k - 中間子原子核研究の現状 1.introduction expanding the nuclear world exotic properties...

K- 中間子原子核研究の現状

1. Introduction • Expanding the nuclear world• Exotic properties of kaonic nuclei with a phenomenological KbarN potential

2. Variational calculation of K-pp with a chiral SU(3)-based KbarN potential

3. Recent status of the study of K-pp• Theoretical side• Experimental side

4. Summary and future plan

Akinobu Doté (IPNS/KEK)

Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN)

T. Hyodo (TITech), W. Weise (TU Munich)

JAEA seminar　’ 10.05.13 @ JAEA, Tokai, Japan

Prototype of kaonic nuclei “K-pp”

1. Introduction

Expanding the nuclear world原子核＝陽子・中性子からなる有限量子多体系、　安定核　…　約３００種

Large isospin　　　　不安定核…約 3000 種、 RIBF ＠理研で展開

http://www.rarf.riken.go.jp/newcontents/contents/facility/RIBF.html

Expanding the nuclear world原子核＝陽子・中性子からなる有限量子多体系、　安定核　…　約３００種

Large isospin　　　　不安定核…約 3000 種、 RIBF ＠理研で展開

Strangeness　　　　ハイパー核 … J-PARC (JAEA+KEK) で展開

Kaonic nuclei

Another form of nuclear system with strangeness

K-

Nucleus containing K- meson

Leading actors

Key person

N

K

,0

,0

p

n938940

2 [ ]Mc MeV

1 1,

2 2J I

Baryon uududd

0K 498 1

0 ,2

J I Mesonds

K 494 us

14061

, 02

J I

Baryon uds

1116 Baryon

:1189, 0 :1193,

:1197

:140, 0 :135

1, 0

2J I

1, 1

2J I

0 , 1J I

Baryon : , 0 : , :uu uds ds sd

Meson 1: , 0 : , :

2ud uu d d du

uds

Actors in Kbar nuclei

Supporting players

Excited state of Λ

940 p,n

1115 Λ

1190 Σ

p + K-1435

Λ(1405)1405

1250 Λ + π

Σ + π1325E

nerg

y [M

eV]

940 p,n

1115 Λ

1190 Σ

p + K-1435

Λ(1405)1405

1250 Λ + π

Σ + π1325E

nerg

y [M

eV]

I=0 Proton-K- bound state with 30MeV binding energy?

　 Not 3 quark state?　　←　 can’t be explained with 　　　　　 a simple quark model…

I=0 Proton-K- bound state with 30MeV binding energy?

　 Not 3 quark state?　　←　 can’t be explained with 　　　　　 a simple quark model…

Leading actors

Key person

N

K

,0

,0

p

n938940

2 [ ]Mc MeV

1 1,

2 2J I

Baryon uududd

0K 498 1

0 ,2

J I Mesonds

K 494 us

14061

, 02

J I

Baryon uds

1116 Baryon

:1189, 0 :1193,

:1197

:140, 0 :135

1, 0

2J I

1, 1

2J I

0 , 1J I

Baryon : , 0 : , :uu uds ds sd

Meson 1: , 0 : , :

2ud uu d d du

uds

Actors in Kbar nuclei

Supporting players

Excited state of Λ

940 p,n

1115 Λ

1190 Σ

p + K-1435

Λ(1405)1405

1250 Λ + π

Σ + π1325E

nerg

y [M

eV]

Σπ channel is open at about 100 MeV below the Proton-K- threshold.

Σπ channel is open at about 100 MeV below the Proton-K- threshold.

What is Kaonic nucleus?

KNNN…

ΣπNN…

K nuclear state

Deeply bound below πΣ threshold (main decay channel)

Possible to exist as a quasi-bound state

with narrow width

Kaonic nucleus

K-

• Bound by strong interaction • Inside of nucleus

• The nuclear structure may be changed, if the interaction is so attractive.

1. free KbarN scattering data2. 1s level shift of kaonic hydrogen atom3. binding energy and width of Λ(1405)

Phenomenological KbarN potential (AY KbarN potential)

Strongly attractive 0

KNIV

• Y. Akaishi and T. Yamazaki, PRC 52, 044005 (2002)

Λ(1405) = I=0 K- p quasi-bound state with 27 MeV binding energy

Studies with a phenomenological KbarN potential

• A. Doté, H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, 044313 (2004)

Systematic study of various light kaonic nuclei (3HeK- to 11CK-) with

AMD + G-matrix (effective NN potential ) + AY KbarN potential

shows their interesting properties…

By a calculation of a few kaonic nuclei with a simple model, 3HeK- turns out to be deeply bound by 100MeV with a narrow width of 20MeV.

Deeply bound kaonic nuclei !

Kaon'sB.E.

Width(π Y )

Averageddensity

[MeV] [MeV] [fm- 3]

ppnK - 110.3 21.2 0.53pppK - 96.7 12.5 0.66pppnK - 105.0 25.9 0.436BeK - 104.2 33.3 0.379BK - 118.5 33.0 0.3311CK - 117.4 46.0 0.36

① 　 Deeply bound and Dense

③ 　 Isovector deformation ④ 　 proton satellite

pppK-

② 　 Drastic change of structure

8Be 8BeK-

Theoretical studies of nuclear system with anti-kaons

• Medium to heavy nuclei with multi-antikaons

• Nuclear matter with antikoans

Neutron star, kaon condensation…

- T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009)

- D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, 055204 (2007); PRC77, 045206 (2008)

• Light nuclei with a single antikaon3HeK- ～ 11CK- studied with AMD + G-matrix + AY potential

E(K) 100MeV≒

• Light nuclei with double antikaons3HeK-K- etc studied with AMD + G-matrix + AY potential

E(2K) 200MeV≒

Studied with Relativistic Mean Field

… Antikaon part is based on non-linear chiral Lagrangian

Strongly repulsive KbarKbar interaction

Saturation for the number of antikaonsIn case of 15O+xK-, central nuclear density and –B/x are saturated for x>8.

2. Variational calculation of K-pp with a chiral SU(3)-

based KbarN potential

Are kaonic nuclei really exotic?

•The phenomenological KbarN potential is all right?

πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory.

KbarN πΣ ηΛ KΞ

Chiral SU(3)AY potential

•The phenomenological KbarN potential is all right?

πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory.

•The G-matrix treatment is adequate?

NN repulsive core is too smoothed out? As a result, such a dense state is formed??

Are kaonic nuclei really exotic?

More theoretical study of the most essential kaonic nucleus

K-pp system “Prototype of kaonic nuclei” studied with

a chiral SU(3)-based KbarN potential

Variational calculation of K-pp with a chiral SU(3)-based KbarN potential

Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV).

A. Doté, T. Hyodo and W. Weise,Nucl. Phys. A804, 197 (2008)Phys. Rev. C79, 014003 (2009)

1E1E

Strong repulsive core(3 GeV)

Strong repulsive core(3 GeV)



Effective KbarN potential based on Chiral SU(3) theory

… reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics.

Single channel, Energy dependent, Complex, Gaussian-shape potential


Local KbarN potential based on Chiral SU(3)

I=0 KbarN scattering amplitude

Chiral unitary; T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003)

Chiral Unitary

1420

Resonance position in I=0 KbarN channel

In Chiral unitary model,

1420 MeVnot 1405 MeV !

Effective potential

T. Hyodo and W. Weise, PRC77, 035204(2008)







I=0 KbarN resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV

Variational method… Trial wave function contains NN/KbarN correlation functions.

The NN repulsive core can directly be treated.

N N

Kbar

1KNF2KNF

1 2N NF 2

( ) ( )expij iji jij a a

a

F C b r r

0 , 1/ 2, 1/ 2

0, 0Z

NN

J T T

L S






Four variants of chiral unitary modes

2N K

N K

M m B Ks

M m B K

×

Total B. E. : 20 ± 3 MeVG （ KbarN→pY ） : 40 ～ 70 MeV

Total B. E. : 20 ± 3 MeVG （ KbarN→pY ） : 40 ～ 70 MeV

Shallow binding and large decay width


I=0 KbarN resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV

Variational method… Trial wave function contains NN/KbarN correlation functions.

The NN repulsive core can directly be treated.

Structure of K-pp

N N

Kbar

KbarN potential based on “HNJH”

“Corrected”, N Ks M m B K

Structure of K-pp

Kbar

2.21 fm

1.97 fm

N N



Cf)

NN distance in normal nuclei ～ 2 fm Size of deuteron ～ 4 fm

Structure of K-pp

Kbar

N N

Mixture of TN=0 component = 3.8 %



NN distance = 2.21 fm KbarN distance = 1.97 fm

1.97 fm

Structure of K-pp

Kbar

N N


I=0 KbarN

1.82 fm

2 0.4l




Structure of K-pp

Kbar

N N


I=0 KbarN I=1 KbarN

1.82 fm 2.33 fm

2 0.4l 2 1.9l




Structure of K-pp

N


I=0 KbarN I=1 KbarN

1.82 fm 2.33 fm

2 0.4l 2 1.9l


“Λ(1405)” as I=0 KbarN calculated with this potential

1.86 fm

2 0.0l Kbar

NAlmost “Λ(1405)”Almost “Λ(1405)”



Structure of K-ppKbarN potential based on “HNJH”


Density distribution: KbarN pair in K-pp vs “L(1405)”

NKbar

“Λ(1405)”

Isospin 0Isospin 0 KbarN pair

Isospin 1 KbarN pair

N

“K-pp ”

Isospin 0 and 1 mixed

N Kbar

“L(1405)” almost survives in K-pp!

• Dispersive correction (Effect of imaginary part)

+6 ～ +18 MeV

• p-wave KbarN potential ～ -3 MeV 10 ～ 35 MeV

• Two nucleon absorption 4 ～ 12 MeV

s-wave KbarN potential (Variational calculation)

B .E. Width

20 ± 3 MeV 40 ～ 70 MeV

Rough estimation 20 ～ 40 MeV

Total B .E.

55 ～ 120 MeV

Total Width

K-pp …

Very large…



3. Recent status of the study of kaonic nuclei

Prototype of kaonic nuclei “K-pp”

Kbar nuclei = Exotic system !?

To make the situation more clear …

K-pp= Prototye of Kbar nuclei

Studied with various methods, because it is a three-body system:

•Doté, Hyodo, Weise Variational with a chiral SU(3)-based KbarN potential PRC79, 014003(2009)

•Akaishi, Yamazaki ATMS with a phenomenological KbarN potential PRC76, 045201(2007)

•Ikeda, Sato Faddeev with a chiral SU(3)-derived KbarN potential PRC76, 035203(2007)

•Shevchenko, Gal , Faddeev with a phenomenological KbarN potential PRC76, 044004(2007)

Mares•Wycech, Green Variational with a phenomenological KbarN potential (with p-wave) PRC79, 014001(2009)

•Arai, Yasui, Oka Λ* nuclei model PTP119, 103(2008)

continued by Uchino, Hyodo, Oka•Nishikawa, Kondo Skyrme model PRC77, 055202(2008)

All calculations predict that K-pp can be bound.

Experiments concerned to this topics: FINUDA (Frascatti), KEK, DISTO (Sacley), OBELIX (CERN)Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti)

There are several experiments:

50 60 70 80 90 100 110 120 130

-140

-120

-100

-80

-60

-40

-20

0

Width (KbarNN→πYN) [MeV]

- B

.E.

[MeV

]

Doté, Hyodo, Weise [1](Variational, Chiral SU(3))

Akaishi, Yamazaki [2](Variational, Phenomenological)

Exp. : FNUDA [5]

Exp. : DISTO [6](Finalized)

Using S-wave KbarN potentialconstrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc.

Ikeda, Sato [4](Faddeev, Chiral SU(3))

Shevchenko, Gal, Mares [3](Faddeev, Phenomenological)

[1] PRC79, 014003 (2009)[2] PRC76, 045201 (2007)[3] PRC76, 044004 (2007)[4] PRC76, 035203 (2007)

[5] PRL94, 212303 (2005)[6] PRL104, 132502 (2010)

Recent results of calculation of K-pp Recent results of calculation of K-pp and related experiments

50 60 70 80 90 100 110 120 130

-140

-120

-100

-80

-60

-40

-20

0

Width (KbarNN→πYN) [MeV]

- B

.E.

[MeV

]

Exp. : FNUDA [5]

Exp. : DISTO [6](Finalized)

Using S-wave KbarN potentialconstrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc.

Shevchenko, Gal, Mares [3](Faddeev, Phenomenological)

[1] PRC79, 014003 (2009)[2] PRC76, 045201 (2007)[3] PRC76, 044004 (2007)[4] PRC76, 035203 (2007)

[5] PRL94, 212303 (2005)[6] PRL104, 132502 (2010)

Recent results of calculation of K-pp Recent results of calculation of K-pp and related experiments

Akaishi, Yamazaki [2](Variational, Phenomenological)

Ikeda, Sato [4](Faddeev, Chiral SU(3))

Wycech, Green [7](Variational, phenomenological,

P-wave)

[7] PRC79, 014001 (2009)

Including P-wave KbarN potential, and other effects.

Doté, Hyodo, Weise [1](Variational, Chiral SU(3))

Recent results with various calculations of K-pp

B. E. Γ (mesonic) Method KbarN Int.Channels

at final step

DHW 20 ± 3 40 ～ 70 Variational Chiral SU(3) KbarN

AY 47 61 Variational Phenom. KbarN

IS 60 ～ 95 45 ～ 80 Faddeev Chiral SU(3) KbarN, πY (AGS) (Separable)

SGM 50 ～ 70 90 ～ 110 Faddeev Phenom. KbarN, πY (AGS) (Separable)

Exp.FINUDA 115±7 67±14 K- absorption, Λp inv. mass DISTO 103±3±5 118±8±10 p+p→K++Λ+p, Λp inv. mass (Finalized)

All four calculations shown above are constrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Only s-wave KbarN potential is used.



at final step





DHW vs AY

Difference of the used KbarN interactions.

Comparison of AY potential and Chiral-based potential

AY potential

Weinberg-Tomozawa term derived from Chiral SU(3) effective Lagrangian

KbarN πΣ ηΛ KΞ

Coupled channel Chiral dynamics

• Energy independent potential• No πΣ-πΣ interaction

• Energy dependent potential• Somewhat strongly attractive πΣ-πΣ interaction

Λ(1405) = a quasi-bound state of I=0 KbarN at 1405MeV.

Appears in I=0 KbarN channel.

I=0 KbarN resonance @ 1405MeV.

Two poles (double pole); one couples strongly to KbarN, the other couples strongly to πΣ.

Λ(1405) (experimentally observed) appears in I=0 πΣ-πΣ channel.

I=0 KbarN resonance @ 1420MeV.

I=0 KbarN full scattering amplitude

Almost same in the on-shell region

Quite different in the sub-threhold region

Comparison of AY potential and Chiral-based potential



at final step





DHW vs AYIn Chiral SU(3) theory, the πΣ-πΣ interaction is so attractive to make a resonance, while AY potential doesn’t have it.

“Λ(1405)” is I=0 KbarN bound state at 1420 MeV or 1405 MeV?

AY potential is twice more attractive than Chiral-based one.



at final step





DHW vs IS

• Separable approximation?

• Different energy dependence of interaction kernel Vij?

• πΣN three-body dynamics … may not be included in DHW. (Y. Ikeda and T. Sato, PRC79, 035201(2009))

Although both are based on Chiral SU(3) theory, results are very different from each other.

Variational cal. vs Faddeev

The KbarN potentials used in both calculations are constrained with Chiral SU(3) theory, but …

Total B. E. = 20±3 MeV, Decay width = 40 ～ 70 MeV

A. Doté, T. Hyodo and W. Weise,Phys. Rev. C79, 014003 (2009)

Variational calculation(DHW)

Faddeev calculation(IS)

Total B. E. = 60 ～ 95 MeV, Decay width = 45 ～ 80 MeV

Y. Ikeda, and T. Sato,Phys. Rev. C76, 035203 (2007)

??? Discrepancy between Variational calc. and Faddeev calc.

Separable potential used in Faddeev calculation? Non-relativistic (semi-relativistic) vs relativistic? Energy dependence of two-body system (KbarN) in the three-body system (KbarNN)? …???

Why ?

Variational cal. vs Faddeev

The KbarN potentials used in both calculations are constrained with Chiral SU(3) theory, but …

Total B. E. = 20±3 MeV, Decay width = 40 ～ 70 MeV

A. Doté, T. Hyodo and W. Weise,Phys. Rev. C79, 014003 (2009)

Variational calculation(DHW)

Faddeev calculation(IS)

Total B. E. = 60 ～ 95 MeV, Decay width = 45 ～ 80 MeV

Y. Ikeda, and T. Sato,Phys. Rev. C76, 035203 (2007)

??? Discrepancy between Variational calc. and Faddeev calc.

A possible reason is

πΣN thee-body dynamics

In the variational calculation (DHW), πΣ channel is eliminated and incorporated into the effective KbarN potential.

Y. Ikeda and T. Sato, PRC79, 035201(2009)

Three-body system calculated with the effective KbarN potential

Σ Σ

K

N+ …

…=

πK

N

πK

N

K

N

N N N NN N

barK NNE

conserved

Experiments related to K-pp

• FINUDA collaboration (DAΦNE, Frascatti)


• K- absorption at rest on various nuclei (6Li, 7Li, 12C, 27Al, 51V)• Invariant-mass method

Strong correlation between emitted p and Λ (back-to-back)

Invariant mass of p and Λ

K-pp

p

Λ

If it is K-pp, …Total binding energy = 115 MeVDecay width = 67 MeV

PRL 94, 212303 (2005)

6 35 4

14 211 3

• Re-analysis of KEK-PS E549

• DISTO collaboration

- p + p -> K+ + Λ + p @ 2.85GeV- Λp invariant mass- Comparison with simulation data

T. Yamazaki et al. (DISTIO collaboration), PRL104, 132502 (2010)

- K- stopped on 4He target- Λp invariant mass

T. Suzuki et al (KEK-PS E549 collaboration), arXiv:0711.4943v1[nucl-ex]

K- pp???B. E.= 103 ±3 ±5 MeVΓ = 118 ±8 ±10 MeV

K- pp???B. E.= 103 ±3 ±5 MeVΓ = 118 ±8 ±10 MeV

Strong Λp back-to-back correlation is confirmed.Unknown strength is there in the same energy region as FINUDA.

Strong Λp back-to-back correlation is confirmed.Unknown strength is there in the same energy region as FINUDA.


J-PARC will give us lots of interesting data!

E15: A search for deeply bound kaonic nuclear states by 3He(inflight K-, n) reaction --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto)

E17: Precision spectroscopy of kaonic 3He atom 3d→2p X-rays --- Spokespersons: R. Hayano (Tokyo), H. Outa (Riken)

All emitted particles will be measured.

Dr. Fujioka’s talk (KEK workshop, 7-9. Aug. 08)

4. Summary and future plan

4. SummaryKaonic nuclei are exotic system !?

Variational calc. of K-pp with a chiral SU(3)-based KbarN pot.

• B. E. =20±3 MeV, Γ(KbarNN → πYN) = 40 – 70MeV• With p-wave KbarN pot., dispersion correction, and two-nucleon absorption, B. E. =20 – 40 MeV, Γ = 55 – 120MeV

• AMD calculation with G-matrix method using a phenomenological KbarN potential (AY potential) shows that kaonic nuclei may have lots of interesting properties:

Deeply bound and narrow widthdense system with interesting structure…

• Kaonic nuclei are another form of nuclear system involving strangeness. They might be exotic system because of the strong attraction of I=0 KbarN potential.

• However, these properties have not been established and there are some questions.

• Two protons distance = 2.2fm ≒NN mean distance of normal nucleus• Λ(1405) structure (correlation) remains in K-pp.

K-pp is a shallowly bound and not so dense system.

4. Summary

Current status of studies of K-ppThe most essential Kbar nuclei “K-pp” (KbarNN, Jp=1/2-, T=0) has been investigated in various ways. But the situation is still controversial…

Theory

Variational + Phenom. KbarN B.E. = 47MeV, Γ= 61MeV PRC76, 045201(2007)

Variational + Chiral-based KbarN B.E. = 20±3MeV, Γ= 40 ～ 70MeV PRC79, 014003(2009)

Faddeev + Phenom. KbarN B.E. = 50 ～ 70MeV, Γ= ～ 100MeV PRC76, 044004(2007)

Faddeev + Chiral-based KbarN B.E. = 60 ～ 95MeV, Γ= 45 ～ 80MeV PRC76, 035203(2007)

Experiment (Unknown object which seems related to K-pp)FINUDA B.E. = 115MeV, Γ= 67MeV PRL94, 212303(2005)

DISTO B.E. = 103MeV, Γ= 118MeV PRL104, 132502 (2010)

Discrepancy between theoretical studies of K-pp• DHW (Variational with Chiral-based) vs AY (Variational with phenomenological) … Difference of KbarN attraction Λ(1420) scheme and Λ(1405) scheme

• DHW (Variational with Chiral-based) vs IS (Faddeev with Chiral-based) … πΣN three-body dynamics (might be also different energy dependence of interaction kernel? )

… if it is K-pp

4. Future plan• What is the object measured experimentally?

A bound state of K-pp, or another object such as πΣN ???

Only what we can say from only this spectrum is “There is some object with B=2, S=-1, charge=+1”…

• Since the signal position is very close to π+Σ+N threshold, the πΣN degree seems important in the observed state.

• As pointed out by Dr. Ikeda and Prof.Sato, the πΣN dynamics may be important. (especially, in case that K-pp is deeply bound???)

Direct treatment of πΣN degree, dealing with a resonant state, based on variational scheme.

Coupled channel Complex Scaling

Thank you for your attention!

k - 中間子原子核研究の現状 1.introduction expanding the nuclear world exotic properties...

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