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The resonance pole of strange dibaryon in KNN – p YN system. Yoichi Ikeda (Osaka Univ.) in collaboration with Hiroyuki Kamano (JLab) and Toru Sato (Osaka Univ.). Introduction Our model of KN interaction Coupled-channel Faddeev equations Numerical Results Summary. KN. L(1405). pS. - PowerPoint PPT Presentation
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Yoichi Ikeda (Osaka Univ.)Yoichi Ikeda (Osaka Univ.)in collaboration within collaboration with
Hiroyuki Kamano (JLab) and Toru Sato (Osaka Univ.) Hiroyuki Kamano (JLab) and Toru Sato (Osaka Univ.)
IntroductionIntroduction
Our model of KN interactionOur model of KN interaction
Coupled-channel Faddeev equationsCoupled-channel Faddeev equations
Numerical ResultsNumerical Results
SummarySummary
IntroductionIntroduction
Our model of KN interactionOur model of KN interaction
Coupled-channel Faddeev equationsCoupled-channel Faddeev equations
Numerical ResultsNumerical Results
SummarySummary
The resonance pole of strange dibaryon The resonance pole of strange dibaryon in KNN – in KNN – YN systemYN system
Introduction Introduction
KN interaction in isospin I=0 channelKN interaction in isospin I=0 channelStrong Strong attractionattraction
The The (1405) (1405) resonanceresonance
Quasi-bound state of KN Quasi-bound state of KN statestate
CDD pole coupling with CDD pole coupling with mesonsmesons
Multi-quark stateMulti-quark state
Quasi-bound state of KN Quasi-bound state of KN statestate
CDD pole coupling with CDD pole coupling with mesonsmesons
Multi-quark stateMulti-quark state
KN - KN - coupled system coupled system
Strange dibaryon resonanceStrange dibaryon resonance
KNN – KNN – YN coupled systemYN coupled system
IntroductionIntroduction
Two poles on KN physical and Two poles on KN physical and unphysical sheet (chiral unitary model) unphysical sheet (chiral unitary model)
taken form Jido et al. NPAtaken form Jido et al. NPA725725 (2003). (2003). taken form Hyodo and Weise. PRCtaken form Hyodo and Weise. PRC7777 (200 (2008).8).
Structure of the Structure of the (1405)(1405)
Structure of strange dibaryonStructure of strange dibaryon
We investigate We investigate
possible strange dibaryon resonance poles.possible strange dibaryon resonance poles.
S=-1, B=2, Q=+1S=-1, B=2, Q=+1
JJππ=0=0--
(3-body s-wave state)(3-body s-wave state)
We consider s-wave state.We consider s-wave state. We can expect We can expect most strong attractive interactionmost strong attractive interaction
in this configure.in this configure.
L=0 (s-wave interaction)
NN
KK
NN
IntroductionIntroduction
Potential derived from Weinberg-Tomozawa termPotential derived from Weinberg-Tomozawa termPotential derived from Weinberg-Tomozawa termPotential derived from Weinberg-Tomozawa term
: : Meson field Meson field , , BB : : Baryon Baryon fieldfield
Chiral effective LagrangianChiral effective LagrangianChiral effective LagrangianChiral effective Lagrangian
…
on-shell factorizationon-shell factorization
Our model of KN interactionOur model of KN interaction
Unitarized by Lippmann-Schwinger equationUnitarized by Lippmann-Schwinger equation
Our model of KN interactionOur model of KN interaction
E-dep. potentialE-dep. potentialE-dep. potentialE-dep. potential
Cutoff parametersCutoff parameters
Our model of KN interactionOur model of KN interaction
Poles of the amplitudePoles of the amplitude
(KN bound state)(KN bound state)1428.8-i15.3(MeV)1428.8-i15.3(MeV)
(( resonance) resonance)1344.0-i49.0(MeV)1344.0-i49.0(MeV)
Hyodo, Weise PRCHyodo, Weise PRC7777(2008).(2008).Consistent with chiral unitary modelConsistent with chiral unitary model
(coupled-channel chiral dynamics)(coupled-channel chiral dynamics)
Faddeev EquationsFaddeev EquationsFaddeev EquationsFaddeev Equations
W : 3-body scattering energyW : 3-body scattering energy
i(j) = 1, 2, 3i(j) = 1, 2, 3 (Spectator particles) (Spectator particles)
T(W)=TT(W)=T11(W)+T(W)+T22(W)+T(W)+T33(W) (T : 3-body amplitude)(W) (T : 3-body amplitude)
ttii(W, E(p(W, E(pii)) : 2-body t-matrix )) : 2-body t-matrix with spectator particle iwith spectator particle i
GG00(W) : 3-body Green’s function ((W) : 3-body Green’s function (relativistic kinematicsrelativistic kinematics))
W : 3-body scattering energyW : 3-body scattering energy
i(j) = 1, 2, 3i(j) = 1, 2, 3 (Spectator particles) (Spectator particles)
T(W)=TT(W)=T11(W)+T(W)+T22(W)+T(W)+T33(W) (T : 3-body amplitude)(W) (T : 3-body amplitude)
ttii(W, E(p(W, E(pii)) : 2-body t-matrix )) : 2-body t-matrix with spectator particle iwith spectator particle i
GG00(W) : 3-body Green’s function ((W) : 3-body Green’s function (relativistic kinematicsrelativistic kinematics))
W : 3-body scattering energyW : 3-body scattering energy
i(j) = 1, 2, 3i(j) = 1, 2, 3 (Spectator particles) (Spectator particles)
Z(pZ(pii,p,pjj;W) : Particle exchange potentials;W) : Particle exchange potentials
(p(pnn;W) : Isobar propagators;W) : Isobar propagators
Faddeev equation with separable potentialsFaddeev equation with separable potentials
i
j
i
j
=XXijij
i j
XXijij
nn
+n
Alt-Grassberger-Sandhas(AGS) EquationAlt-Grassberger-Sandhas(AGS) EquationAlt-Grassberger-Sandhas(AGS) EquationAlt-Grassberger-Sandhas(AGS) Equation
KNN-pYN coupled-channel systemKNN-pYN coupled-channel system
Alt-Grassberger-Sandhas(AGS) EquationAlt-Grassberger-Sandhas(AGS) EquationAlt-Grassberger-Sandhas(AGS) EquationAlt-Grassberger-Sandhas(AGS) Equation
i
j
i
j
=XXijij
i j
XXijij
nn
+n
: 1-particle exchange term: 1-particle exchange term
ππ
Σ,ΛΣ,Λ
NN
NNKK NN
NN
KK
NN
ππΣ,ΛΣ,Λ
NN ππ
Σ,ΛΣ,ΛNN
NN potential -> Two-term separable potentialNN potential -> Two-term separable potential
AttractionAttraction Repulsive coreRepulsive core
XXijij
Two-body potentials –NN interaction-Two-body potentials –NN interaction-
NN
NN
KK
NNNN
Two-body potentials –Two-body potentials – interaction- interaction-
XXijij
Σ,ΛΣ,Λ
ππ
NN
E-dep. potentialE-dep. potentialE-dep. potentialE-dep. potential
I=1/2I=1/2 I=3/2I=3/2=500 (MeV)=500 (MeV) =500 (MeV)=500 (MeV)
Scattering lengthScattering length Scattering lengthScattering length
YN potential -> One-term separable potentialYN potential -> One-term separable potential
XXijijΣ,ΛΣ,Λ
ππ
NN YNYN
Two-body potentials –YN interaction-Two-body potentials –YN interaction-
I=1/2I=1/2
I=3/2I=3/2
Scattering lengthScattering length Scattering lengthScattering length
Torres, Dalitz, Deloff, PLBTorres, Dalitz, Deloff, PLB174174 (1986). (1986).
Pole of the AGS amplitudesPole of the AGS amplitudes
WWpolepole = -B –i = -B –i/2 /2
Eigenvalue equation for Fredholm kernelEigenvalue equation for Fredholm kernel
three-body resonance pole at Wthree-body resonance pole at Wpolepole
Formal solution for three-boby amplitudesFormal solution for three-boby amplitudes
Fredholm kernelFredholm kernel
Possible singularities of the amplitudesPossible singularities of the amplitudes
Z(pZ(pii,p,pjj;W) : Particle exchange potentials;W) : Particle exchange potentials
(p(pnn;W) : Isobar propagators;W) : Isobar propagators
We search for three-body resonance poles We search for three-body resonance poles
on KNN physical, on KNN physical, YN unphysical, and YN unphysical, and “………”“………” sheet. sheet.
Numerical resultsNumerical results
We construct the model of We construct the model of energy-dependent KN interactionenergy-dependent KN interaction. .
(chiral unitary approach)(chiral unitary approach)
We solve the Faddeev equations.We solve the Faddeev equations.
： ： We found We found two poles of strange dibaryontwo poles of strange dibaryon..
： ： -B-i -B-i /2 = (-13.7-i29.0, -37.2-i93.3) MeV/2 = (-13.7-i29.0, -37.2-i93.3) MeV
Pole I -> KNN physical, Pole I -> KNN physical, YN unphysical, YN unphysical, *N physical sheet*N physical sheet
Pole II -> KNN physical, Pole II -> KNN physical, YN unphysical, YN unphysical, *N unphysical sheet*N unphysical sheet
SummarySummary
FutureFuture reaction
This production mechanism will be investigated by LEThis production mechanism will be investigated by LEPS and CLAS collaborations. @SPring8, JlabPS and CLAS collaborations. @SPring8, Jlab
