K-中間子原子核研究の現状
Prototype of kaonic nuclei “K-pp”
Akinobu Doté (IPNS/KEK)
1. Introduction
•
•
Expanding the nuclear world
Exotic properties of kaonic nuclei with
a phenomenological KbarN potential
Y. Akaishi (Nihon/RIKEN),
T. Yamazaki (RIKEN)
2. Variational calculation of K-pp with a chiral SU(3)T. Hyodo (TITech),
based KbarN potential
W. Weise (TU Munich)
3. Recent status of the study of K-pp
•
•
Theoretical side
Experimental side
4. Summary and future plan
JAEA seminar
’10.05.13 @ JAEA, Tokai, Japan
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
Actors in Kbar nuclei
Leading actors
1435Mc2 [MeV ]
1405
p
N
n
1325
938
940
Energy [MeV]
0
K
Key person
498
K

494
K 1250
p + KΛ(1405)

uud
1
1
Baryon
J  , I 
udd
2
2
Σ + π- bound state
I=0 Proton-K
with 30MeV binding energy?
1
ds
Meson
J   0  , Not
I 3 quark
2 Λ + πstate?
us
← can’t be explained with
a simple
quark model…
Σ
1190
 1115 1406

1
J  , I 0 Λ
2

uds
Baryon
Excited state of Λ
Supporting players


 ,0
 ,0
1116
 :1189, 0 :1193,
940
 :1197
 :140, 0 :135

1
J  , I 0
2

Baryon

1
J  , I 1
2
p,n
Baryon
J   0 , I  1
Meson

uds
 : uus, 0 : uds,  : dds
 : ud , 0 :


1
uu  d d ,  : du
2
Actors in Kbar nuclei
Leading actors
1435Mc2 [MeV ]
1405
p
N
n
1325
938
940
Energy [MeV]
0
K
Key person

1
1
J  , I 
2
2
p + KΛ(1405)
uud
udd
Baryon
Σ+π
1
ds
J   0  , I  Λ + π Meson
2
Σπ channel
is open
us
at about 100 MeV below
Σ
the Proton-K- threshold.
498
K

494
K 1250
1190
 1115 1406

1
J  , I 0 Λ
2

uds
Baryon
Excited state of Λ
Supporting players


 ,0
 ,0
1116
 :1189, 0 :1193,
940
 :1197
 :140, 0 :135

1
J  , I 0
2

Baryon

1
J  , I 1
2
p,n
Baryon
J   0 , I  1
Meson

uds
 : uus, 0 : uds,  : dds
 : ud , 0 :


1
uu  d d ,  : du
2
What is Kaonic nucleus?
Kaonic nucleus
• Bound by strong interaction
• Inside of nucleus
K• The nuclear structure may
be changed, if the interaction
is so attractive.
 Deeply
bound below πΣ threshold
(main decay channel)
KNNN…
Possible to exist as
a quasi-bound state
with narrow
width
ΣπNN…
K nuclear state
Studies with a phenomenological KbarN potential
• Y. Akaishi and T. Yamazaki, PRC 52, 044005 (2002)
Phenomenological KbarN potential (AY KbarN potential)
1. free KbarN scattering data
2. 1s level shift of kaonic hydrogen atom
3. binding energy and width of Λ(1405)
Strongly
attractive
KN
I 0
V
Λ(1405) = I=0 K- p quasi-bound state
with 27 MeV binding energy
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 !
• 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…
① Deeply bound
and Dense
ppnK pppK pppnK 6
Be K 9
BK 11
CK -
② Drastic change
of structure
Kaon's
B.E.
[MeV]
Width
(πY )
[MeV]
Averaged
density
[fm-3]
110.3
96.7
105.0
104.2
118.5
117.4
21.2
12.5
25.9
33.3
33.0
46.0
0.53
0.66
0.43
0.37
0.33
0.36
③ Isovector deformation
8Be
8BeK-
④ proton satellite
pppK-
Theoretical studies of nuclear system with anti-kaons
• Light nuclei with a single antikaon
3HeK-
～ 11CK- studied with AMD + G-matrix + AY potential
E(K)≒100MeV
• Light nuclei with double antikaons
3HeK-K-
etc studied with AMD + G-matrix + AY potential
E(2K)≒200MeV
• Medium to heavy nuclei with multi-antikaons
Studied with Relativistic Mean Field
- D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, 055204 (2007);
PRC77, 045206 (2008)
- T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009)
… Antikaon part is based on non-linear chiral Lagrangian
Strongly repulsive KbarKbar interaction
Saturation for the number of antikaons
In case of 15O+xK-, central nuclear density and –B/x are saturated for x>8.
• Nuclear matter with antikoans
Neutron star, kaon condensation…
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.
AY potential
Chiral SU(3)
KbarN
πΣ
ηΛ
KΞ
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.
•The G-matrix treatment is adequate?
NN repulsive core is too smoothed out?
As a result, such a dense state is formed??
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
K-pp
Variational calculation of
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)
 Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV).
1E
Strong repulsive core
(3 GeV)
K-pp
Variational calculation of
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)
 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
Local KbarN potential based on Chiral SU(3)
I=0 KbarN scattering amplitude
T. Hyodo and W. Weise, PRC77, 035204(2008)
Chiral Unitary
Effective potential
In Chiral unitary model,
Resonance position in I=0 KbarN channel
1420 MeV
not 1405 MeV !
1420
Chiral unitary; T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003)
K-pp
Variational calculation of
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)
 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
I=0 Kbarobtained
N resonance “Λ(1405)”appears
with coupled channel chiral dynamics.
at 1420 MeV, not 1405 MeV
Single channel, Energy dependent, Complex, Gaussian-shape potential
 Variational method
… Trial wave function contains NN/KbarN correlation functions.
The NN repulsive core can directly be treated.
J   0 , T  1/ 2, TZ  1/ 2
Kbar
FKN1
N
FKN2
FN N
N
L  0, S NN  0
Fij   C
( ij )
a
a


2
( ij )

exp ba r i  r j 


K-pp
Variational calculation of
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)
 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
I=0 Kbarobtained
N resonance “Λ(1405)”appears
with coupled channel chiral dynamics.
at 1420 MeV, not 1405 MeV
Single channel, Energy dependent, Complex, Gaussian-shape potential
 Variational method
… Trial wave function contains NN/KbarN correlation functions.
The NN repulsive core can directly be treated.
Four variants of chiral unitary modes
Total B. E.
G（KbarN→Y）
×

 M N  mK  B  K 
s 

 M N  mK  B  K  2
: 20 ± 3 MeV
: 40 ～ 70 MeV
Shallow binding
and large decay width
KbarN potential based on “HNJH”
Structure of K-pp
“Corrected”,
Kbar
N
N
s  M N  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
“Corrected”,
Kbar
1.97 fm
N
N
2.21 fm
Cf)
NN distance in normal nuclei ～ 2
Size of deuteron
fm
～ 4 fm
s  M N  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
“Corrected”,
Kbar
1.97 fm
N
 NN distance = 2.21 fm
KbarN distance = 1.97 fm
 Mixture of TN=0 component = 3.8 %
N
s  M N  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
“Corrected”,
I=0 KbarN
1.82 fm
Kbar
l 2  0.4
N
 NN distance = 2.21 fm
KbarN distance = 1.97 fm
 Mixture of TN=0 component = 3.8 %
N
s  M N  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
I=0
KbarN
I=1
KbarN
1.82 fm
2.33 fm
l 2  0.4
l 2  1.9
N
 NN distance = 2.21 fm
KbarN distance = 1.97 fm
 Mixture of TN=0 component = 3.8 %
“Corrected”,
Kbar
N
s  M N  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
I=0 KbarN
I=1 KbarN
1.82 fm
2.33 fm
l 2  0.4
l 2  1.9
“Corrected”,
s  M N  mK  B  K 
“Λ(1405)” as I=0 KbarN
calculated with this potential
1.86 fm
Kbar
l 2  0.0
Almost “Λ(1405)”
N
 NN distance = 2.21 fm
KbarN distance = 1.97 fm
 Mixture of TN=0 component = 3.8 %
N
KbarN potential based on “HNJH”
“Corrected”, s  M N  mK  B  K 
Structure of K-pp
Density distribution: KbarN pair in K-pp vs “(1405)”
“Λ(1405)”
Kbar
Isospin 0
KbarN pair
N
Isospin 0
“K-pp ”
N
Isospin 1
KbarN pair
Kbar
N
Isospin 0 and 1 mixed
“(1405)” almost survives in K-pp!
K-pp
Variational calculation of
with a chiral SU(3)-based KbarN potential
 s-wave KbarN potential
(Variational calculation)
B .E.
20 ± 3 MeV
• Dispersive correction
(Effect of imaginary part)
+6～ +18 MeV
• p-wave KbarN potential
～ -3 MeV
• Two nucleon absorption
A. Doté, T. Hyodo and W. Weise,
Nucl. Phys. A804, 197 (2008)
Phys. Rev. C79, 014003 (2009)
Width
40 ～ 70 MeV
10 ～ 35 MeV
4～ 12 MeV
K-pp …
Rough estimation
Total B .E.
Total Width
20 ～ 40 MeV
55 ～ 120 MeV
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
•Akaishi, Yamazaki
•Ikeda, Sato
•Shevchenko, Gal ,
Mares
•Wycech, Green
Variational with
ATMS
with
Faddeev with
Faddeev with
a chiral SU(3)-based
a phenomenological
a chiral SU(3)-derived
a phenomenological
All calculations
predict that
Variational with a phenomenological K
•Arai, Yasui, Oka
Λ* nuclei model
continued by Uchino, Hyodo, Oka
•Nishikawa, Kondo
Skyrme model
KbarN potential
KbarN potential
KbarN potential
KbarN potential
K-pp
barN
PRC79, 014003(2009)
PRC76, 045201(2007)
PRC76, 035203(2007)
PRC76, 044004(2007)
can be bound.
potential (with p-wave)
PRC79, 014001(2009)
PTP119, 103(2008)
PRC77, 055202(2008)
There are several experiments:
Experiments concerned to this topics: FINUDA (Frascatti), KEK,
DISTO (Sacley), OBELIX (CERN)
Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti)
Recent results of calculation of K-pp and related experiments
Width (KbarNN→πYN) [MeV]
0
20
40
60
80
100
120
140
0
Doté, Hyodo, Weise [1]
(Variational, Chiral SU(3))
-20
-40
Akaishi, Yamazaki [2]
(Variational, Phenomenological)
-60
-80
Ikeda, Sato [4]
(Faddeev, Chiral SU(3))
Exp. : DISTO [6]
(Finalized)
-100
-120
Exp. : FNUDA [5]
-140
[1] PRC79, 014003 (2009)
[2] PRC76, 045201 (2007)
[3] PRC76, 044004 (2007)
[4] PRC76, 035203 (2007)
Shevchenko, Gal, Mares [3]
(Faddeev, Phenomenological)
[5] PRL94, 212303 (2005)
[6] PRL104, 132502 (2010)
Using S-wave KbarN potential
constrained by experimental data.
… KbarN scattering data,
Kaonic hydrogen atom data,
“Λ(1405)” etc.
Recent results of calculation of K-pp and related experiments
Width (KbarNN→πYN) [MeV]
0
20
40
60
80
100
120
140
0
Doté, Hyodo, Weise [1]
(Variational, Chiral SU(3))
-20
-40
Akaishi, Yamazaki [2]
(Variational, Phenomenological)
Wycech,
Green [7]
-60
(Variational, phenomenological,
P-wave)
Ikeda, Sato [4]
-80
(Faddeev, Chiral SU(3))
Exp. : DISTO [6]
(Finalized)
-100
-120
Exp. : FNUDA [5]
-140
[1] PRC79, 014003 (2009)
[2] PRC76, 045201 (2007)
[3] PRC76, 044004 (2007)
[4] PRC76, 035203 (2007)
Shevchenko, Gal, Mares [3]
(Faddeev, Phenomenological)
[5] PRL94, 212303 (2005)
[6] PRL104, 132502 (2010)
Using S-wave KbarN potential
constrained by experimental data.
[7] PRC79, 014001 (2009)
… KbarN scattering data,
Including P-wave KbarN potential,
Kaonic hydrogen atom data,
and other effects.
“Λ(1405)” etc.
Recent results with various calculations of K-pp
B. E.
Γ (mesonic)
Method
KbarN
Int.
Channels
at final step
20 ± 3
40 ～ 70
Variational
Chiral SU(3)
KbarN
AY
47
61
Variational
Phenom.
KbarN
IS
60 ～ 95
45 ～ 80
Faddeev
(AGS)
DHW
SGM
Exp.
FINUDA
DISTO
50～70
90 ～ 110
115±7
67±14
103±3±5 118±8±10
Faddeev
(AGS)
K- absorption,
p+p→K++Λ+p,
Chiral SU(3)
(Separable)
KbarN, πY
Phenom.
(Separable)
KbarN, πY
Λp inv. mass
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
20 ± 3
40 ～ 70
Variational
Chiral SU(3)
KbarN
AY
47
61
Variational
Phenom.
KbarN
IS
60 ～ 95
45 ～ 80
Faddeev
(AGS)
DHW
SGM
50～70
90 ～ 110
Faddeev
(AGS)
Chiral SU(3)
(Separable)
KbarN, πY
Phenom.
(Separable)
KbarN, πY
DHW vs AY
Difference of the used KbarN interactions.
Comparison of AY potential and Chiral-based potential
Coupled channel
Chiral dynamics
AY potential
Weinberg-Tomozawa term derived from
Chiral SU(3) effective Lagrangian
Two poles (double pole);
one couples strongly to KbarN,
KbarN strongly
πΣ
ηΛto πΣ.
KΞ
the other couples
Λ(1405) =
a quasi-bound state of I=0 KbarN
at 1405MeV.
Appears in I=0
KbarN
channel.
Λ(1405) (experimentally observed)
appears in I=0 πΣ-πΣ channel.
I=0 KbarN resonance
@ 1420MeV.
I=0 KbarN resonance
@ 1405MeV.
• Energy independent potential
• No πΣ-πΣ interaction
• Energy dependent potential
• Somewhat strongly attractive
πΣ-πΣ interaction
Comparison of AY potential and Chiral-based potential
I=0 KbarN full scattering amplitude
Quite different
in the sub-threhold
region
Almost same
in the on-shell
region
Recent results with various calculations of K-pp
B. E.
Γ (mesonic)
Method
KbarN
Int.
Channels
at final step
20 ± 3
40 ～ 70
Variational
Chiral SU(3)
KbarN
AY
47
61
Variational
Phenom.
KbarN
IS
60 ～ 95
45 ～ 80
Faddeev
(AGS)
DHW
SGM
50～70
90 ～ 110
Faddeev
(AGS)
Chiral SU(3)
(Separable)
KbarN, πY
Phenom.
(Separable)
KbarN, πY
DHW vs AY
In 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
20 ± 3
40 ～ 70
Variational
Chiral SU(3)
KbarN
AY
47
61
Variational
Phenom.
KbarN
IS
60 ～ 95
45 ～ 80
Faddeev
(AGS)
DHW
SGM
50～70
90 ～ 110
Faddeev
(AGS)
Chiral SU(3)
(Separable)
KbarN, πY
Phenom.
(Separable)
KbarN, πY
DHW vs IS
Although both are based on Chiral SU(3) theory,
results are very different from each other.
• 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))
Variational cal. vs Faddeev
???
Discrepancy between Variational calc. and Faddeev calc.
The KbarN potentials used in both calculations are constrained with Chiral SU(3) theory,
but …
Variational calculation
(DHW)
Faddeev calculation
(IS)
Total B. E. = 20±3 MeV,
Decay width = 40～70 MeV
Total B. E. = 60～95 MeV,
Decay width = 45～80 MeV
A. Doté, T. Hyodo and W. Weise,
Phys. Rev. C79, 014003 (2009)
Y. Ikeda, and T. Sato,
Phys. Rev. C76, 035203 (2007)
Why ?
 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)?
 …???
Variational cal. vs Faddeev
???
Discrepancy between Variational calc. and Faddeev calc.
The KbarNsystem
potentials
used in both
areKbar
constrained
with Chiral SU(3) theory,
Three-body
calculated
withcalculations
the effective
N potential
but …
K
N
Variational calculation
K (DHW)
N
=
EK bar NN
Total B. E. = 20±3 MeV,
Decay width = 40～conserved
70 MeV
N
N
A. Doté, T. Hyodo and W. Weise,
Phys. Rev. C79, 014003 (2009)
K
Faddeev
calculation
π
π
K
(IS)
…
N
N
N
N
+…
Σ E. = 60Σ～95 MeV,
Total B.
Decay width = 45～80 MeV
Y. Ikeda, and T. Sato,
Phys. Rev. C76, 035203 (2007)
A possible reason is
πΣN thee-body dynamics
Y. Ikeda and T. Sato,
PRC79, 035201(2009)
In the variational calculation (DHW),
πΣ channel is eliminated and incorporated into the effective KbarN potential.
Experiments
related to K pp
Experiments related to K-pp
• FINUDA collaboration (DAΦNE, Frascatti)
• K- absorption at rest on various nuclei (6Li, 7Li, 12C, 27Al, 51V)
• Invariant-mass method
p
p
K-p
If it is K-pp, …
Total
binding energy =
Λ
Decay width
=
Strong correlation between
emitted p and Λ (back-to-back)
6  3
115 5  4 MeV
2
67 14
MeV
11

3
Invariant mass of p and Λ
PRL 94, 212303 (2005)
Experiments related to K-pp
• Re-analysis of KEK-PS E549
- K- stopped on 4He target
- Λp invariant mass
Strong Λp back-to-back correlation is confirmed.
Unknown strength is there
in the same energy region as FINUDA.
T. Suzuki et al (KEK-PS E549 collaboration),
arXiv:0711.4943v1[nucl-ex]
• DISTO collaboration
- p + p -> K+ + Λ + p @ 2.85GeV
- Λp invariant mass
- Comparison with simulation data
K- pp???
B. E.= 103 ±3 ±5 MeV
Γ = 118 ±8 ±10 MeV
T. Yamazaki et al. (DISTIO collaboration), PRL104, 132502 (2010)
Dr. Fujioka’s talk
(KEK workshop, 7-9. Aug. 08)
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)
3Hemeasured.
All emitted
particles
will be
E17: Precision
spectroscopy
of kaonic
atom
3d→2p X-rays
--- Spokespersons: R. Hayano (Tokyo), H. Outa (Riken)
4. Summary
and future plan
4. Summary
Kaonic nuclei are exotic system !?
• 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.
• 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 width
dense system with interesting structure…
• However, these properties have not been established and there are some questions.
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
• 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-pp
The 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
Variational
Faddeev
Faddeev
+
+
+
+
Phenom. KbarN
Chiral-based KbarN
Phenom. KbarN
Chiral-based KbarN
B.E. = 47MeV,
B.E. = 20±3MeV,
B.E. = 50～70MeV,
B.E. = 60～95MeV,
Γ= 61MeV
Γ= 40～70MeV
Γ=～100MeV
Γ= 45～80MeV
PRC76, 045201(2007)
PRC79, 014003(2009)
PRC76, 044004(2007)
PRC76, 035203(2007)
Experiment (Unknown object which seems related to K-pp)
FINUDA
DISTO
B.E. = 115MeV,
B.E. = 103MeV,
Γ= 67MeV
Γ= 118MeV
PRL94, 212303(2005)
PRL104, 132502 (2010)
… if it is K-pp
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? )
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???)
Coupled channel Complex Scaling
Direct treatment of πΣN degree, dealing with a resonant state,
based on variational scheme.
Thank you
for your attention!

Resonance poles in the coupled