Toru Harada /KEK - - PowerPoint PPT Presentation

SLIDE 1

1 KEK理論センター研究会「ハドロン・原子核の最前線2017」 2017年11月20-22日，ＫＥＫ, つくば市

原田 融

Toru Harada

大阪電気通信大学/KEK理論センターJ-PARC分室

Osaka E.-C. Univ./KEK Theory Center, J-PARC Branch

ハイパー核の物理

SLIDE 2

2

Contents

1. Introduction 2. NN,YN,YY Interaction 3. S= -1 Hypernuclei

• L hypernuclei
• ( S hypernuclei )

4. S= -2 Hypernuclei

• X hypernuclei
• LL hypernuclei

5. Summary

Keywords Hyperon mixing + Coupled-channels

SLIDE 3

• 原子核深部を探る

–ハイペロンはパウリ排他律を受けないためプローブ（探針）となる

• Impurity Physics （不純物物理）

– “糊”としての役割 – 原子核構造（１粒子運動、殻構造、クラスター構造、集団運動）の変化

• Baryon-Baryon Interaction

– YN, YY Interaction based on SUf (3) – 核力の統一的理解・斥力芯の起源

• “Exotic” Nuclear Physics

– ストレンジネスが拓く新しい原子核の面白さ

• Neutron Starの構造と進化

– 高密度核物質への戸口, EOS, 最大質量, 冷却, … ハイパー核物理の課題

3

SLIDE 4

4

3-Dimensional Nuclear Chart with Strangeness

SLIDE 5

5

N L S X

Our understanding of hyperon s.p. potentials

+30MeV

0(N)

U

0( )

U L

0( )

U S

0( )

U X

• 51MeV
• 30MeV
• 14MeV
• 30MeV
• 3MeV

Re. Re. Im. Im. Re. Re.

𝑽𝟏~−30 MeV 𝑽𝑴𝑻~ 2 MeV LLN 3BF ? S mixing Prob.? Strong repulsive, Spin-isospin dep. 𝑽𝟏~+30 MeV 𝑽𝑴𝑻 ?, S width ? 𝑽𝟏~ (−14)฀(0)MeV ? X width ? LL-XN mixing ? H-particle ? 𝑽𝟏~−51 MeV 𝑽𝑴𝑻~ 22 MeV

? ?

SLIDE 6

6

Neutron star core

[F. Weber, PPNP 54(2005)193]

Cassiopeia A nebula NASA/CXC/SAO.

= “An interesting neutron-rich hypernuclear system”

Hyperon-mixing

[R. Knorren, M. Prakash, P.J.Ellis, PRC52(1995)3470]

( , , )

iY iY iN

x g g i      Coupling constant ratio;

U U

S X

 

U U

S X

 

U U

S X

  L,S,X,.. K-, ..

SLIDE 7

 P. B. Demorest et al., Nature, 467 (2010) 1081.  J.Antoniadis et al., Science 340(2013) 6131. PSR J0348-0432 M=(2.01 ± 0.04)Msun PSR J1614-2230 M=(1.97 ± 0.04)Msun

(NS:2.01M☉+WD: 0.172M☉) (NS:1.97M☉+WD: 0.50M☉)

シャピロ遅延 (Shapiro delay）

“Hyperon Puzzle’’ in Massive Neutron Stars

→ Collapse of massive NS !?

With hyperons

SLIDE 8

8

Repulsive MBF in “Hyperon Puzzle’’

3B/4B repulsion NNN+YNN 3B/4B repulsion NNN only

ESC MPa w/o hyp

• Y. Yamamoto, et al.,PRC90(2014)045805

Haidenbauer, et al.

• Eur. Phys. J.

A53(2017) 121. RMF w/multibody coupling Ohnishi, et al., SCHDM2017

NSC97f Julich04 NLO NLO+3BF

SLIDE 9

J-PAR ARC (Japan Proton Accelerator Research Complex)

9

SLIDE 10

NN, YN, YY 相互作用

SLIDE 11

11

One-Boson-Exchange model

• Nijmegen potential

NHC-D/FNSC89NSC97e,fESC04a-d ESC06ESC08a-c [Th.A. Rijken, M. M. Nagels,Y. Yamamoto, PTPS185(2010)14

• Funabashi-Gifu potential

[I. Arisaka et al., PTP104(2000)995]

Quark Cluster model

• Kyoto-Niigata potential

RGM-FFSSfss2 [Y. Fujiwara et al, PRC54(1996) 2180; PPNP58 (2007)439]

Chiral LO, NLO Effective Field Theory

• Julich potential

[H.Polinder, et al., NPA779 (2006) 244;PLB653 (2007) 29] [J.Haidenbauer, et.al., NPA 915(2013)24]

Latice QCD

• HAL QCD Collaboration

[H. Nemura, et al., PLB 673 (2009) 136; T. Inoue, et al., PTP124 (2010) 591; PRL106 (2011) 162002]

Hyperon-nucleon (YN) Interaction

SLIDE 12

C.B. Dover and H. Feshbach, Ann. Phys. 198(1990)321 NN: 4233 data ( 0<Tlab<350 MeV)

s a

[10*] [10 [8] [8] [27] [8 ] [1 ] 8 ] ] [       

NN NN SN,SN-LN,LN 35 data SS,XN-SL-SS,XN-SS-LL XS,XS-XL XX XX

S= 0 S= -1 S= -2 S= -3 S= -4

1S0 3S1

LL

NN, , YN YN, , YY YY In Inter teracti actions

• ns

Flavor SU(3)f symmetry symmetric antisymmetric

SLIDE 13

13

Short-range repulsive core in baryon-baryon interaction

Spin-flavor SU(6) symmetry

[3] [3] [6] [4 [51] 2] [33]     

symmetric antisymmetric L=0 Pauli forbidden state

S = 0 state

[51] [33]

1 LL-XN-SS(I0), H-dibaryon 8S 1 SN(I=1/2,1S0) Pauli forbidden 27 4/9 5/9 NN(1S0) S = 1 state

[51] [33]

8A 5/9 4/9 10 8/9 1/9 SN(I=3/2,3S1) almost Pauli forbidden 10* 4/9 5/9 NN(3S1), LN-SN(I=1/2, 3S1)

Quark Cluster Model

Quark-exchange

(anti-symmetrized)

M.Oka,K.Shimizu,K.Yazaki, PLB130(1983)365; NPA464(1987)700

• SU(6)sp symm.  Strongly spin-isospin dependence
• rbital x flavor-spin x color singlet

SLIDE 14

14

SN threshold cusp state or bound state

(I =1/2, 3S1)

Bound state Cusp state ND NF

NSC97f NSC89

SLIDE 15

K-d→p-Lp

S+n S(1385)

SN threshold cusp (I =1/2, 3S1)

R.H.Dalitz, Deloff, Czech.J.Phys.B32(1982)1021 T.H.Tan, PRL23(1969)395. O.Braun et al., NPB124(1977)45. D.Eastwood et al.,PRD3(1971)2603.

• H. Machneret al., NPA 901, 65 (2013).

d(p＋, K+)

• Y. Ichikawa et al., PTEP2014, 101D03
• S=‐1 dibaryon search
• YN interaction study
• (K-,p) reaction study

SLIDE 16

16

Baryon-Baryon force in SU(3) basis from lattice QCD

[27] [8s] [1] [10*] [10] [8a]

1S0 3S1-3D1

a s

[8] [8] [27] [8 ] [ [10*] [10 1 ] [ ] ] 8       

• T. Inoue et al., HAL QCD Collaboration, NPA881 (2012) 28.
• at the SU(3)F limit corresponding to Mπ = MK = 837 MeV.
• possibility of a bound H-dibaryon in the limit.

SLIDE 17

17

• T. Inoue, et al., (HAL QCD Collaboration), PoS INPC2016, 277 (2016).

Hyperon single-particle potentials from QCD on lattice

SLIDE 18

S = -1 Hypernuclei (1)

SLIDE 19

Lハイパー核

L粒子の１粒子ポテンシャルとスピン軌道力 Gamma-ray spectroscopy of light hypernuclei (p+,K+)反応によるハイパー核の生成 Overbinding Problem on s-Shell Hypernuclei (e,e’K+)反応によるハイパー核の生成 Recent topics 中性子過剰ハイパー核 CSB(Charge Symmetry Breaking) Lハイパー核の弱崩壊

19

SLIDE 20

20

30.05 MeV UL 

0.6 fm a  1.165fm r 

2 4 6 8 10 –30 –20 –10

Pb

Λ

208

POTENTIAL （MeV) r (fm)

Woods-Saxon form

0 /(1 exp[(

)/ ]) U U r R a

L L

 - +

• 1/3

0(

1) fm R r A 

• A.Gal, E.V. Hungerford, D.J. Millener,

Rev.Mod.Phys. 88 (2016) 035004.

Binding energies of L single-particle states

30 MeV

2 3

N

U 

SLIDE 21

G-matrix calculation in symmetric nuclear matter

( , ) , | ( ) | ,

N

F N N N N

U k g    

L L L L L L

  +



k

k k k k

L single-particle potential depth ( ) ( )

N YN YN YN YN

Q g v v g QTQ     +

• G-matrix

Pauli-operator

Effects of the LN-SN coupling in nuclear matter

Y.Nogami, E.Satoh, NPB19(1970)93

as= -1.8fm, at= -1.6fm

• 50
• 40
• 30
• 20
• 10

(unit in MeV)

Exp. ～-28

LNN NN three-bod body force

• 50.6
• 52.9
• 34.2

, , N N N N N N

Q v v e

L S L S S

LN single channel LN-SN coupled channel

repulsive suppressed

L

N

+

L N N L N

=

Spin-isospin saturated

Overbinding!

L N

L N

+ +

L N S N

L N S

=

Spin-isospin saturated

N‘

1

1.35fm

F

k

• 

kF N N’

21

SLIDE 22

L single-particle energies in symmetric nuclear matter

1

1.35fm

F

k

• 
• Y. Yamamoto, H. Bando, PTP.Suppl.81(1985)9; Y. Yamamoto, et al.,PTP.Suppl.117(1994)361;

Th.A.Rijken, V.G.J.Stoks, Y.Yamamoto, PRC59(1999)21; Th.A.Rijken, Y.Yamamoto, PRC73(2006) 044008; Y.Yamamoto, T.Motoba, T.A.Rijken, PTP.Suppl.185(2010)72.

( , )

F

U k 

L L

OBEP: Nijmegen YN potential Models

G-matrix calc.

22

• 1.90fm
• 1.96fm
• 2.29fm
• 1.88fm
• 2.78fm
• 1.41fm
• 2.51fm
• 1.75fm
• 2.10fm
• 1.86fm

Scattering length

as at

Bando- Yamamoto 1985

(unit in MeV)

• 40
• 30
• 20
• 10

Exp.

• 28
• 40.5

NHC-D

• 31.6

NHC-F

• 30.8

NSC89

• 23.3

１S0 3S1- 3D1

• dd
• 8.0
• 7.4
• 25.1

+0.4

• 9.2
• 14.6
• 0.9
• 10.0
• 20.7

Yamamoto et al. 1999 NSC97e

• 34.3

NSC97f

• 31.1

+4.5

• 12.8
• 26.0

+6.9

• 14.4
• 22.9

Rijken- Yamamoto 2009 NSC04a

• 38.5
• 3.2
• 13.7
• 21.5

NSC08a NSC08b

• 34.0

Rijken- Yamamoto 2006

• 35.6

+0.9

• 12.7
• 23.8
• 0.2
• 12.3
• 21.4
• 2.70fm
• 1.65fm

NSC08c

• 40.8
• 2.1
• 13.1
• 28.1

Nagels- Rijken- Yamamoto 2016

• 2.54fm
• 1.73fm

SLIDE 23

L s.p. potential and L spin-orbit splitting in 89

LY

23

• H. Hotchi et al.,

PRC64(2001)044302

G-matrix folding model

• Y. Yamamoto et al.,

PTPS185(2010)72

• T. Motoba et al.,

PTPS185(2010)197

[O. Hashimoto, T. Tamura, PPNP57(2006)564]

SM analysis

• LN-1 particle-hole ex.
• inter-shell coupling

30 MeV V L

• (

) A 

WS analysis

0.6 fm a 

(Exp.) 1.7 MeV 2 MeV

LS

V L

0.2 MeV

LS

V L

( ) A  

37.2 MeV V L

• VL ?

SLIDE 24

24

Microscopic Shell-Model including LN-SN coupling effects

• H. Tamura et al.,

NPA853(2010)3

693 (72) 494 (74) 44 (-8) 267 (56) 504 (61) 153 (61) 92 (42) 507 (65) 23 (-33) 248 (92) xxx (xx)

E(calc) keV E(LS) keV (Millener)

Spin-dependence of the effective LN interaction

[R.H.Dalitz, A.Gal, AnnPhys.116(1978)167]

A = 7,9 A > 9 [D.J.Millener,NPA835(2010)11]

• LN spin-dependent force/LN-SN coupling force/Charge symmetry breaking (Lp≠Ln)
• Magnetic moments mL in a nucleus from B(M1)

4 LHe, 10 LB, 11 LB, 19 LF

E13@J-PARC

Gamma-ray spectroscopy of light hypernuclei

SLIDE 25

25

• T. Motoba, et al.,PTP70(1983)189
• E. Hiyama, et al.,PRC59(1999)2351
• Shrinkage effects (19% for the 6Li core)
• neutron-skin or neutron halo
• E. Hiyama, et al.,PRC59(1999)2351

Tretyakova, Lanskoy, EPJ.A5(1999) 391.

Role of the L-hyperon in nuclei

“gule” “Stabilizing”+“Deformation”

M.T. Win, K.Hagino et al, PRC83 (2011) 014301 19 L C, 29 L Si, 25 L Mg, (CSHF+BCS) unbound

n

L

n

L

6 L He

(a+N+L calc)

• M. Isaka et al, PRC83(2011)054304

21 LNe, 25 L Mg (AMD)

g.s.

SLIDE 26

26

Deformation of L hypernuclei

145-155 L Sm [MR-CDFT+RMF+BCS]

• M. Isaka, et al., PRC89(2014)024310

46 LSc, 48 L Sc [AMD+GCM]

• H. Mei, K.Hagino et al,PRC96(2017)014308

Transition from vibrational to rotational character Superdeformed hypernuclei

SLIDE 27

27

Effects of a hyperonic many-body force on L binding energies

MPP = multi-Pomeron exchange potential (repulsive) TBA = phenomenological three-body attraction

• M. Isaka, et al., PRC 95(2017)044308

Hyper-AMD+GCM

Full GCM Spherical GCM

Esc08c+MPP+TBA

SLIDE 28

p+ K+ p+

K+ L

n

Y

p

K

p

pp

Incident particle Target Nucleon

（p＋, K＋)

Emitting particle

28

Distorted-wave Impulse Approximation (DWIA)

• J. Hufner et al, NPA234 (1974) 429;

E.H. Auerbach et al., Ann. Phys. (N.Y.) 148 (1983) 381; C.B. Dover et al.,PRC22 (1980) 2073.

SLIDE 29

29

Hypernuclear Production Reactions

(K-,p-)

720 MeV/c

(p+,K+)

1040 MeV/c

qL～280MeV/c qL～400MeV/c qL ～60-100MeV/c

1 max

[ ]

N J J

j j

• 

L  1

[( ) ( ) ]

N J

n j n j

• L



“Spin-Stretched’’ “Substitutional”

H.Bando, T.Motoba, J.Zofka, Int.J.Mod.Phys. A5(1990)4021

(K-,p-)

Stooped K-

p+ K+

neutron Lambda

1s 1p 1d 2s 1f d f7/2

3/2 n

L

by R.Hausmann and W.Weise

(p+,K+) reaction

Theoretical calculations

56Fe target

Momentum transfer

SLIDE 30

30

Morimatsu, Yazaki, NPA483 (1988) 493.

Completeness relation

bound states, quasibound states Continuum states, resonance states

Double-differential Lab Cross Sections Strength functions

Green’s function method

Production cross sections in A(a,b)YB reacrions

Green’s function

SLIDE 31

31

ImE ReE

Sheet I Sheet II Bound state Anti-bound state Decay resonance Capture resonance

Poles positions of S-matrix ( )

2 2 2

1 2 2

R I R I

k k ik k m 

• +

𝑙(𝑞𝑝𝑚𝑓) = 𝑙𝑆 + 𝑗𝑙𝐽

(pole) 2

( ) 2 2 k E B i m    -

• Imk

Rek

Bound state Anti-bound ( virtual state) Decay resonance Capture resonance state

complex k

[+] top (Im k >0) [-] bottom (Im k < 0) Complex momentum Complex energy

SLIDE 32

32

L spectrum by (p+,K+) reaction at 1.2 GeV/c (6◦)

12C

Harada, Hirabayashi, NPA744 (2004) 323.

Sensitivity of the spectrum to the L–nucleus potential parameters

−40 MeV r0 =1.155 fm

r0 = 1.155 fm U0=−29.39 MeV

−20 MeV U0=−29.39 MeV 1.10 fm 1.27 fm

SLIDE 33

33

s-Shell L Hypernuclei

核内Σ粒子の 役割

SLIDE 34

The Underbinding Problem

3H L 4He L 5He L

• 0.31 MeV

[Exp.]

• 3.12 MeV

1+ -1.24 MeV 0+ -2.39 MeV 0.0 0+ 1+

Akaishi et al., PRL 84 (2000) 3539. g-matrix calc. with LN-SN(D2)

Underbound

The Overbinding Problem

Dalitz et al., NP B47 (1972) 109.

Overbinding Problem on s-Shell Hypernuclei

3H L 4He L 5He L

• 0.31 MeV

[Exp.]

• 3.12 MeV

1+ -1.24 MeV 0+ -2.39 MeV 0.0 Overbound spin-spin

N

( )  L 

LN single-channel calc.

suppressed

ΛN,ΣN ΣN,ΛN

Q V V e

SLIDE 35

by Y. Akaishi

Coherent LS coupling

SLIDE 36

“The 0+-1+ difference is not a measure of LN spin-spin interaction.” by B.F. Gibson



L p p n



S



L p p n



S



L p p n



S

+ +

LNN three-body force

4He L

• Y. Akaishi, T.Harada, S.Shinmura, Khun Swe Myint,

PRL84(2000)3539

Coherent coupling

1+

• 1.03

1+

• 1.04
• 1.04

0+

• 2.27

0+

D2

coh.Σ

9% 1. P 

1+

• 1.20

1+

• 1.21
• 1.52

0+

• 2.10

0+

SC97e(S)

coh.Σ

7% 0. P  1+

• 0.68

1+

• 0.70
• 1.43

0+

• 2.18

0+

SC97f(S)

coh.Σ

9% 0. P 

• 0.68

1+

• 0.70

1+

• 0.97

0+

• 2.51

0+

SC89(S)

coh.Σ

0% 2. P 

Coherent coupling Coherent coupling Coherent coupling

Breuckner-Hartree-Fock

• R. Sinha, Q.N.Usmani,

NPA684(2001)586c

(unit in MeV)

0.0

1+

• 1.24
• 2.39

0+

Exp.

1+

• 1.08
• 2.28

0+

VMC

4

( H)

L

6.20 V  0.38 0.86 spin-spin

LNN force

ΛN ΛNN

V +V phenomenological

SLIDE 37

37

• E. Hiyama et al., PTP. Suppl. 185 (2010) 106

Effects of the LS coupling (1) : S channel components

YN: NSC97e-f(e) 𝑄

𝛵 0+ ≅ 2 %

𝑄

𝛵 1+ ≅ 1 %

S mixing prob.

SLIDE 38

38

Effects of the LS coupling (2): LNN Three Body Force

• E. Hiyama et al., PTP. Suppl. 185 (2010) 106

YN: NSC97e-f(e) LNN TBF

SLIDE 39

39

Nogga, Kamada, Glockle, PRL88(2002)172501

Faddeev-Yakubovsky calculations

L separation energies for 3

LH, 4 LH(0+), 4 LH(1+) hypernuclei 3 LH 4 LH

SLIDE 40

40

Ab initio calculation of L

5He with full realistic interactions

H.Nemura et al., PRL89(2002)142504

Better understanding of the L-S coupling and Tensor force

C

T  L 1

C

T  S

a

*

a

~ 1.5 % admixture

“Incoherent L-S coupling”

• The S admixture of

~1.5 % appears in 5

LHe.

• The a-particle is not

a rigid core. The incoherent S admixture is also important.

Hyperon-mixing

SLIDE 41

～72 MeV

NS NL

～28 MeV

LS LL SS NX

～300 MeV

N NN

41

• Various effects on the hyperon mixing
• Related to the 3BF in nuclei

Dynamics in Strangeness Nuclear Systems

S = 0 S = -1 S = -2

N N N  N L N S L L N X Nuclei

Fujita-Miyazawa 3BF

Hypernuclei

Strong LNN 3BF ?

XN-LL coupling LN-SN coupling

～1-2 % very large ?

SLIDE 42

KEK-PS-E521

• P. K. Saha, et al., PRL94(2005)052502

9Li+L 9Li+L

2.5 MeV FWHM

g.s. g.s.

Cross sections

L

d d   

11.3±1.9 nb/sr

• pp=1.20 GeV/c

～1/1000 17.5±0.6 mb/sr

(1.2 GeV/c)

12 12

C( , ) C K p

+ + L

• pp=1.05 GeV/c

L

d d   

5.8±2.2 nb/sr

L spectrum by DCX (p-,K+) reaction at 1.2GeV/c

10 10

B( , ) Li K p -

+ L

First production of neutron-rich L hypernuclei

42

11.3±1.9 nb/sr

SLIDE 43

Two-step process:

p K p -  L

0 p

K p

+

 L p n p p

• 

K p K n

+

 p K p -

+

• 

S p n

• S

 L

K+

p p p L n

p-

p n L

K0

K p K n

+



p K p

• 

L K+

p p p p S- L n

p-

n L

Doorway

p K p

• +
• 

S

(p－, K+) －Double Charge Exchange (DCX) Reaction

One-step process:

43

via S- doorways caused by LN-SN coupling Hyperon-mixing

SLIDE 44

L spectrum by DCX (p-,K+) reactions at 1.2GeV/c

11 MeV

X

U 

is fixed. PS-=0.57%

Spreading potential dep.

• WS =

(pL) (sL)

9Li+L

3+ 2-

WS

44

Two-step mechanism Harada, Umeya,Hirabayashi, PRC79(2009)014603

10B

UX =

SLIDE 45

45

Production of neutron-rich 6

ΛH hypernucleus

0+ 0+ 0+

5802.87 MeV

Gal, Millener, PLB725(2013)445

• E. Hiyama et al., NPA908(2013)29

Dalitz, Levi Setti, Nuovo Cimento 30(1963)498 Khin Swe Myint, Akaishi, PTP Suppl.146(2002)599

BHF + Coherent L-S coupling SM SM+L-S coupling t+n+n+L 4-body calc. FINUDA Exp.

6 ΛH Agnello et al., PRL108(2012)042501

• Double charge-exchange (DCX) reaction
• Coherent ΛN-ΣN mixing in neutron-rich environment

Status

6 ΛH

6 6

(252MeV/c)

Li H

Stop

K p

• +

L

+  +

6 6

(130MeV/c)

H He p -

L

 + LN-SN mixing

1.4 MeV

L glue effects

4.4 MeV

SLIDE 46

46 H.Sugimura et al.,(J-PARC E10 Collaboration) PLB 724 (2014)39.

E10

No peak of the bound state is observed. Search for the 6

ΛH hypernucleus by 6Li(p-, K+) reactions

1.2GeV/c@J-PARC E10

• R. Honda, et al., (J-PARC E10 Collaboration), PRC96 (2017) 014005

SLIDE 47

Green’s function method

47

Coupled-channels DWIA calculation for L production

0,0 0,1 0, 1,0 1,1 ,0 ,

ˆ

N N N N

U U U U U U U             

U

 ( )  ( )  ( )   ( )

( ) ( )

G G G UG E E E E

f f f f

 +

Coupled-channel Green’s function

1

(0) (0) (0) (0)

ˆ ( )

N

f

G G E G

L L L

               G

Coupled channel equation

for example, 2 x 2

SLIDE 48

48

Schematic illustration of 6

LH production in the 6Li(p-,K+) reaction

One-step mechanism

SN  LN couplings

s1/2 p3/2 p1/2

L p n

5H(g.s.)

s1/2 p3/2 p1/2

S- p n

5He*

s1/2 p3/2 p1/2

S- p n

5He(g.s.)

6 LH(1+ exc.)

S- doorways

6 LH(0+ g.s.) forbidden

p-p  K+S- reactions

s1/2 p3/2 p1/2

p n

p- K+

6Li(1+ g.s.)

Non-spinflip Δ𝑇 = 0 dominant

…..

SLIDE 49

49

Production cross section of 6Li(p-,K+) reactions

BL  3.10 MeV PS= 1.54 % BL  2.33 MeV PS= 0.79 % BL  1.84 MeV PS= 0.32 % BL  1.58 MeV PS= 0.07 %

A B C D

6 LH(1+)

Data: H.Sugimura et al.,(J-PARC E10 Collaboration) PLB 724 (2014)39.

s-hole p-hole

SLIDE 50

50

Dependence of the calculated spectra for the 6Li(p-,K+) reaction pp- =1.2 GeV/c

The shape and magnitude of the spectrum are sensitive to the strengths of (VS, WS).

(VS, WS) = ( +30, -26) MeV

WS potential

3.0 MeV FWHM

VS dependence

WS= -26 MeV is fixed VS= +30 MeV is fixed

WS dependence

The c2-value distribution in VΣ, WΣ

c2/N = 1.28 with fs (N=66) Data: R. Honda, et al., (J-PARC E10 Collaboration), PRC96 (2017) 014005

Repulsive and absorptive

SLIDE 51

Charge Symmetry Breaking (CBS)

Yamamoto, et al., PRL. 115 (2015) 222501.

SLIDE 52

52

Yamamoto, et al., PRL. 115 (2015) 222501.

Charge Symmetry Breaking for the A = 4 s-shell hypernuclei

2.12±0.10

• A. Esser et al.,
• PRL. 114(2015)232501.

SLIDE 53

53

Charge Symmetry Breaking (CSB)

R.H. Dalitz, F. Von Hippel, Phys. Lett. 10 (1964) 153.

SLIDE 54

54

Charge Symmetry Breaking (CSB)

A.Gal, PLB 744 (2015) 352.

• D. Gazda, A. Gal, PRL 116 (2016)122501

SLIDE 55

55

Ab initio Calculation of Charge Symmetry Breaking in A=4 Hypernuclei

• D. Gazda, A. Gal, PRL116 (2016) 122501

Ab initio no-core shell model (NCSM) calculations Bonn-Jülich LO chiral EFT hyperon-nucleon potentials plus a CSB Λ-Σ0 mixing vertex

SLIDE 56

Weak Decay of L Hypernuclei Lifetime

Since 1969, ANL

37.8 MeV p p - L  + + 41.1 MeV n p L  + +

(64.2%) (35.8%)

(free) 10

/ 2.63 10 s 

• L

L

   

SLIDE 57

57

Life time of 3

LH hypernucleus in Heavy-Ion Collisions 3 LH “puzzle”

ALICE Collaboration, PLB754(2006)360 STAR Collaboration, Science 328(2010)50

3 LH

181 ps

Free 263.2±2.0 ps

• AVE. 215+18-16ps

BL(3

LH) = 0.13 MeV

SLIDE 58

S = -2 Hypernuclei

SLIDE 59

X, LLハイパー核

エマルジョンによるLLハイパー核の発見

LL bond energy

X single-particle potentialの性質

(K-,K+)反応スペクトルの解析 X -原子のX線の測定

(K-,K+)反応によるX,LLハイパー核の生成 Recent topics Xハイパー核の存在確認 X--14N 12C(K-,K+)反応によるXハイパー核の生成 7Li(K-,K+)7

XH

7 XH5 LLH+2n; Decay pion spectroscopy

SLIDE 60

Observation of LL Hypernuclei in E176/E373 Hybrid Emulsion

NAGARA

10 *

Be

LL

DEMACHI- YANAGI

11 12

Be or Be

LL LL

HIDA

“weak attractive”

1

( ) ( ) 2 ( )

A A A

B Z B Z B Z

• LL

LL LL LL L L

 

• H

2M B M

L LL

• 

H-dibaryon

Jaffe, PRL38(1977)195

LL bound energy

6He LL

12 6 4

C He He t

• LL

+X  + +

5He

p p

• L

+ +

H.Takahashi et al.,PRL87(2001)212502 K.Nakazawa , NPA 835 (2010)207 K.Nakazawa , H.Takahashi,NPA 835 (2010)207

4.7 1.01 0.67

6

( He) BLL

LL



Prowse, 1966 Nagara,2001 X mass update

Hiyama et al.

PRL104(2010)212502

CM[MeV]

BLL (6.91) 11.88 18.23 14.74 (g.s.)

60

SM[MeV]

BLL (6.91) 18.40 20.27 23.21 14.97 (g.s.)

Gal-Millener,

PLB701(2011)342

SLIDE 61

X- 2p absorption Scenario ?

61

＃13-11-14

4 LH 9 LBe*

＃10-9-6

4 LH 9 LBe

Aoki, et al., NPA 828 (2009) 191–232

KEK E176 Collaboration

𝚶− + 𝟐𝟑𝐃 → 𝚳

𝟓𝐈 + 𝚳 𝟘𝐂𝐟

𝚶− + 𝟐𝟑𝐃 → 𝚳

𝟓𝐈 + 𝚳 𝟘𝐂𝐟

∗

X- binding energies related with twin L hypernuclei in X- capture

2p 0.82 MeV

SLIDE 62

Cluser-Model Calculations for A=6-10 LL Hypernuclei

• E. Hiyama et al, PRC 66(2002)024007

・・・・ 理論的予想

• d

a

VNN

• -

d a L

VLN

• - -

d a L L

VLL NAGARA event High resolution g spectroscopy

10 *

Be

LL

Demachi-Yanagi event

12.28 12.33(exp.)

6He LL

determined from YNG kF=0.84fm-1

OCM+LN potential+LL potential

YNG NF HN, KKNN

62

Danysz et al.

SLIDE 63

• E. Hiyama et al., PRL104(2010)212502

Five-body Cluster Calculations of the LL Hypernucleus

11Be

n a a

LL

 + + + L+ L

OCM + 3BF + LN pot. + LL pot.

YNG NF HN, KKNN Pheno. Gaussian

6He

a

LL

 L L ＋ ＋

10Be

a a

LL

 L L ＋ ＋ ＋

exp. + ΛΛ gs

(0 ) 6.91 MeV B 

exp. ΛΛ 1

(2 ) 11.88 MeV B

+ 

The subsystems are reproduced:

0.9 MeV

bond

vLL 0.5 MeV

• E. Hiyama et al., PTPS183(2010)152

LL bound energy

63

SLIDE 64

64

• A. Gal, D.J. Millener, PLB 701 (2011) 342.

Shell-model predictions for LL hypernuclei

SLIDE 65

65

ΛΛ correlation from production nuclei

S=-2 dibaryon (uuddss) “H” 2 σ bump at EΛΛ ~ 15 MeV

C.J.Yoon et al., (KEK-E522),PRC75(2007)022201(R)

• STAR data clearly show enhanced ΛΛ

correlation

• Preferred ΛΛ interactions 1/a0 < -0.8

fm-1, reff > 3 fm.

Data: N.Shah, et al. (STAR Collab.)

 From (K-,K+ΛΛ) reaction

• A. Ohnishi, T. Furumoto, K. Morita (2012)

 From Heavy-ion Collisions

P42@J-PARC

Search for H-Dibaryon with a Large Acceptance Hyperon Spectrometer (J.K. Ahn, K. Imai)

SLIDE 66

NHC-D NSC97f NSC97e NSC89 NSC03 NHC-F 66

Coupled Channel Approach to Doubly Strange Hypernuclei

• H. Nemura et al.,

PRL94(2005)202502

Ab initio calculations by SVM

• D. E. Lanskoy and Y. Yamamoto, PRC69(2004)014303.
• T. Yamada, PRC69(2004)044301.
• Y. Yamamoto and Th.A. Rijken, PRC69(2004)014303.

X-LL coupled-channel calculations aXN-aLL coupled-channel calculations LL-XN s-wave: P(X) < 1 % 1sL

2: P(X) < 1 %, 1sL1pL: P(X) ～10 %

1.01 0.67

6

( He) BLL

LL



Nagara,2001 X mass update

2keV?

Hyperon-mixing

SLIDE 67

～72 MeV

NS NL

～28 MeV

LS LL SS NX

～300 MeV

N NN

67

• Various effects on the hyperon mixing
• Related to the 3BF in nuclei

Dynamics in Strangeness Nuclear Systems

S = 0 S = -1 S = -2

N N N  N L N S L L N X Nuclei

Fujita-Miyazawa 3BF

Hypernuclei

Strong LNN 3BF ?

XN-LL coupling LN-SN coupling

～1-2 % very large ?

SLIDE 68

68

X s.p. poteintials determined by the emulsion data (1959-1979)

(1959) (1969) (1979) (1968) (1968) (1968) (1968)

Woods-Saxon potential: Binding energies (exp.)

attractive potential for X- !? Dover, Gal, Ann. Phys. 146 (1983) 348.

SLIDE 69

Studies of X- s.p. potentials

[C.B. Dover, A.Gal, Ann. Phys. 146 (1989) 309.]

X-hypernuclei via (K-,K+) reactions

28Si

24 4 MeV for 1.1 fm V r

X  -

 

BNL-E885

( 1 MeV) WX

• 69

VX ?

fss2

DWIA analysis of 12C(K-,K+) data at 1.8GeV/c

Tadokoro et al.,PRC51(1995)2656

16 MeV VX

• 14 MeV

VX

• P.Khaustov et al., PRC61(2000)054603

T.Iijima et al.,NPA546(1992)588.

Semi-Classical Distorted Wave Model Analysis

• M. Kohno et al.,PTP123(2010)157;NPA835(2010)358.

20, 10, 0, 10, 20MeV VX  -

• +

+

12C 12C

SLIDE 70

70

Hyperon s.p. potentials in finite nuclei

• M. Kohno, Y. Fujiwara, PRC79(2009)054318.

G-matrix+local density approximation

fss2 : SU6 quark-model BB interaction by Kyoto-Niigata group

12C 12C 90Zr 90Zr

SLIDE 71

X- s.p. energies in symmetric nuclear matter

71 T.Motoba, S.Sugimoto, NPA835(2010)223.

( , )

F

U k 

X X

1

1.35 fm

F

k

• 

G-matrix calc. Yamamoto 2006 Yamamoto et al. 2006

• 30
• 20
• 10

(unit in MeV)

+20 +10 +40 +30 Rijken-Yamamoto 2009

• 5.0

ESC04d

• 18.7
• 6.9

+6.4

• 19.6

+6.4

• 12.1
• 5.9

+6.3

• 18.4

+7.2 ESC04d*

• 1.7
• 20.2
• 5.8

+6.0

• 1.0

+8.5 ESC08a

• 28.0
• 14.5
• 5.8

+5.6

• 1.1

+8.4 ESC08a*

• 21.5
• 31.8
• 7.4

+2.4 +1.9 +9.1 ESC08b

• 37.8

NHC-D

1,1S0

• dd
• 21.4
• 16.8
• 2.6

+0.7

• 0.4
• 2.3

1, 3S1- 3D1 3,1S0 3, 3S1- 3D1

Ehime

• 22.3
• 10.9
• 1.3
• 0.5
• 8.6
• 0.5

SLIDE 72

15N+X-

14 MeV

• 0( )

3 MeV W E

X

• 24 MeV

VX  -

Woods-Saxon 1.1 fm, 0.6 fm r a  

1.5MeV FWHM

16O

X- spectrum in DCX (K-,K+) reactions at 1.8GeV/c

• Spin-stretched Ξ– states can be populated due to the high momentum transfer.

72

ds/d[15N(1/2-)⊗sX ](1-) = 6 nb/sr, ds/d [15N(1/2-)⊗pX](2+) = 9 nb/sr for VX=-14 MeV.

• T. Harada, Y. Hirabayashi, A. Umeya, PLB690(2010)363.

SLIDE 73

73

X-ΛΛ spectrum in DCX (K-,K+) reactions at 1.8GeV/c

Doorway

One-step mechanism Two-step mechanism K p p

• 

L

0p

K p

+

 L K p K

• +
• 

X p

• X

 LL

XN-LL coupling

[T. Harada, Y. Hirabayashi, A. Umeya, PLB690(2010)363]

15N+X-

X- LL Hyperon-mixing

E07@J-PARC

16O

w/o XN-LL coupling with XN-LL coupling

• 14MeV

SLIDE 74

7 nb/sr (5.2 %) 12 nb/sr (8.8 %)

X- spectrum in DCX (K-,K+) reactions at 1.8GeV/c

16O

1.5MeV FWHM 14 MeV VX  -

74

The large momentum transfer qΞ− ≃ 400 MeV/c leads to the spin-stretched Ξ− doorways states followed by [15N(1/2−, 3/2−) ⊗ sΞ−]1− → [14C(0+, 2+) ⊗ sΛpΛ]1−

• T. Harada, Y. Hirabayashi, A. Umeya, PLB690(2010)363.

SLIDE 75

75

X- spectrum in DCX (K-,K+) reactions on 12C

Motoba, Sugimoto, NPA

Core-excitation

NHCD

NHCD Ehime ESC04d ESC08c

SLIDE 76

76

Isospin dependence

Isovector components of the hyperon-nucleus potentials For S For X

SLIDE 77

77

5 LHe 10 LBe

KISO Nakazawa, et al., PTEP,2015, 033D02

SLIDE 78

78

X- binding energies related with twin L hypernuclei in X- capture

Nakazawa, et al., PTEP,2015, 033D02

1.1 ± 0.25 MeV < 𝐶𝛰− < (4.38 ± 0.25) MeV

X- 2p absorption Scenario?

SLIDE 79

79

Observation of X bound states in the 12C(K-,K+)X reaction at 1.8 GeV/c in J-PARC

Nagae, et al., PoS(INPC2016)038

12 XBe

J-PARC E05

SLIDE 80

80

X--nucleus optical potentials in 56Fe+X-

DD tρ NHC-D Ehime ESC08c ESC04d

DD tρ NHC-D Ehime ESC08c ESC04d

J-PARC E03: X- atomic X-ray on 56Fe

SLIDE 81

81

Recent topics

“Hyperon puzzle’’ in massive Neutron Stars Charge symmetry breaking (CSB) for the A=4 s- shell hypernucle Lifetime of 3

LH hypernucleus in Heavy-Ion Collisions

X- bound state determined by twin L hypernuclear decay X- bound state produced by 12C(K-,K+) reaction No peak of the 6

LH bound state in 6Li(p-,K+) reactions

Repulsive S nucleus potential for S-5He Search for excited state of S hypernucleus

SLIDE 82

• 原子核深部を探る

–ハイペロンはパウリ排他律を受けないためプローブ（探針）となる

• Impurity Physics （不純物物理）

– “糊”としての役割 – 原子核構造（１粒子運動、殻構造、クラスター構造、集団運動）の変化

• Baryon-Baryon Interaction

– YN, YY Interaction based on SUf (3) – 核力の統一的理解・斥力芯の起源

• “Exotic” Nuclear Physics

– ストレンジネスが拓く新しい原子核の面白さ

• Neutron Starの構造と進化

– 高密度核物質への戸口, EOS, 最大質量, 冷却, … ハイパー核物理の課題

82

Keywords Hyperon mixing + Coupled-channels

SLIDE 83

83

Studies of the production and spectroscopy of hypernuclear states are very interesting and exciting at J-PARC.

Conclusion

from http://j-parc.jp/ J-PARC (Japan Proton Accelerator Research Complex)

SLIDE 84

Thank you very much.

84