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Faddeev 計算による K 中間子原子核
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Transcript of Faddeev 計算による K 中間子原子核
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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).
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ContentsContents
Our motivationOur motivation
KNN system with coupled channel KNN system with coupled channel
Numerical resultsNumerical results
Summary and future workSummary and future work
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Our motivationOur motivation
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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)
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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
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KNN systemKNN system
with coupled channelwith coupled channel
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Separable interaction :
Two-body t-matrix :
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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
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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
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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
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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
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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
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Experimental data (total cross Experimental data (total cross section)section)
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(I=1 channel)
Experimental data (total cross Experimental data (total cross section)section)
(I=0 channel)
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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
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NN potential -> 2-term Yamaguchi typeNN potential -> 2-term Yamaguchi type
AttractiveAttractive Repulsive Repulsive corecore
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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, ……)
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Numerical resultsNumerical results
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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
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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
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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
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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)