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Three-body resonance in the KNN-π Ｙ N coupled system
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Y. Ikeda and T.Sato (Osaka Univ.) Three-body resonance Three-body resonance in the KNN-π in the KNN-π Ｙ Ｙ N coupled N coupled system system Table of contents 1. Motivation 2. Formalism (3-body equation) 3. Results (KNN resonance state) 4. Summary
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Three-body resonance in the KNN-π Ｙ N coupled system. Table of contents 1. Motivation 2. Formalism (3-body equation) 3. Results (KNN resonance state) 4. Summary. Y. Ikeda and T.Sato (Osaka Univ.). 1. Our Motivation. Kaon absorption?? (Magas et al.). Λ(1405). K - pp system. - PowerPoint PPT Presentation
Transcript of Three-body resonance in the KNN-π Ｙ N coupled system
Y. Ikeda and T.Sato (Osaka Univ.)
Three-body resonanceThree-body resonancein the KNN-πin the KNN-π ＹＹ N coupled N coupled systemsystem
Table of contents
1. Motivation
2. Formalism (3-body equation)
3. Results (KNN resonance state)
4. Summary
Table of contents
1. Motivation
2. Formalism (3-body equation)
3. Results (KNN resonance state)
4. Summary
Kaon absorption??(Magas et al.)
Kaon absorption??(Magas et al.)
1. Our Motivation1. Our Motivation
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
φ : Meson field , B : Baryon field
2-body Meson-Baryon Potential2-body Meson-Baryon PotentialChiral effective LagrangianChiral effective Lagrangian
2. Formalism2. Formalism
The The ＫＮＮＫＮＮ -πΣ-πΣ Ｎ Ｎ resonanceresonance
: 1-particle exchange term: 1-particle exchange term
: 2-body scattering term: 2-body scattering term
ＫＮＮＫＮＮ -π-π ＹＮ 共鳴状態を理解するための全体の目ＹＮ 共鳴状態を理解するための全体の目標標本研究での枠組み本研究での枠組み ->KN interaction ->KN interaction に注目に注目
KN-KN-ππY(Y(I=0, 1)I=0, 1)
ππN(I=1/2,3/2)N(I=1/2,3/2)NNNN 散乱散乱
反対称化を考慮反対称化を考慮
π
Σ
Ｎ
Parameter fitParameter fit
-> cut-off of dipole form factor
fit : Martin’s analysis and Kaonic hydrogen datafit : Martin’s analysis and Kaonic hydrogen data
Our parameterOur parameter
Non relativistic
RelativisticI=0 (-1.70 + i0.68 fm)KN =946 MeVπΣ=988 MeV------------------------I=1 (0.72 + i0.59 fm)KN =920 MeVπΣ=960 MeVπΛ=640 MeV
I=0 (-1.70 + i0.68 fm)KN =1095 MeVπΣ=1450 MeV------------------------I=1 (0.68 + i0.60 fm)KN =1100 MeVπΣ=850 MeVπΛ=1250 MeV
ππN scattering (S11 and S31)N scattering (S11 and S31)
Rel.
Non-rel.
Rel.
Non-rel.
-> Fit to the scattering length and phase shift.
Phys. Lett. B 469 (1999) 25.
(S11) (S31)
NN potential -> 2-term Yamaguchi typeNN potential -> 2-term Yamaguchi type
Phys. Rev. 178 (1969) 1597.
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, ……)
spectator energyspectator energy
3. Numerical 3. Numerical ResultsResults
KN amplitude bellow threshold
WKN (MeV)
2-body T-matrix in the 3-body 2-body T-matrix in the 3-body systemsystem :spectator
energy
How this attractive KN interaction How this attractive KN interaction contributes to 3-body binding system contributes to 3-body binding system is determined by solving dynamical 3-body eq. directly!!is determined by solving dynamical 3-body eq. directly!!
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
The three-body resonance poles (other The three-body resonance poles (other parameters)parameters)
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
Rel. model
The pole position strongly depends on KN interaction. -> Form factor (dipole -> monopole)
-> Structure dependence on Λ(1405) Effects of kaon absorption (p-wave interaction)
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 πΣπΣN unphysicalN unphysical energy plane. energy plane. (W(Wpolepole = -79.7-i36.4 MeV using relativistic kinematics) = -79.7-i36.4 MeV using relativistic kinematics)
SummarySummary
In the futureIn the future
