k - 中間子原子核研究の現状 1.introduction expanding the nuclear world exotic properties...
TRANSCRIPT
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)
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).
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
A. Doté, T. Hyodo and W. Weise,Nucl. Phys. A804, 197 (2008)Phys. Rev. C79, 014003 (2009)
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)
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).
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
A. Doté, T. Hyodo and W. Weise,Nucl. Phys. A804, 197 (2008)Phys. Rev. C79, 014003 (2009)
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
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).
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
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
A. Doté, T. Hyodo and W. Weise,Nucl. Phys. A804, 197 (2008)Phys. Rev. C79, 014003 (2009)
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
KbarN potential based on “HNJH”
“Corrected”, N Ks M m B K
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 %
KbarN potential based on “HNJH”
“Corrected”, N Ks M m B K
NN distance = 2.21 fm KbarN distance = 1.97 fm
1.97 fm
Structure of K-pp
Kbar
N N
Mixture of TN=0 component = 3.8 %
I=0 KbarN
1.82 fm
2 0.4l
KbarN potential based on “HNJH”
“Corrected”, N Ks M m B K
NN distance = 2.21 fm KbarN distance = 1.97 fm
Structure of K-pp
Kbar
N N
Mixture of TN=0 component = 3.8 %
I=0 KbarN I=1 KbarN
1.82 fm 2.33 fm
2 0.4l 2 1.9l
KbarN potential based on “HNJH”
“Corrected”, N Ks M m B K
NN distance = 2.21 fm KbarN distance = 1.97 fm
Structure of K-pp
N
Mixture of TN=0 component = 3.8 %
I=0 KbarN I=1 KbarN
1.82 fm 2.33 fm
2 0.4l 2 1.9l
NN distance = 2.21 fm KbarN distance = 1.97 fm
“Λ(1405)” as I=0 KbarN calculated with this potential
1.86 fm
2 0.0l Kbar
NAlmost “Λ(1405)”Almost “Λ(1405)”
KbarN potential based on “HNJH”
“Corrected”, N Ks M m B K
Structure of K-ppKbarN potential based on “HNJH”
“Corrected”, N Ks M m B K
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…
Variational calculation of K-pp with a chiral SU(3)-based KbarN potential
A. Doté, T. Hyodo and W. Weise,Nucl. Phys. A804, 197 (2008)Phys. Rev. C79, 014003 (2009)
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.
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)
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
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)
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.
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)
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)
Experiments related to K-pp
• 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.
Experiments related to K-pp
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!