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Faddeev 計算による K 中間子原子核. based on PRC76, 035203 (2007). 池田 陽一,佐藤 透(阪大理・原子核理論). 原子核・ハドロン物理:横断研究会@ KEK 2007 年 11 月 19 日 -21 日. Contents Our motivation KNN system with coupled channel Numerical results Summary and future work. Our motivation. Akaishi and Yamazaki, PRC65(2002). - PowerPoint PPT Presentation
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池田 陽一,佐藤 透(阪大理・原子核理論)池田 陽一,佐藤 透(阪大理・原子核理論)
FaddeevFaddeev 計算による計算による KK 中間子原子核中間子原子核
原子核・ハドロン物理:横断研究会@ KEK 2007 年 11 月 19 日 -21日
based on PRC76, 035203 (2007).
ContentsContents
Our motivationOur motivation
KNN system with coupled channel KNN system with coupled channel
Numerical resultsNumerical results
Summary and future workSummary and future work
Our motivationOur motivation
Kaon absorption??(Magas et al.)
Kaon absorption??(Magas et al.)
Akaishi and Yamazaki, Akaishi and Yamazaki, PRC65(2002)PRC65(2002)
Agnello et al., PRL94(2005)Agnello et al., PRL94(2005)
Our Investigation We investigate the possible We investigate the possible
[KNN][KNN](I=1/2,J=0)(I=1/2,J=0) 3-body resonance 3-body resonance state.state.
PP
K-
K-pp system
S=-1, B=2, Q=+1Jπ=0-
(3-body s-wave state)
We consider s-wave state.We consider s-wave state. We expect We expect most strong attractive interactionmost strong attractive interaction in this in this configure.configure.
L=0 (s-wave interaction)
Λ(1405)
-> the resonance in the KN-πΣ coupled channel system
It will be very important It will be very important to to take into account the dynamics of KN-take into account the dynamics of KN-πΣπΣ system system in order to investigate whether KNN resonance may exist. in order to investigate whether KNN resonance may exist.
-> Coupled channel Faddeev equation-> Coupled channel Faddeev equation
Solve
-> KNN 3-body resonance-> KNN 3-body resonanceFind
KNN systemKNN system
with coupled channelwith coupled channel
Separable interaction :
Two-body t-matrix :
例えば、一部のダイアグラムは…例えば、一部のダイアグラムは…
=
Kernel Kernel
t
t
g τ g
g τ g
Formal solution of AGS Formal solution of AGS equationequation
Fredholm type kernel
Eigenvalue equation for Fredholm kernelEigenvalue equation for Fredholm kernel
Formal solution for 3-boby amplitudeFormal solution for 3-boby amplitude
3-body resonance pole at W3-body resonance pole at Wpolepole
AGS AGS EquationEquation
The The KNNKNN -π-π YN YN resonanceresonance
: 1-particle exchange term: 1-particle exchange term
: 2-body scattering term: 2-body scattering term
KN-KN-ππY(Y(I=0, 1)I=0, 1)
ππN(I=1/2,3/2)N(I=1/2,3/2)
NN scatteringNN scattering
(Anti-symmetrized)(Anti-symmetrized)
ππ
Σ,ΛΣ,Λ
NN
NNKK NN
NN
KK
NN
ππΣ,ΛΣ,Λ
NN ππ
Σ,ΛΣ,ΛNN
本研究での枠組み:本研究での枠組み: KNKN 相互作用に注目相互作用に注目
Meson-Baryon Meson-Baryon scatteringscattering
Baryon-Baryon Baryon-Baryon scatteringscattering
φ : Meson field , B : Baryon field
2-body Meson-Baryon Potential2-body Meson-Baryon Potential
Chiral effective LagrangianChiral effective Lagrangian
Coupling Coupling const.const.
Form Form factorfactor
S-wave separable potentialS-wave separable potential
Parameter fit (KN interaction)Parameter fit (KN interaction)
Our parameters -> cut-off of dipole form factor
Fit ① : Scattering length given by MartinFit ① : Scattering length given by Martin
Fit ② : Fit ② : ΛΛ(1405) pole position given by Dalitz(1405) pole position given by Dalitz
Experimental data (total cross Experimental data (total cross section)section)
(I=1 channel)
Experimental data (total cross Experimental data (total cross section)section)
(I=0 channel)
πN scattering (S11 and S31)πN scattering (S11 and S31)
S11 phase shift
S31 phase shift
Exp. Exp.
Our scattering Our scattering lengthlength
Our scattering Our scattering lengthlength
NN potential -> 2-term Yamaguchi typeNN potential -> 2-term Yamaguchi type
AttractiveAttractive Repulsive Repulsive corecore
AGS equation for 3-body amplitude
K, N,π KN-π Y , NN, πN
Eigenvalue equation for Fredholm kernel
Pole of 3-body Pole of 3-body amplitudeamplitude
WWpp = -B –iΓ/2 = -B –iΓ/2
Similar to πNN, ηNN, K-d analyses. (Matsuyama, Yazaki, ……)
Numerical resultsNumerical results
The pole trajectories of three-body systemThe pole trajectories of three-body system
a:KN onlya:KN onlyb:+NNb:+NNc:+c:+ππ YY in in ττdd:π :π exchangeexchange
KNN physicalKNN physicalπΣπΣN unphysicalN unphysical energy plane energy plane
Fit to Dalitz pole
The three-body resonance poleThe three-body resonance pole
Martin
-1.80-i0.68 fm
-1.70-i0.68 fm
-1.60-i0.68 fm
-1.70-i0.59 fm
-1.70-i0.78 fm
KNN physicalKNN physicalπΣπΣN unphysicalN unphysical energy plane energy plane
KK--pppp 研究の現状研究の現状
Shevchenko et al.Shevchenko et al.
Akaishi, YamazakiAkaishi, Yamazaki
MartinMartin-1.70-i0.68 -1.70-i0.68 fmfm DalitzDalitz
KNN physicalKNN physicalπΣπΣN unphysicalN unphysical energy plane energy planeNishikawa, KondoNishikawa, Kondo
Dote et Dote et al.al.
DAΦNEDAΦNE
The pole position strongly depends on KN interaction. -> Structure dependence on Λ(1405) Arai, Oka, Yasui reaction
We solve 3-body equation directly.We solve 3-body equation directly. We can find the resonance pole We can find the resonance pole
in the in the KNN physicalKNN physical and and ππ YY N unphysicalN unphysical energy energy plane.plane.
SummarySummary
In the futureIn the future
Effects of KNN --> Y N (p-wave interaction)