Transcript K bar N - 東京大学駒場原子核理論研究室

K-中間子原子核、最近の状況
Prototype of kaonic nuclei “K-pp”
1. Introduction
•
•
KEK Theory center J-PARC branch /IPNS
Akinobu Doté
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)-based KbarN potential
T. Hyodo (TITech),
W. Weise (TU Munich)
3. Current status of the K-pp study
4. Experiments related to Kbar nuclear physics
5. Summary and future plan
東大駒場セミナー
’12.05.23 @ 東京大学駒場キャンパス
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
What is Kaonic nucleus?
Hypernuclei…
d
u
s
Hyperon
baryon = qqq
Nucleus
Strangeness is introduced
through baryons.
What is Kaonic nucleus?
Strangeness is introduced
through mesons …
ubar
s
K- meson
meson = qqbar
quark (q) and
anti-quark (qbar) pair
Nucleus
Kaonic nuclei !
Actors in Kbar nuclei
Leading actors
1435Mc2 [MeV ]
1405
p
n
N
1325
938
940
Energy [MeV]
0
K
Key person
498
K

494
K1250

1
1
J  , I 
2
2
J   0 , I 
p + KΛ(1405)
Baryon
uud
udd
1
Meson
Λ
+
π
2
ds
us
Σ+π
Σ
1190
 1115 1406
1
J  , I 0 Λ
2

uds
Baryon
Excited state of Λ
Supporting players

1116
1
J  , I 0
2

 :1189, 0:1193,
940
 :1197
1
J  , I 1
2
p,n
Baryon
J   0 , I  1
Meson
,0
 ,0
 :140, 0:135


Baryon
uds
 : uus, 0: uds,  : dds
 : ud , 0:


1
uu  dd ,  : du
2
Mysterious state; Λ(1405)
Quark model prediction … calculated as 3-quark state
Λ(1405) can’t be well reproduced
as a 3-quark state!
calculated Λ(1405)
observed Λ(1405)
q
qq
N. Isgar and G. Karl, Phys. Rev. D18, 4187 (1978)
Actors in Kbar nuclei
Leading actors
1435Mc2 [MeV ]
1405
p
n
N
1325
938
940
Energy [MeV]
0
K
Key person
498
K

494
K1250
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
q
qq
1116
 :1189, 0:1193,
940
 :1197
 :140, 0:135
1
J  , I 0
2

u
Baryon
ud
1
J  , I 1
2
p,n
Baryon
J   0 , I  1
Meson

ubar
s
uds
 : uus, 0: uds,  : dds
 : ud , 0:


1
uu  dd ,  : du
2
Actors in Kbar nuclei
Leading actors
1435Mc2 [MeV ]
1405
p
n
N
1325
938
940
Energy [MeV]
0
K
Key person
498
K

494
K1250

1
1
J  , I 
2
2
p + KΛ(1405)
Baryon
uud
udd
1
Meson
Λ
+
π
2
Σπ channel
is open
ds
us
Σ+π
J   0 , I 
at about 100 MeV below
Σ
the Proton-K- threshold.
1190
 1115 1406
1
J  , I 0 Λ
2

uds
Baryon
Excited state of Λ
Supporting players

1116
1
J  , I 0
2

 :1189, 0:1193,
940
 :1197
1
J  , I 1
2
p,n
Baryon
J   0 , I  1
Meson
,0
 ,0
 :140, 0:135


Baryon
uds
 : uus, 0: uds,  : dds
 : ud , 0:


1
uu  dd ,  : du
2
Interests of Kaonic nuclei
Kaonic nucleus
Proton
K-
=
K-
• Nuclear structure change.
Highly dense state.
if the interaction is so attractive…
Λ(1405)
 Deeply
• Self-bound
Kbar-nuclear system
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
3HeK-
… 100MeV binding with a narrow width of 20MeV.
(a simple model calculation)
Deeply bound kaonic nuclei !
• A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, 044313 (2004)
Systematic study of light kaonic nuclei (3HeK- to 11CK-) with
AMD + G-matrix (effective NN potential ) + AY KbarN potential
shows their interesting properties…
① Deeply bound
② Drastic change
and Dense
of structure
ppnK pppK pppnK 6
Be K 9
BK 11
CK -
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
bar
K N 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.
Kbar
FKN1
N
FKN2
FN N
N
J   0 , T  1/ 2, TZ  1/ 2
L  0, SNN  0


2
(ij )

Fij  C exp ba r i  r j 


a
(ij )
a
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  mK  B  K 
s  N
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  MN  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
“Corrected”,
s  MN  mK  B  K 
Kbar
K-pp中の二核子は普通の原子核の断片！
1.97 fm
通常核密度に対応していると思える。
N
N
2.21 fm
NN distance in normal nuclei ～ 2 fm
Size of deuteron
～ 4 fm
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  MN  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  MN  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  MN  mK  B  K 
KbarN potential based on “HNJH”
Structure of K-pp
I=0 KbarN
“Corrected”,
“Λ(1405)” as I=0 KbarN
calculated with this potential
I=1 KbarN
1.82 fm
2.33 fm
l 2 = 0.4
l 2  1.9
s  MN  mK  B  K 
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  MN  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. Current status of
the K pp study
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
Shevchenko, Gal, Mares [3]
(Faddeev, Phenomenological)
Ikeda, Sato [4]
(Faddeev, Chiral SU(3))
-100
-120
Exp. : FNUDA [5]
if it is a K-pp bound state.
-140
[1] PRC79, 014003 (2009)
[2] PRC76, 045201 (2007)
[3] PRC76, 044004 (2007)
[4] PRC76, 035203 (2007)
[5] PRL94, 212303 (2005)
[6] PRL104, 132502 (2010)
Exp. : DISTO [6]
if it is a K-pp bound state.
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))
Shevchenko, Gal, Mares [3]
(Faddeev, Phenomenological)
-100
-120
Exp. : FNUDA [5]
if it is a K-pp bound state.
-140
[1] PRC79, 014003 (2009)
[2] PRC76, 045201 (2007)
[3] PRC76, 044004 (2007)
[4] PRC76, 035203 (2007)
[5] PRL94, 212303 (2005)
[6] PRL104, 132502 (2010)
Exp. : DISTO [6]
if it is a K-pp bound state.
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
A possible reason is
πΣN thee-body dynamics
Y. Ikeda and T. Sato,
PRC79, 035201(2009)
Three-body system calculated with the effective KbarN potential
K
K
N
N
=
K
EKbar NN
N
π
Σ
…
π
Σ
K
N
conserved
N
N
N
In the variational calculation (DHW),
πΣ channel is eliminated and incorporated into the effective KbarN potential.
N
+…
4. Experiments
related to
bar
K nuclear physics
Ｋ原子核に関係する実験
 Ｋ原子 (Kaonic atom)
• Kaonic 4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570)
S. Okada et. al., Phys. Lett. B653, 387 (2007)
• Kaonic 3He atom, 2pレベルシフト (3d→2p X線測定)
@ J-PARC (E17, DAY-1)
• Kaonic hydrogen atom, 1sレベルシフト @ DEAR group, DAΦNE,
G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)
Frascati National Laboratories
• Kaonic hydrogen, deuterium @ SIDDHARTA group
M. Bazzi et al., Phys. Lett. B704, 113 (2011)
 Λ(1405)
πΣ invariant mass測定
γ + p → K+ + Λ(1405), Λ(1405) → π Σ
• LEPS / SPring-8
J. K. Ahn, Nucl. Phys. A835, 329 (2010)
K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010)
• CLAS / JLab
π-Σ+, π0Σ0, π+Σ- が全て押さえられた
Ｋ原子核に関係する実験
 Ｋ原子 (Kaonic atom)
• Kaonic 4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570)
S. Okada et. al., Phys. Lett. B653, 387 (2007)
• Kaonic 3He atom, 2pレベルシフト (3d→2p X線測定)
@ J-PARC (E17, DAY-1)
• Kaonic hydrogen atom, 1sレベルシフト @ DEAR group, DAΦNE,
G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)
Frascati National Laboratories
• Kaonic hydrogen, deuterium @ SIDDHARTA group
M. Bazzi et al., Phys. Lett. B704, 113 (2011)
 Λ(1405)
πΣ invariant mass測定
γ + p → K+ + Λ(1405), Λ(1405) → π Σ
• LEPS / SPring-8
J. K. Ahn, Nucl. Phys. A835, 329 (2010)
K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010)
• CLAS / JLab
π-Σ+, π0Σ0, π+Σ- が全て押さえられた
DEAR exp. for kaonic hydrogen atom
G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)
Kaonic hydrogen atom, 1sのレベルシフト
@ DEAR Collaboration, DAΦNE, Frascati National Laboratories
cf) KEK exp.
M.Iwasaki et al., Phys. Rev. Lett. 78, 3067 (1997)
シフトの符号は同じだが、ＫＥＫの前回の実験（ＫｐＸ）と重ならない
KEK exp.
DEAR
Coupled channel chiral dynamics
(Chiral unitary model) で
DEARの結果を合わすのには苦労する。
かろうじてギリギリ合わせられる程度。。。
B. Borasoy et al., Phys. Rev. Lett. 94, 213401 (2005)
SHIDDARTA exp. for kaonic hydrogen atom
M. Bazzi et al., Phys. Lett. B704, 113 (2011)
Kaonic hydrogen atom, 1sのレベルシフト
@ SHIDDARTA Collaboration, DAΦNE, Frascati National Laboratories
K-p散乱長が精密に決定
理論計算にとって重要な
インプットに強い拘束条件
KbarN subthresholdでの
散乱振幅の振る舞い、
Λ(1405)のポールの位置、
が制限される。
KEK実験（ＫｐＸ）とコンシステントな結果
Y. Ikeda, T. Hyodo and W. Weise,
Phys. Lett. B706, 63 (2011)
Ｋ原子核に関係する実験
 Ｋ原子 (Kaonic atom)
• Kaonic 4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570)
S. Okada et. al., Phys. Lett. B653, 387 (2007)
• Kaonic 3He atom, 2pレベルシフト (3d→2p X線測定)
@ J-PARC (E17, DAY-1)
• Kaonic hydrogen atom, 1sレベルシフト @ DEAR group, DAΦNE,
G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)
Frascati National Laboratories
• Kaonic hydrogen, deuterium @ SIDDHARTA group
M. Bazzi et al., Phys. Lett. B704, 113 (2011)
 Λ(1405)
πΣ invariant mass測定
γ + p → K+ + Λ(1405), Λ(1405) → π Σ
• LEPS / SPring-8
J. K. Ahn, Nucl. Phys. A835, 329 (2010)
K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010)
• CLAS / JLab
π-Σ+, π0Σ0, π+Σ- が全て押さえられた
KEK E570 for kaonic 4He atom
S. Okada et. al., Phys. Lett. B653, 387 (2007)
Kaonic 4He atom, 2pのレベルシフト
3d→2p X線測定
@ KEK, E570
“Kaonic helium puzzle”
理論の予言がほぼ0eVに対して、
過去の実験ではシフトは平均-43 eV
S. Hirenzaki et al.,
Phys. Rev. C61, 055205 (2000)
シフトは 0 eV とconsisitent
パズルは解けた！
J-PARC for kaonic 3He atom
Kaonic 3He atom, 2pのレベルシフト
3d→2p X線測定
Kaonic 4He atom, 2pのレベルシフト
…ほぼ 0 eV と確定
@ J-PARC, E17 DAY-1
S. Okada et. al., Phys. Lett. B653, 387 (2007)
赤石氏の計算
Y. Akaishi, Proceedings of EXA’05,
Austrian Academy of Sciences press, Vienna, 2005, p.45
＋
KbarN potentialの強度が
二つの領域に絞られた。
※特定領域研究「ストレンジネスで探るクォーク多体系」研究会2007 での岡田氏のスライドより引用
さらに3Heでシフトが測定されることで
KbarN potentialの強度に絞りを
掛けることが期待できる。
Ｋ原子核に関係する実験
 Ｋ原子 (Kaonic atom)
• Kaonic 4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570)
S. Okada et. al., Phys. Lett. B653, 387 (2007)
• Kaonic 3He atom, 2pレベルシフト (3d→2p X線測定)
@ J-PARC (E17, DAY-1)
• Kaonic hydrogen atom, 1sレベルシフト @ DEAR group, DAΦNE,
G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)
Frascati National Laboratories
• Kaonic hydrogen, deuterium @ SIDDHARTA group
M. Bazzi et al., Phys. Lett. B704, 113 (2011)
 Λ(1405)
πΣ invariant mass測定
γ + p → K+ + Λ(1405), Λ(1405) → π Σ
• LEPS / SPring-8
J. K. Ahn, Nucl. Phys. A835, 329 (2010)
K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010)
• CLAS / JLab
π-Σ+, π0Σ0, π+Σ- が全て押さえられた
Λ(1405) - πΣ invariant mass 測定 •LEPS / Spring-8
• CLAS / Jefferson Laboratory
J. K. Ahn, Nucl. Phys. A835, 329 (2010)
K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010)
p (γ, K+ π) Σ at Eγ = 1.5-2.4GeV
Charged πΣを測定
γ + p → K+ + Λ(1405), Λ(1405) → π Σ
三つの異なる電荷状態が抑えられた
理論
ピークの順番が理論
(chiral unitary)と違う？
Highest peak
実験： Σ+ π理論： Σ- π+
Experiments
for
K pp search
Ｋ原子核に関係する実験
 Ｋ原子核 (Kaonic nuclei)
K-pp search
• K- absorption on various targets / Invariant mass Λp
@ FINUDA collaboration, DAΦNE, Frascati National Laboratories
M. Angello et. al., Phys. Rev. Lett. 94, 212303 (2005)
• Heavy ion collision (?+?) / Invariant mass Λp
@ FOPI group, GSI
N. Herrmann, Proc. of EXA’05, Austrian Academy of Sciences Press, (2005), p73
• Anti-proton annihilation on 4He / Invariant mass Λp
@ OBELIX group, CERN
G. Bendiscioli et. al., Nucl. Phys. A789, 222 (2007)
• p+p -> K+ + Λ + p / Invariant mass Λp
@ DISTO group, SATURNE, Saclay
T. Yamazaki et. al., Phys. Rev. Lett. 104, 132502 (2010)
K-ppn search
• 4He (Stopped K-, n), 4He (Stopped K-, p) / Mssing mass
Search for
heavier
kaonic nuclei
• 16O (in-flight K-, n) 15OK- / Missing mass @ AGS, BNL
@ KEK-E471, E549
M. Sato et. al., Phys. Lett. B659, 107 (2008),
H. Yim et. al., Phys. Lett. B688, 43 (2010)
•
12C
(in-flight
K -,
T. Kishimoto et. al., Nucl. Phys. A754, 383 (2005)
n or p) / Missing mass @ KEK-E548
T. Kishimoto et. al., Prog. Theor. Phys. Suppl. 168, 573 (2007)
Ｋ原子核に関係する実験
 Ｋ原子核 (Kaonic nuclei)
K-pp search
• K- absorption on various targets / Invariant mass Λp
@ FINUDA collaboration, DAΦNE, Frascati National Laboratories
M. Angello et. al., Phys. Rev. Lett. 94, 212303 (2005)
• Heavy ion collision (?+?) / Invariant mass Λp
@ FOPI group, GSI
N. Herrmann, Proc. of EXA’05, Austrian Academy of Sciences Press, (2005), p73
• Anti-proton annihilation on 4He / Invariant mass Λp
@ OBELIX group, CERN
G. Bendiscioli et. al., Nucl. Phys. A789, 222 (2007)
• p+p -> K+ + Λ + p / Invariant mass Λp
@ DISTO group, SATURNE, Saclay
T. Yamazaki et. al., Phys. Rev. Lett. 104, 132502 (2010)
K-ppn search
• 4He (Stopped K-, n), 4He (Stopped K-, p) / Mssing mass
Search for
heavier
kaonic nuclei
• 16O (in-flight K-, n) 15OK- / Missing mass @ AGS, BNL
@ KEK-E471, E549
M. Sato et. al., Phys. Lett. B659, 107 (2008),
H. Yim et. al., Phys. Lett. B688, 43 (2010)
•
12C
(in-flight
K -,
T. Kishimoto et. al., Nucl. Phys. A754, 383 (2005)
n or p) / Missing mass @ KEK-E548
T. Kishimoto et. al., Prog. Theor. Phys. Suppl. 168, 573 (2007)
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
K-
p
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)
What is the object observed experimentally?
• DISTO collaboration
A bound state of K-pp,
or another object such as πΣN ???
Only what we can say from only this spectrum is that
“There is some object with B=2, S=-1, charge=+1”…
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)
J-PARC will give us
lots
at K1.8BR
beamof
line
interesting data!
1.8GeV/c
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
Dr. Fujioka’s talk
(KEK(Riken)
workshop, 7-9. Aug. 08)
--- Spokespersons: R. Hayano (Tokyo), H. Outa
Invariant
mass
J-PARC will give us
lots
at K1.8BR beamof
spectroscopyline
interesting data!
1.8GeV/c
Missing
mass
E15: A search for deeply bound kaonic nuclear
states
by 3He(inflight K-, n) reaction
spectroscopy
--- Spokespersons: M. Iwasaki (RIKEN), T. Nagae
(Kyoto)
E17: Precision spectroscopy of kaonic 3He atom
All emitted
particles
3d→2p
X-rays will be measured. Dr. Fujioka’s talk
(KEK(Riken)
workshop, 7-9. Aug. 08)
--- Spokespersons: R. Hayano (Tokyo), H. Outa
「完全実験」
Preceding E15,
E27 experiment will be performed in June.
E27: d (π+, K+) K-pp at K1.8 beam line
Missing mass measured.
K+
π+
d
n
p
Λ(1405)
Kp
p
5. Summary
and
Future plan
5. 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 = 2.0fm ≒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.
5. 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)
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? )
5. Future plan
Studied with coupled-channel Complex Scaling Method
Direct treatment of πΣN degree in K-pp.
Deal with a resonant state, based on variational scheme.
• πΣN dynamics as pointed out by Dr. Ikeda and Prof.Sato.
• The signal position of DISTO experiment … very close to π+Σ+N threshold
Go to charm sector!
K- (subar)
D0 (cubar)
494 MeV
1870 MeV
Do D-mesic nuclei exist
such as DNN analog to KbarNN???
M. Bayar, C. W. Xiao,
T. Hyodo, A. Dote, M. Oka, E. Oset,
arXiv:1205.2275 [hep-ph]
Thank you
for your attention!
http://www-conf.kek.jp/hadron1/JPARC-hadsalon/