Current theoretical topics onK-pp quasi-bound state
SNP Meeting @ J-PARCAugust 3, 2015
Yoshinori AKAISHI and Toshimitsu YAMAZAKI
K- + p
MeV -27K =EMeV 04=Γ
1 2 3 r fm0
-50
-200
-300
-400
-500
nuclKU
MeV
Λ(1405)Σ+π
Λ+π
K- + pp
MeV-48K =EMeV61=Γ
1 2 3 r fm0
-50
-200
-300
-400
nuclKU
MeV
H2KΣ+π
Λ+π
K- + 3He
MeV-108K =EMeV02=Γ
1 2 3 r fm0
-50
-200
-300
-400
nuclKU
MeV
H3K
Σ+π
Λ+π
Shrinkage!
-500 -500
N.V. Shevchenko, A. Gal & J. Mares, Phys. Rev. Lett. 98 (2007) 082301E = -55~-70 MeV, Γ = 90~110 MeV
Y. Ikeda & T. Sato, Phys. Rev. C 76 (2007) 035203E = -80 MeV, Γ = 73 MeV
A. Dote, T. Hyodo & W. Weise, Phys. Rev. C 79 (2009) 014003E = -20+-3 MeV, Γ = 40~70 MeV
Y. Akaishi & T. Yamazaki, Phys. Rev. C 65 (2002) 044005T. Yamazaki & Y. Akaishi, Phys. Lett. B 535 (2002) 70
DAΦNE Conf. (1999) , HYP Conf. (2000) ; rejected from Proc.
"Λ(1405) Ansatz" A. Dote et al.
KbarN scattering amplitude
s
T. Hyodo and W. Weise, Phys. Rev. C 77 (2008) 035204
Akaishi-Yamazaki
Chiral
Chiral SU(3) dynamics
1405"ORB": E. Oset, A. Ramos & C. Bennhold, Phys. Lett. B 527 (2002) 99"HNJH": T. Hyodo, S.I. Nam, D. Jido & A. Hosaka, Phys. Rev. C 68 (2003) 018201"BNW": B. Borasoy, R. Nissler & W. Weise, Eur. Phys. J. A 25 (2005) 79"BMN": B. Borasoy, U.G. Meissner & R. Nissler, Phys. Rev. C 74 (2006) 055201
"JOORM": D. Jido, J.A. Oller, E. Oset, A. Ramos & U.G. Meissner, Nucl. Phys. A 725 (2003) 181
1420
The most relevant issue is:
1405 or 1420 ?
Σπ invariant mass from stopped K- on 4HeJ. Esmaili, Y. Akaishi & T. Yamazaki, Phys. Lett. B686 (2010) 23
χ 2 as a function of 1st pole’s M and Γ.
Data : B. Riley et al., Phys. Rev. D 11 (1975) 3065
Λ(1405) from HADESG. Agakishiev et al., Phys. Rev. C 87 (2013) 025201
M. Hassanvand et al., Phys. Rev. C 87 (2013) 055202
PDG
14
Interpretation of the Λ(1405) shift in HADES dataJ. Siebenson & L. Fabbietti, Phys. Rev. C 88 (2013) 055201
c.m.2
21p.s.2
)1405( )()( 1 qmBWemBWCT i += − φΛ
iiiii immm
AmBWΓ+−
= 221)(
Best fit
Coherent sum
Interference between double poles !
1300 1350 1400 1450 1500 1550MM(n) MeV
QF-K
Λ(1405)PDG
I =1
I =0
np
K- n
pK-
D(K-, n) missing mass spectrum calculation
1.0 GeV/c J-PARCE31
np
K- n1.0 GeV/c
p
QF-K
QF-Λ*
K-pp
E15
Useful informationfor
1300 1350 1400 1450 1500
D(K-, n) missing mass spectrum
react-Kpi/d_Kn_Ls1.f
PK- = 1.0 GeV/c
+ 1.1 – I 12.4- 2.4 – I 14.9- 6.3 – I 17.3-10.8 – I 19.5 -15.8 – I 21.6-21.1 – I 23.5-26.9 – I 25.3
E(Λ*) MeV
MM(n) MeV/c2
I =0 onlyo0n =θ
1300 1350 1400 1450 1500
MM MeV/c2
I =0
I =1
QF-K-
IM(Σπ)
o0n =θMissing-mass spectrum of ( ) mπΣnKD - ±,
1360 1380 1400 1420
I =0
I =1
IM(Σπ) MeV/c2
InclusiveI =0 ΣπI =1 Σπ, Λπ
2611
210
31πΣ
2320
31πΣ
2611
210
31πΣ
00
-
=+=−==
=+=−=
=+=+==
+−
+
III
II
III
Missing and invariant mass spectra
np
K- n
Missing massEigenstate of H(Kp-Σπ)εiHE
G+−
=1
On-shell
Green’s function
Singularities appearabove threshold.
Moon-shaped singularityε =0.1 MeV with Δcosθ =0.002
000
000
11000
0
10
1100
0
011
0
)(
)(
TGGGG
TGGVGG
GGGGGG
VGTG
GTGTV
GGTGV
VTGVT
VHHGG
+=
==
−=−
=
−+=
−+=
+=
=−=−
−−
−
−−
−−
Identity
εε
ε iHEi
+−≡
′→0lim ( ) 0=−= EEE HE, ΨΨΨ
Non-eigenstate of H
+Quasi-free K :
Invariant mass (Σπ, ..)00TGG
εiHEG
+−=
00
1
=
Off-shellΣ
π
Σπ invariant-mass spectrum
1300 1350 1400 1450 1500
+ 1.0 – I 12.5-11.0 – I 19.5 -27.0 – I 25.0
E(Λ*) MeV
Formationweight
“Peak shift”
IM(Σπ) MeV/c2
np
K- n1.0 GeV/c
D Λ*Σ
π
I =0 onlyo0n =θ
( ) 00- πΣnKD ,I =0 main,
no I =1
Σπ invariant-mass spectrumDeuteron-size dependence
1300 1350 1400 1450 1500IM(Σπ) MeV/c2
PK- = 1.0 GeV/c
2241
d fm19940 −=−= .a),arexp()r(ψafa →
f = 100101
0.10.010.001
Free
N
1300 1350 1400 1450 1500IM(Σπ) MeV/c2
Shevchenko interactionPhys. Rev. C 85 (2012) 034001
MeV025514062Λ * .i.cM −=
o0n =θMissing-mass spectrum of ( ) mπΣnKD - ±,
I =0
I =1
Deviation spectrum
Total
1300 1350 1400 1450 1500
IM(Σπ) MeV/c2
I =0
I =1
AMY interaction
MeV025014052Λ * .i.cM −=
Deviation spectrum
Total
o0n =θMissing-mass spectrum of ( ) mπΣnKD - ±,
1300 1350 1400 1450 1500
react-Kpi/d_Kn_Ls2D.f
IM(Σπ) MeV/c2
I =0
I =1
AMY interaction
MeV025014202Λ * .i.cM −=
Deviation spectrum
Total
o0n =θMissing-mass spectrum of ( ) mπΣnKD - ±,
IM(Σπ) MeV/c2
o0n =θMissing-mass spectrum of ( ) mπΣnKD - ±,
K-+p
thre
shol
d
Χ 2 -fitting
must be done !Shev1407AMY1405AMY1420
Semi-inclusive neutron spectrum
np
K-
p
n
pK-
p
1.0 GeV/c
T. Hashimoto et al., Prog. Theor. Exp. Phys. 2015, 061D01
KH : T. Koike & T. Harada, Phys. Lett. B 652 (2007) 262
Phys. Rev. C 80 (2009) 055208
Theoretical works
Phase space suppression factor (Mares-Friedman-Gal)for Im Vopt(E)
YJNH: J. Yamagata-Sekihara, D. Jido, H. Nagahiro& S. Hirenzaki, Phys. Rev. C 80 (2009) 045204
NNK EtEV ρ⋅∝ )()(opt
E=0
E=-100 MeV
E=-50 MeV
BE (Width)
r [fm]
[MeV
]
E-indep.
NNKvV ρ⋅∝ eff.opt
E-dep. real part
E-dep. imaginary part
K-
NN
1
2 3
43ˆ,
41ˆ NK1
12NK0
12ττττ rrrr
+=
−= == II PP
Variational wave function of K-pp
( )[ ] ( ) ( ) ⎥⎦
⎤⎢⎣
⎡+−+== 3
1,1213
0,1213
0,021 3
231
41
432/1 nNKpNKpNKT
Λ*p
ATMS Amalgamation of Two-body correlations into Multiple Scattering process
{ } { }[ ] 2/1ˆ)(ˆ)()()()()(ˆ)(ˆ)( 13131
103131
023NN123123NN
11212
101212
0 =+++=Ψ ======== TPrfPrfrfrfrfrfPrfPrf IIIIIIII
{ } { }{ } { }2
fmMeV1
NK
2fmMeV
0NK
)66.0/(exp105175)(
)66.0/(exp83595)(
rirv
rirvT
T
−−−=
−−−==
=
{ } { } { }2fmMeV
2fmMeV
2fmMeVNN )5.2/(exp5)942.0/(exp270)447.0/(exp2000)( rrrrv −−−−−=
{ } 0=− ΨΨλΨΨδ Hf
Euler-Lagrange equation
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Density distributions of Kbar-N
r fm
Kbar-N in Λ(1405)
Kbar-N in K-ppx0.625
I = 0
I = 1
KI =0
Λ*
N N
K
Λ*
NNI =0
I =0: 0.5x(1+0.25)=0.625I =1: 0.5x0.75= 0.375
I =0; 0.25I =1; 0.75
Dynamicallyfavored
)(2 rr ρ
T. Yamazaki and Y. Akaishi, Phys. Rev. C 76 (2007) 045201
Adiabatic p-p potential in K-pp
-200
-150
-100
-50
0
50
100
150
0.0 0.5 1.0 1.5 2.0 2.5 3.0
R [fm]
[MeV fm2]
1.0 2.0 3.0
Normal nuclear force : virtual meson exchange
R2 V(R)
pp K-
Super-strong nuclear force : real Kbar migration
Super strong / Normal ~ 4.1− volume integral ratio −
pp
T. Yamazaki & Y. Akaishi,Proc. Japan Academy, B 83 (2007) 144Λ*N system with meson exchange
A. Arai, M. Oka & S. Yasui, Prog. Theor. Phys. 119 (2008) 103
K-pp quasi-bound state
pp K-
1.90 fmrms distance
1.36 f
m
2002
2007
np
K-
p
n
pK-
p
1.0 GeV/c
np
K-
p
n
Λ*p
T. Hashimoto
pn=1000 MeV/cpn=1494 MeV/c
QF-Λ
MeV392423HeK =+ cME
2nMeV
2nin
2miss )-1000()( cpEEcM −−=
Quasi-freeY’s in E15 missing mass spectrum
2812 MeV for pn=0
“n-spectator window”
Δπ π
MM GeV/c2
pn=1254 MeV/c
"n-knockout window"
p
Y
1000 MeV/c - pn
K-
p0
QF-Λ1405
QF-Σ
2N absorption
2150 2200 2250 2300 2350 2400 2450 2500
Missing mass spectrum of Λ*-p systemo0n =θ
MM MeV/c2
DISTO int.
YA int.
No Λ*p int.
Without Λ* width
With Λ* widthof 50 MeV
Λ*+
p
Σ +π
+ p
“QF”-Λ*
K-+
p +
p
QF- KX 1/5
nKn""K +→+ −−
nKp""K 0 +→+−
2150 2200 2250 2300 2350 2400 2450 2500MM MeV/c2
Without Λ* width
Λ*+
p
Σ +π
+ p
K-+
p +
p
o0n =θ
o20n =θ
o40 o60
DISTO int.
With Λ* widthof 50 MeV
All the integrated spectra
are normalized to unity.
o40o0n =θ
o60
psQF Λ* is obtained by 3N absorption calculation!
observedK-
Y
pp
nn
pseudoQF-Y
3N absorption
pnθ
oo 200n ~=θ
Pseudo-QF Λ*
2150 2200 2250 2300 2350 2400 2450 2500IM. [MeV/c2]
2150 2200 2250 2300 2350 2400 2450 2500
Λ* w
idth
.
Pseudo-QF Λ* and K-pp
psQF Λ*
IM. [MeV/c2]react-Kpi/h_Kn_Mod5B.f
np
K-
p
n
p
DIS
TO in
t.
o0n =θ
Λ* w
idth
DIST
O in
t.
Λ∗
K-pppsQF Λ*
DISTOT. Yamazaki et al.,Phys. Rev. Lett.
104 (2010) 132502
MeV-48K =EMeV61=Γ
MeV-103K =EMeV118=Γ
Theor.Yamazaki-Akaishi
17% enhancedKbarN interaction
E27@J-PARCY. Ichikawa et al.,
Prog. Theor. Exp. Phys. 2015, 021D01
2150 2200 2250 2300 2350 2400 2450 2500MM [MeV/c2]
ΓΛ∗= 50 MeVYA int.
ΓΛ∗= 50 MeVDISTO int.
ΓΛ∗= 0No Λ*p int.
ΓΛ∗= 50 MeVNo int.
Λ*+
p
Σ +π
+ p
Missing mass spectrum of Λ*-p systemfor E27@J-PARC
DISTOYA%17
→S. Maeda, Y. Akaishi & T. Yamazaki,
Proc. Jpn. Acad. B 89 (2013) 418
cp /MeV5.100,πpΛ p =+→ −
cp /MeV0.189,πpΣ p0 =+→+
cp /MeV7.282,pΛpΣ p0 =+→+
cp /MeV0.476,pΛKpp pDISTO =+→
ΣΝ-ΛΝ conversion
"K-pp"= Λ*-p QBS
Coincidenceby T. Nagae et al.
K-
K+
pp
K-pp structure
Which isof ground?
K-
K+
Λ*
p
p
Λ*- p structure
n p
π+
K-pp = Λ*-pwith real Kbar migration
(17% enhanced int.)
2200 2300 2400
Preliminary
!
E27@J-PARCY. Ichikawa et al.,
Prog. Theor. Exp. Phys. 2015, 021D01
3.87.7 ≤≤ θ
QF-Σ∗+
Simulation by Y. Ichikawa
No width
A stable particle withLorentzian mass distribution
An unstable particlewith decay width
p*Σ*Σ HHH +=
p*Σ*Σ*ΣΣQF T)iWE(H * ++⎯⎯ →⎯
⎥⎦
⎤⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
+−−=−∝
επδ
iHEIm)HE(S
XX
11
3.87.7 ≤≤ θ
QF-Λ∗
Mass distribution
Decay widthHADES fit
Simulation by Y. Ichikawa
Decay width
~15 MeV
K-pp quasi-bound state
pp K-
1.90 fmrms distance
1.36 f
mDISTO
0
-40
-80
-120
-160
-200
-240
[MeV]
K-pp L=0ground state
(Λ*-p or K--pp)
K--pp L=1excited state
Λ*-p L=1excited state
K- + p + pΛ*+ p
Stronger KN attraction
2002
2007
2150 2200 2250 2300 2350 2400 2450 2500
L= 0
4≤L
12≤L
2≤L
Angular-mom. decomposition of the Λ*-p pair
QF Λ*
react-piK/D_piK_Mod1B.f
n
π+
p
K+
Λ*
1.7 GeV/c
L8≤L
1≤L
L= 0
MM [MeV/c2]
Λ*+
p
Σ +π
+ p No Λ*p int.
DISTO Λ*p int.
~40 MeV
Λ*
K-
p
Concluding remarks
The Λ*= Λ(1405) plays an essential role in forming "anti-Kaonic Nuclear Clusters",the simplest one of which is
K-pp = (K-p)−p = Λ*−p.
The Λ*−p structure interacting with "super-strong force" due to Kbar migration provides a possible explanation of recent J-PARC data on K-pp.
[ ]11 −⊗Σ −+ ZA
[ ]ZA 1−⊗Σ0
[ ]11 +⊗Σ − ZA-
[ ]ZA 1−⊗Λ
[ ]ZA 2−⊗ΛΛ
[ ]ZA 1−⊗Ξ0
[ ]11 +⊗Ξ − ZA-
[ ]1+⊗π ZA-
[ ]ZA [ ]1+ZA [ ]2+ZA
S=0 nucleiS=-1S=-2
500
400
300
200
100
0
Excitation energy(MeV)
)K,K( - +
)K,(),,K( -- ++ ππ)K,(),,K( - ++− ππ
)N,K( -
[ ]ZA⊗0K[ ]1+⊗ ZA-K
Nuclei of 2nd generationThe s quark combined with ubar
plays a leading role in forming a dense and cold nucleus.
(p,K+),
Yamazaki diagram
A new paradigm of nuclear physics“Swan Nuclear Physics”
Nuclei of
1st generation