 3He+Λ 3H+Λ 0 MeV 0 MeV -1.00 -0.98 1+ 1+
1.406±0.002±0.003
T. O. Yamamoto, et.al.,
Phys. Rev. Lett. 115,
(2015)
-2.39 0+
0.35 MeV 0+ n n p n Λ p Λ p 4H
4He Λ Λ

14. Exp. 4H 4He In S= -1 sector 3He+Λ 3H+Λ Questions to experimentalist:
The ground state of 4ΛHe　is
confirmed?
(2) The excited state of 4ΛH　is
If the answer is no,
・It is important to measure the
excited state of 4ΛH at JLab.
4He(e,e’K+) 4ΛH reaction at JLab is
very powerful way to obtain it.
ground state of 4ΛHe at J-PRAC.
Or please analyze all states of A=4
hypernuclei by emulsion data
by Prof. Nakazawa and
his collaborators.
Exp.
3He+Λ
3H+Λ
0 MeV
0 MeV
-1.00
-0.98 1+ 1+
0.24 MeV
-2.12±0.01±0.09 MeV
1.406±0.002±0.003
T. O. Yamamoto, et.al.,
Phys. Rev. Lett. 115,
(2015)
-2.39 0+
0.35 MeV 0+ n n p n Λ p Λ p 4H
4He Λ Λ

15. Exp. 4H 4He In S= -1 sector 3He+Λ 3H+Λ Open Questions
The ground state of 4ΛHe　is
not confirmed.
(2) The excited state of 4ΛH　is
In S= -1 sector
Exp.
3He+Λ
3H+Λ
0 MeV
0 MeV
-1.00
-0.98 1+ 1+
0.24 MeV
It is planned by γ-ray at J-PARC.
-2.12±0.01±0.09 MeV
1.406±0.002±0.003
Reported by H. Tamura
-2.39 0+
0.35 MeV 0+ n n p n Λ p Λ p 4H
4He Λ Λ

16. Charge symmetry breaking (2) ΛN－ΣN coupling
In S= -1 sector,
what are important to study YN interaction?
Charge symmetry breaking
(2) ΛN－ΣN coupling
GSI-HYPHI collaboration n n 　Λ

17. What is interesting to study nnΛ system?　Λ
S=0
The lightest nucleus to have a bound state is deuteron.
n+p threshold n p
J=1+ d
-2.22 MeV
Exp.
S=-1 (Λ　hypernucear sector)
n+p+Λ
Lightest hypernucleus to have a bound state n p
d+Λ
3H (hyper-triton)
0.13 MeV Λ
J=1/2+ 　Λ
Exp.

18. Observation of nnΛ system (2013) One of the lightest bound hypernuclei
nn unbound
nnΛ　breakup threshold n n ?
They did not report the
binding energy. 　Λ
scattering length:-2.68fm
Observation of nnΛ system (2013)
One of the lightest bound hypernuclei

19. Theoretical important issue: Do we have bound state for nnΛ system?
If we have a bound state for this system, how much is
binding energy?
nnΛ　breakup threshold n n ?
They did not report the
binding energy. 　Λ
NN interaction : to reproduce the observed binding energies
of 3H and 3He
NN: AV8 potential
We do not include 3-body force for nuclear sector.
How about YN interaction?

20. To take into account of Λ particle to be converted into
Σ particle, we should perform below calculation using
realistic hyperon(Y)-nucleon(N) interaction. n n n n + 　Λ Σ
YN interaction: Nijmegen soft core ‘97f potential (NSC97f)
proposed by Nijmegen group
reproduce the observed binding energies of 3H, 4H and 4He Λ Λ Λ

21. -BΛ
0 MeV
d+Λ p n 3H Λ Λ
1/2+
1/2+
-0.19 MeV
-0.13 ±0.05 MeV
Cal.
Exp.

22. What is binding energy of nnΛ?p n n
4He n Λ Λ 4H Λ
-BΛ p Λ p
4He
-BΛ Λ 4H Λ Λ
3He+Λ
0 MeV
0 MeV
3H+Λ 1+ 1+ 1+ 1+
-0.57
-0.54
-1.24
-1.00 0+ 0+ 0+
-2.39
-2.04 0+
-2.28
-2.33
Exp.
Cal.
Cal.
Exp.
What is binding energy of nnΛ?

23. H. Garcilazo and A. Valcarce, PRC89, 057001(2014).
-BΛ
1/2+
nnΛ threshold
We have no bound state in nnΛ system.
This is inconsistent with the data. n n
0 MeV 　Λ
H. Garcilazo and A. Valcarce, PRC89, (2014).
Gal and H. Garcilazo, PLB736, 93 (2014).
They also concluded to have no bound state in nnΛ system.
In this way, theoretically, it was difficult to reproduce GSI data.
It is planned to have search experiment again at GSI in (talk by Prof. Saito)
Also, we might have a possibility to have resonant state in nnΛ system.
 It is planned to perform experiment at JLab. (Talk by Prof. Tang)

24. S=-2 hypernuclei and YY interaction

25. What is the structure when one or more Λs are added to a nucleus?
So far, we have discussed about single Λ hypernuclei.
What is the structure when one or more Λs are
added to a nucleus? + + +
+ ・・・・ Λ Λ Λ Λ Λ
It is conjectured that extreme limit, which includes
many Λs in nuclear matter, is the core of a neutron star.
nucleus
In this meaning, the sector of S=-2 nuclei ,
double Λ hypernuclei and Ξ hypernuclei is
just the entrance to the multi-strangeness world.
　However, we have hardly any knowledge of the YY interaction
　because there exist no YY scattering data.
Then, in order to understand the YY interaction, it is crucial to
study the structure of double Λ hypernuclei and Ξ hypernuclei.

26. 10Be 13B Before 2000 Only three double Λ hypernuclei 11Bα
10Be
13B ΛΛ ΛΛ
Ambiguity for identifying these double Λ hypernuclei
There was NO observed double Λ hypernuclei
without ambiguity.

27. In 2001, the epoch-making data
　　has been reported by the　
　　KEK-E373 experiment.
Observation of 　6He ΛΛ
Uniquely 　identified 　without 　ambiguity
for　the first time Λ Λ
α+Λ+Λ α
６．９1±0.16 MeV 0+

28. ① ③ α ② ④ Accurate structure calculation
Strategy of how to determine YY interaction from the study of light hypernuclear structure
YY interaction
Nijmegen model D
6He
Suggest reducing the strength of
spin-independent force by half ①
use ③ ΛΛ Λ Λ
Accurate structure calculation α
compare between the theoretical result
and the experimental data of the biding
energy of 6He ②
prediction of new
double Λ hypernuclei ④ ΛΛ
Spectroscopic experiments
Emulsion experiment (KEK-E373)
by Nakazawa and his collaborators

29. the identification of the state
Approved proposal at J-PARC
・E07
“Systematic Study of double strangness systems at J-PARC”
by Nakazawa and his collaborators
Done in this July
and analysis
Just has been started.
It is difficult to determine
(1) spin-parity
(2) whether the observed state is
the ground state or an excited state
My theoretical contribution
using few-body calculation
comparison
Emulsion experiment
Theoretical calculation
input: ΛΛ interaction to reproduce
the observed binding energy of 6He ΛΛ
the identification of the state

30. 10Be 10Be Successful example to determine spin-parity of
double Λ hypernucleus --- Demachi-Yanagi event for 10Be ΛΛ
Observation of 　10Be
--- KEK-E373 experiment ΛΛ Λ Λ
8Be+Λ+Λ α α
11.90±0.13 MeV
10Be
ground state ?
excited state ? ΛΛ
10Be ΛΛ
Demachi-Yanagi event

31. Successful interpretation of spin-parity ofΛ Λ α α
E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. Yamamoto
Phys. Rev. 66 (2002) ,
11.83
11.90
α+Λ+Λ
6.91 ±0.16 MeV Λ Λ
Demachi-Yanagi
event
-14.70 α

32. Hoping to observe new　double Λ hypernuclei in near
future analysis of E07-experiment,
I predicted level structures of these　double Λ
hypernuclei
within the framework of the α+x+Λ+Λ 4-body model.
E. Hiyama, M. Kamimura, T. Motoba, T.Yamada and Y. Yamamoto
Phys. Rev. C66, (2002) Λ Λ
3He x = t n p d = = = = = α x
7He
7Li
8Li
8Li
9Be ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ

33. Spectroscopy of ΛΛ-hypernuclei
E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. Yamamoto
Phys. Rev. 66 (2002) ,
I have been looking forward to having
new data in this mass-number region.

34. Future Subjects
In S=-2 sector, what subjects should be studied?

35. 1)ΛΛ-ΞN coupling One of the major goals in hypernuclear physics :
To study the structure of multi-strangeness
systems (extreme limit : neutron star) ΔN
Multi-strangeness systems
300MeV N N N ΞN N N
25MeV N N NN ΛΛ Λ Λ Λ Λ Λ
threshold energy
difference
is very small !
ΛΛ→ΞN particle conversion is
is strong in multi-strangeness system.

36. For the study of ΞN interaction, it is important to study Ξ-
core
nucleus
For the study of ΞN interaction, it is important to study
the structure of Ξ hypernuclei.

37. Recently, we observed bound Ξ hypernucleus, for the first time
0 MeV
-1.11 ±0.25 or ± 0.25 MeV Ξ-
14N
Recently, we observed bound Ξ hypernucleus, for the first time
in the world by emulsion data.
Question: The observed event is for the ground state or any excited state?

38. T. T. Sun, E. Hiyama, H. Sagawa, H-J. Schulze, J
T.T. Sun, E. Hiyama, H. Sagawa, H-J. Schulze, J. Meng, PRC 94, (2016)
14N-Ξ-
To interpret the state, using mean filed theory,
we calculated the binding energy for 14N+Ξ hypernuclei.
we interpret that the event should be observation of
14N(ground state) +Ξ(0p) state.
However, for further analysis, we need more sophisticated
ΞN interaction.
For this purpose, we need more data for Ξ hypernuclei.
0 MeV
-1.11 ±0.25 or ± 0.25 MeV Ξ-
14N

39. t α Ξ- Ξ- Ξ- α α α α α Ξ- (9Be+Ξ-) (6He+Ξ-) p n n p n p Ξ- Ξ- (d+Ξ-)
For this purpose, recently, I studied these Ξ hypernuclei. p n n p n p α Ξ- Ξ- Ξ-
(５Li+Ξ-)
(d+Ξ-)
(t +Ξ-)- ( Ξ- t n n - Ξ- n α α α α α Ξ-
(9Be+Ξ-)
(6He+Ξ-)
(11B+Ξ-)
(ESC04)

40. α α Spectroscopy of Ξ hypernuclei at J-PARC t α α α α Ξ- Ξ- Ξ- Ξ- Ξ-
MeV
(pn +Ξ)
(pnn+Ξ)
(5He+Ξ)
(6He+Ξ)
( ９Be+Ξ)
(11B+Ξ ) -2
d+Ξ
1/2 +
αn+Ξ -5
(α+Ξ)+nn 1-
1/2+
t +Ξ
(8Be+Ξ) +n
-10 2-
11B+ Ξ 1+ 0+ 2- 1-
-20 1- 2-

41. J-PARC Concluding remark GSI JLab J-PARC Multi-strangeness system
such as Neutron star
J-PARC
GSI
JLab
J-PARC

42. Thank you!