Some Theoretical Problemsin Strangeness Nuclear Physics

S. Shinmura, Gifu University and KEK

In this talk,
1. CSB in ΛN interaction and Light Hypernuclei
2. Coherent Σ mixing in Hypernuclei
3. ΛΛ-ΞN interactions and Doubly Strange Hypernuclei

are picked up.

Shinmura Shoji1

Introduction
1952:Discovery of hypernucleus
1965,1969:International Conference
HYP-I(1982) →→→→ HYP XI(2012)

Heidelberg/Brookhaven/Padova/Simoda/..../Tokai/Barcelona

Experiments:
BNL,CERN,KEK,Jlab, etc
J-PARC an epoch-making development ofStrangeness nuclear physics
Theories:
Sophisticated calculations and applications of powerfulLife of Hypernuclei theoretical methods have been performed.
But, are theoretical achevements very clear?
Strategy of Prof. H.Bando
Production Structure Decay

In my opinion, we have a methodological problem:
How do we deduce two-body interaction from many-body systems?
In this talk, I pick up three theoretical problems as examples.
Shinmura Shoji

2

The First
CSB in ΛN interaction and Light Hypernulei
The Charge symmetry Breaking
CIB and CSB in NN interaction
CSB in ΛN interaction
CSB in s-shell hypernuclei: 4ΛHe-4ΛH
CSB in p-shell hypernuclei

Shinmura Shoji

3

The Charge Symmetry Breaking
Charge Independence(CI) and Charge Symmetry(CS)CI : Inveriance under any rotation in Isospin space
CS: Inveriance under 180°-rotation around I2 in Isospin spaceex. NN caseCI :V(pp)=V(nn)=V(np) in 1S0
CS:
V(pp)=V(nn) in 1S0
In fundamental level:
Breaking of CI and CS∆mdu=md-mu ～ 2.5MeV(PDG2014)
Electromagnetic interaction

Scale of breaking
Using Current quark masses
2∆mdu/(mu+md)=0.7 (70% !)Using Constituent quark masses
2∆mdu/(mu+md)=0.01 (1% )In hadron level :Breaking of CI and CS:
Mass splittings in Hadron Isospin-multiplets
Hadronic Strong interactions (in principle)
Electromagnetic interaction
Isospin mixings in physical states of hadrons(Λ-Σ0, π0-η-η', ρ0-ω-φ, etc)
Shinmura Shoji

4

CIB and CSB in NN interaction
CIB and CSB in 1S0 Scattering lengths and Effective ranges∆aCIB=(ann+app)/2-anp=5.7±0.3fm∆rCIB=(rnn+rpp)/2-rnp=0.05±0.08fm∆aCSB=app-ann=1.5±0.5fm∆rCSB=rpp-rnn=0.10±0.12fm
Theoretical Interpretations
Quark model∆MN, CSB ← ∆mud, (Kin, OGE, EM)
Nasu,Oka and Takeuchi, PRC68,024006(2003)

Meson-exchange model
CIB ← OPE(small π0 mass) + πγ + TPE
CSB←ρ0-ω mixing and ∆MN
Machleidt and Muther, PRC63,034005(2001)

EFT Model
CIB, CSB ← ∆MN, OPE,TPE
Friar, Kolck, et al., PRC70,044001(2004),68,024003(2003)
Epelbaum and Meissner, PRC72,044001(2005)

Shinmura Shoji

5

CSB in ΛN interaction
No direct evidence of CSB in ΛN interaction
Theoretical predictions based on meson-exchange model|Λphys> = cosθ|Λ(I=0)> + sinθ|Σ0(I=1)>|Σ0phys> = -sinθ|Λ(I=0)> + cosθ|Σ0(I=1)>g(ΛphysΛphysπ0)=(sin2θ)g(ΛΣ0π0)g(ΛphysΛphysρ0)=(sin2θ)g(ΛΣ0ρ0)

R.H.Dalitz and F. Von Hippel,
PL10,153(1964)

θ ～ -0.011±0.004(quark model)-0.013±0.0012(SU(3))π-η-η' mixing
ρ-ω-φ mixing
Σ+-Σ- mass difference ∆MΣ=8.0MeV
p-n mass difference∆MN=1.3MeV
Coulomb interaction in Σ-channel
V(Λn) is more attractive thanV(Λp) in 1S0
V(Λp) is more attractive thanV(Λn) in 3S1
Shinmura Shoji

Scattering lengths (in fm)
NSC97e NSC97f
1
S0
aΛp
-2.10
-2.51
aΛn
-2.24
-2.68
3
S1
aΛp
-1.86
-1.75
aΛn
-1.82
-1.66
Th.A. Rijken, et al.,PRC59(1998)21

CSB has strong spin-dependence
6

CSB in s-shell hypernuclei: 4ΛHe-4ΛH

3He+Λ

-1.24±0.05
1+
0+ -2.39±0.03
4

Λ

He

3H+Λ

-1.00±0.04

1+∆BΛ*=0.24±0.06-2.04±0.04
0+∆BΛ =0.35±0.07
4Λ

H

Using new value:BΛ(4ΛH)=2.10±0.02±0.09 (MAMI,2014)∆BΛ =0.29MeV, ∆BΛ*=0.18MeV

Fit by phenomenological CS+CSB ΛN interaction
VCS(r)=(VC+(σΛσΝ)Vσ+S12VT)v(r)UCSB(r)=τ3(UC+(σΛσΝ)Uσ)v(r)(S.S. PTP71(1984)546)
CS part:Vσ/Vc=-0.04 weakly spin-dependent
V(1S0)>V(3S1)
VT/Vc=-0.17 weak tensor force
CSB part:
Uc/Vc =0.018 CSB/CS=1.8%
V(Λp) more attractive than V(Λn)
Uσ/Uc=0.11 weakly spin-dependent(=0.09 Hiyama, NPA835(2010)215)

Theoretical CSB in ΛN interaction
Ccannot explain CSB in 4ΛHe-4ΛH.
“Many-body effect"

Shinmura Shoji

7

Most of theoretical YN interactions fail*Tto explain ∆BΛ =0.35MeV, ∆BΛ =0.24MeV
Jπ
0+

1+

A.Nogga, H. Kamada and W. Glockle,
PRL88(2002)172501

YN intBΛ(4ΛHe)BΛ(4ΛH)∆BΛ

NSC97e1.54/2.02

1.47/2.06

0.07/-0.04

NSC89

2.14/2.47

1.80/2.55

0.34/-0.08

Exp

2.39±0.03

2.04±0.05

0.35±0.07

NCS97e0.72/0.90

0.73/0.92-0.01/-0.02

NSC89

0.02/
unboundunbound/unbound-Exp

1.24±0.04

1.00±0.04

0.24±0.06

H. Nemura, Y. Akaishi, Y. Suzuki,
PRL89(2002)142504(Gaussian fit of YN potential),no CSB

YN potChPT

Julich04

NSC97e

NSC89

Exp

∆BΛ

0.034-0.046-0.029

0.075

0.352

0.35

pΣ

1.6-2.1%

0.9%

1.5%

4.2%

-

Σ-components
Mmay play an
Iimportant role

'We stress that the CSB is strongly related to the Σ-component
Tto properly describe CSB effects in hypernuclei. 'A. Nogga, NPA914(2013)140.

Shinmura Shoji

8

CSB in p-shell hypernuclei∆BΛCSB= BΛ(Iz=I)-BΛ(Iz=-I)∆BΛCIB= (BΛ(Iz=I)+BΛ(Iz=-I))/2-BΛ(Iz=0)A

multiplets

4

4
Λ

6

6

7

He, 4ΛH

Li, 6ΛHeΛ

Isospin ∆BΛCSB∆BΛCIB
0.35±0.07 (0+)
1/20.24±0.09 (1+)
1/20.25±0.5
1-0.57±0.26

Li

1/2

0.04±0.06

B, 9ΛLi1

0.65±0.21

B, 10ΛBe

1/2-0.22±0.25-0.61±0.20

7
Λ

Be, 7ΛLi*, 7ΛHe

8

8
Λ

9

9
Λ

10

10
Λ

12

12
Λ

C, 12ΛB

1/2

14

14
Λ

N, 14ΛC

1/2

16

16
Λ

Be,

8
Λ

0.16±0.13

New data was usedBΛ(7ΛHe)=5.68±0.03±0.25
S.N. Nakamura,
PRL110(2013)012502.

Both signs appear
This suggests
CSB in hypernuclei comesfrom many-body effects

O,16ΛN

Shinmura Shoji

9

Phenomenological CSB ΛN potentials
Ddescribing ∆BΛ in s- and p-shell hypernuclei[

τ3 (1+ Pr ) even
(1− Pr ) odd
even −β r−β r
U USB=(U c +(σ Λ σ N )U σ )e+
(U c +(σ Λ σ N )U odd
)e
σ
2
2
2
even

2

even

]

even

U c =−8.0, U σ =−0.7, βeven =1.0,
odd
odd
U c =16.0, U σ =0.7, β even=1.5
E. Hiyama et al.
PRC80(2009)054321.
NPA855(2010)215.
PTP128(2012)105.
NPA914(2013)130.
If we introduce a strong odd-state CSB
Iinteraction with opposite sign of the evenSstate CSB interaction, we could reproduce
the observed binding energies of A=7 to
10 Λ hypernuclei.
Shinmura Shoji

2

odd

Λ

N
K,κ,K*

Σ-component in
Λphys

CSB
Λ

N

Exchange-type CSB may bemade from κ,K,K*-exchange.
But maybe too small!
10

CSB in A=7-10 hypernuclei
Even-state CSB determined by A=4
BΛ, ∆BΛ

CSB

exp

No CSB+even-state
CSB+odd state
CSB

BΛ(7ΛBe)

5.16±0.08

5.21

5.44

5.27

BΛ(7ΛLi)

5.26±0.03

5.28

5.29

5.28

BΛ(7ΛHe)

5.68±0.03±0.25

5.36

5.16

5.36

∆BΛ

CSB

(7)

-0.57±0.26

-0.16

0.27

-0.09

∆BΛ

CIB

(7)

0.16±0.13

0.01

0.01

0.04

8
Λ Λ

B ( Be)6.84±0.05

6.84

6.90

6.83

BΛ(8ΛLi)

6.80±0.03

6.80

6.74

6.81

CSB

(8)

0.04±0.06

0.04

0.16

0.03

BΛ(10ΛB)

8.89±0.12

8.76

8.85

8.74

BΛ(10ΛBe)

9.11±0.22

8.94

8.83

8.96

CSB

-0.22±0.25

-0.18

0.02

-0.22

∆BΛ

∆BΛ

(10)

Shinmura Shoji

E. Hiyama et al.
PRC80(2009)054321.
NPA855(2010)215.
PTP128(2012)105.
NPA914(2013)130.

No CSB is best ?!
They introduce
Large Odd-state CSB
Tto cancel Even-state CSB

11

Summarizing the CSB problem

1. CSB in ΛN interaction
No direct evidence
CSB in theoretical ΛN interaction is small and strongly spin-dependent
2. CSB in hypernuclei
Theoretical CSB ΛN interaction cannot reproduce CSB in A=4 hypernuclei,
even if full coupled-channel four-body problems are solved.
Many-body effects beyond coupled-channel formalism
are suggested.
A=7-10 hypernuclei may be consistent with small CSB in ΛN interaction.
Many-body effects may be important.
3 At present, we have no method to deduce CSB in ΛN interaction from
CSB in hypernuclei

Shinmura Shoji

12

The Second
The Coherent Σ mixing in Hypernuclei
Coherent Λ-Σ mixing in Nuclear Matter
Coherent Λ-Σ mixing in RMF
Coherent Λ-Σ coupling in hypernuclei
Coherent Λ-Σ coupling effect in 6ΛH

Shinmura Shoji

13

Coherent Λ-Σ mixing in Nuclear Matter
Is this effect a three-body ΛNN force?

Formalism
The Bethe-Goldstone Equations
Q
Q
g
+v
g
Λ
N
Λ
N
Λ
N
Σ
N
eΛ
eΣ Σ NΛ N
Q
Q
g
= v
+v
g
+v
g
Λ NΛ NΛ NΛ NΛ NΛ N eΛ NΛ NΛ NΣ N eΣ NΛ N
Λ
Σ
Q
Q
g
= v
+v
g
+v
g
Λ NΛ NΛ NΛ NΛ NΛ N eΛ NΛ NΛ NΣ N eΣ NΛ N
Λ
Σ
Q
Q
g
= v
+v
g
+v
g
Λ NΛ NΛ NΛ NΛ NΛ N eΛ NΛ NΛ NΣ N eΣ NΛ NΛΣg= v

Λ NΛ Ngg

Λ NΛ NΛ NΣ N,g,g

Λ NΛ NΣ NΣ NΣ NΛ N+v

Λ NΛ NΛ in neutron-rich matterIn symmetric NM
Wwe have transition G-matrices
UΛΣ=UΣΛ=0G
gΛN-ΣN and gΣN-ΛN
which give transition single-particle potentials
UΛΣ and UΣΛΛ‐Nuclear Matter Interaction(lowest order)U Λ Λ = NM ∑ g Λ Ν Λ Ν NM = ∑ii

All N are contribute
Coherently
independently
Bboth in UΛΣ and UΣΛ,

Coherent Λ-Σ couplingU Σ Λ = NM ∑ g Σ Ν Λ Ν NM = ∑: Diagonal part of the G - matrixii

U Λ Σ = NM ∑ g Λ Ν Σ Ν NM = ∑: Nondiagonal part of the G - matrixiiOff-shell ∑‐Nuclear Matter InteractionQ=∑U Σ Σ = NM ∑ g Σ Ν Σ Ν NM = ∑
i

i

1 p1h

Nuclear Part is excited
to 1p1h states

∆U ≈

+

+

+

Diagrammatically, this corresponds to three-body force, but physicalessence is existence of "transition mean field" in Neutron-rich matter.

Shinmura Shoji

14

Coherent Λ-Σ mixing in RMF theory
We find a similar effect in RMF theory
Isovector mesons make 'transition mean fields' in neutron-rich nuclear matterand coupled-channel Dirac equation should be solved:/ Λ−γ 0 g Λ Λ ω ω+g Λ Λ σ σ)ψΛ +(−γ 0 g Λ Σρ ρ0+g Λ Σ a a 0 )ψΣ=0( p−m/ Σ−γ0 g Σ Σω ω+ g Σ Σ σ σ)ψ Σ+(−γ 0 g Σ Λ ρ ρ0+g Σ Λ a a 0 )ψΛ =0( p−m
m2M ϕM =∑ 〈 ̄B Γ B 〉+ g Λ Σ M (〈 Λ̄ Γ Σ〉+〈 ̄Σ Γ Λ〉) (Γ=1, γ0 )BThen we obtain a Λ-Σ mixed state:|'Λ'(p)> = ψΛ|Λ> + ψΣ|Σ>Coherent Λ-Σ mixing in neutron matter (at ρn=0.40 1/fm3)
OBEP
G-matrix
RMF
NSC89
8.0%
0.99%
NCS97e2.0%
0.26%
S.Shinmura. Y. Akaishi, K.S. Myint, T. Hadara, MPLA18(2003)128

Shinmura Shoji

15

Coherent Λ-Σ coupling in hypernuclei
Full coupled-channel
Calculation including
S-channel explicitely

Calculation including
coherent Σ-mixing

Σ-component probability
potential
Nnsc97eNnsc97f
Nnsc97f
Nnsc97e4ΛH 4ΛHeCoh. 0.7%
Coh. 0.9%(Incoh. 1%)
2.02 2.08
1.49 1.45

4
Λ

H* 4ΛHe*
Coh. 0.0% Akaishi et al., PRL84(2000)3539.
Coh. 0.0%(Incoh. 1%)
1.12 1.03 Hiyama et al., PRC65(2001)011301(R).
0.98 0.96 Nemura et al., PRL89(2002)142504.

For Few-body systems, coherent Σ-mixing is strongly state-dependent
Full coupled-channel calculations with Σ-channel reproduce the effect of coherent Σ-mixing.
Shinmura Shoji

16

Coherent Λ-Σ coupling effect in 6ΛH
Large or Small?
M. Agnello et al. PRL108(2012)042501.(FINUDA experiment)
M. Agnello et al.,NPA881(2012)269.(FINUDA experiment)
R.H. Dalitz and R. Levi Setti, Nuovo Cimento 30(1963)489.
Y. Akaishi and T. Yamazaki, Frascati Phys. Series 16(1999)59
K.S. Myint and Y. Akaishi PTP Suppl.146(2002)599.

5805.443

H+n+n+Λ

5803.74

Three candidates
Production Decay(1)5802.33
5801.41(2)5803.455802.73(3)5799.975798.66

5

H+Λ

Averaged Value:5801.43±1.1

(2)
(2)

4

Λ

H+n+n

Dalitz and Levi-Setti

5801.70(1)(1)

5801.245801.435801.04
1.4 MeV:Effect of Coherent Λ-Σ Coupling(3)5799.64(in MeV)(3)6ΛShinmura Shoji

Akaishi and Myint

H

17

Criticism to coherent Λ-Σ coupling effect in 6ΛH
A. Gal and D.J. Millener, arXiv:1305.6716v3 [nucl-th] (2013)
Shell model calculation with Σ components
5805.44 5H+Λ3

4

H+n+n+ΛΛ

H+n+n5803.744.1

5801.705801.435801.04

5801.24
Dalitz and Levi-Setti
6
Λ

H

5.8

3.8
5801.64

J-PARC E10 experiment
to search 6ΛH is decisive!

H. Sugimura (J-PARC E10 collaboration),
HAW2014, EL105802.97(3.24 with
V3b=-65MeV)

Hiyama et al. NPA914(2013)130

Gal and Millener

1.4MeV
5799.64

2.47

Akaishi and Myint

Effect of Σ component
Iis only 0.1MeV larger
Tthan in 4ΛH

None of the large effects conjectured by some authors to arise fromΛΣ coupling is borne out, neither by these realistic p-shell calculations
nor by quantitative estimates outlined for heavier hypernuclei with
substantial neutron excess.
A. Gal and D.J. Millener, arXiv:1305.6716v3(2013)

The Λ-Σ coupling effect was found to be 1.4MeV with 1.6% of coherent Σ component.
The coherent Λ-Σ coupling contribution from two-p-shell neutron in 6ΛH is not so large
due to dilute distribution of two neutrons.
Theingi, K.S. Myint and Y. Akaishi, Genshikaku Kenkyu57(2013)70

Shinmura Shoji18Summerizing Λ-Σ mixing problem

Theoretical coupled-channel YN interaction
Full coupled-channel
problem

Trancated problem(only Λ-channel)
Incoherent Σ-mixing
effective ΛN interaction
Coherent Σ-mixing(included in Three body force)Three-body force

Effective three-body force

Unique method to deduce coherent Σ-mixing from three-body force is
To solve full coupled channel many-body problems

Shinmura Shoji

19

The ThirdΛΛ-ΞN interactions and Doubly Strange Hypernculei
Theoretical ΛΛ and ΞN interactions
Ξ components in ΛΛ hypernuclei

Scatering length aΛΛ(1S0) and ∆BΛΛ(6ΛΛHe)Is ΞN interaction attractive or repulsive?

Shinmura Shoji

20

Theoretical ΛΛ and ΞN interactionsΛΛ

Meson-exchange potential

Sf0,σ,η,η'Short-range(No OPEP)
ω,φWeakly attractive
Λ

Λ

Ξ

Ν
Sκ,Κ,Κ∗ΛΞΛΝ

SSσ,f0,aPπ,η,η'Rρ,ω,φΞ

Coupling potential
Small ∆m=23.06,28.91MeV(Almost degenerate!)

No Exchange force
OPEPΝ

Shinmura Shoji

SU (3)components
NN −NN (1S0) {27}
NN −NN (3S1) {10 ¿ }1127Λ Λ−Λ Λ( I =0){1}+ {8s}+ {27}
8
5
40
1
1
9
Λ Λ−Ξ N (I =0){1}+ {8s}− {27}
4
5
20
1
1
3
Ξ N −Ξ N ( I =0){1}+ {8s}+ {27}
2
5
10
3
2
Ξ N −Ξ N ( I =1){8s }+ {27}55Relative Core Heightsfrom LQCD (in even state)
NN-NN(1S0)
NN-NN(3S1)
ΛΛ-ΛΛ
ΛΛ-ΞN
ΞN-ΞN(I=0)
ΞN-ΞN(I=1)

1
0.8
0.64
-0.44
0.04
0.52
21

Ξ components in ΛΛ hypernuclei

ΛΛ

4

H

BΛΛ=0.06

ΛΛ

5

H

ΛΛ

K.S. Myint, S.S.,Y. Akaishi, Eur. Phys. J. A16(2003)16
H.Nemura, S. S.,Y. Akaishi, K.S. Myint, PRL94(2005)
202502.

6

He

Very weakly boundPΝΞ=0.06%
BΛΛ=3.74PΛΣ=0.25%PΣΣ=0.00% PΝΞ=4.55%
PΛΣ=2.49%PΣΣ=0.06%

α+Λ+Λ and α+Ν +ΞBΛΛ=7.53PΝΞ=0.27%
PΛΣ=1.17%PΣΣ=0.05%

Threshold difference between
t+Λ+Λ and α+Ξ0 is only 3.2MeV

Pauli-suppressed

Many-body effects are important
This is similar to Σ in Λ-hypernuclei

Ξ components depend on ΛΛ hypernuclei
Shinmura Shoji

22

Scatering length aΛΛ(1S0) and ∆BΛΛ(6ΛΛHe)with theoretical ΛΛ potentials
All models predict attractive ΛΛ potential in 1S0 state∆BΛΛ(6ΛΛHe)

PotentialaΛΛ (1S0)

NSC97a-0.33(-0.11)

NSC97e-0.50(-0.25)

ESC04a

-1.15

1.36

ESC04d

-1.32

0.98

ESC08a-0.88():
No ΞN channel

FSS

3.66

fss2

1.41

Ch-EFT

-1.52

fg2014z-0.59

fg2014w-0.65

Nagara and Mikage Events(KEK E373)

NSC97,ESC-models:Th.A. Rijken,V.G.J. Stoks, Y.Yamamoto, PRC59(1999)21.
Th.A. Rijken,Y. Yamamoto, PRC73(2006)044008.
Th.A. Rijken, M.M. Nagels, Y.Yamamoto, PTP suppl.185(2010)14.
Ch-EFT:H.Polinder, J.Haidenbauer, U.-G.Meissner, PLB653(2007)29
FSS,fss2(quark model): Y. Fujiwara, M. Kohno, Y. Suzuki, NPA784(2007)161.
Fg2014z,w :S.Shinmura, Ngo Thi Hong Xiem,(2014)

Shinmura Shoji∆BΛΛ(6ΛΛHe)=0.70±0.17MeV
H. Takahashi, PRL87(2001)212502
K. Nakazawa, NPA835(2010)207aΛΛ(1S0) ～-0.8 fmaΛΛ(1S0) = -1.2±0.6fm

C.J. Yoon,et al. PRC75(2007)044008.

J-PARC E07 experiments23Is ΞN interaction attractive or repulsive?
Ξ in symmetric nuclear matter
potentals

UΞ

UΞ(n)

UΞ(p)

NSC97e44.7(35.8)

9.69

34.98

ESC04a15.1

ESC04b36.3

ESC04c-5.5

ESC04d-18.7

ESC08a-20.2

ESC08b

-32.4

FSS

-14.9

fss2

-5.3

FG-A

-6.65(-5.34)

-0.17

-6.48

FG-B

43.6(34.9)

21.8

21.8

GSOBEP

28.1(22.5)

17.6

10.5

fg2014z22.1(17.7)

16.4

5.7

fg2014w

15.6(12.5)

11.9

3.7

(

Isospin dependence:strongly model-dependent
Recent observation(Kiso event)BΞ(15ΞC)=4.38±0.25MeV

K. Nakazawa, JPS-meeting,HAW2014,
2WF7(2014)):rearrangement effectShinmura Shoji

Theoretical ΞN Interactions give
Vvery scattered results.

Several models are exlcluded!
Calculations(Shell model)BΞ(12ΞBe)=4.38MeV(ESC04d)

T. Motoba, S. Sugimoto NPA(2010)223

J-PARC E05 (K-,K+), E07
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Summary
1. The CSB in ΛN Interaction and Light Hypernuclei
CSB in ΛN interaction : No direct evidence
Theoretical CSB in ΛN interaction cannot explain CSB in hypernculei.
Many-body effects beyond coupled-channel calculations should be considered
Jlab E05-115, Mainz
2. The Coherent Λ-Σ Mixing in Hypernuclei
Existence of Λ-Σ transition mean field in neutron-rich matter is predicted
Its effect in neutron-rich hypernuclei (ex. 6ΛH) should be checked.
J-PARC E10
3. ΛΛ-ΞN Interactions and Doubly Strange Hypernuclei
Most of theoretical ΛΛ interactions are qualitatively consistent with 6ΛΛHe
Theoretical ΞN interactions should be checked by measurements ofΞ-hypernuclei.
J-PARC E05, E07
Shinmura Shoji

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