1. Toshitaka Uchino Tetsuo Hyodo, Makoto Oka Tokyo Institute of Technology 10 DEC 2010

2. I. Introduction The Λ* hypernuclei model We take the viewpoint that the KbarNN bound state is regarded as the bound state of the Λ*N (Λ* hypernuclei). Kbar nuclei bound states attract much attention. From several theoretical works, the Λ* N bound state is found to be a dominant component in the KbarNN bound state. Bound state Λ* and N bounds Λ*-hypernuclei model has advantages ; Including other two body, the ΛN and ΣN contributions. Few body calculation.

3. Arai-Oka-Yasui model[1] and our model AOY model is constructed as follows : s-wave : dominant for the lowest energy state. Λ*is regarded as a elementary particle. Potential : extending the YN OBEP. For S=0, S=1. Variational method. Interaction : determined phenomenologically. Purpose : fitting the results of FINUDA exp. Our model is following AOY model, but ; Interaction : determined with the chiral unitary approach. Purpose : finding possible bound states.

4. Λ* hypernuclei model with chiral dynamics Each Λ* interact with nucleon, whereas the transition between each Λ*N state can take place. Then, we solve the coupled channel Schrödinger Eq. The Λ* is dynamically generated as a superposition of two states. The coupling constant of the Λ* to MB channels are taken from[2,3]. By using the chiral unitary approach, the Λ* is described as meson-baryon multiple scattering.

5. II. Model The Λ*N OBEP We construct the Λ*N potential by extending the Juelich (Model A) potential[4]. It is the simplest one-boson-exchange potential which includes hyperon. Because isospin of the Λ* =0, isoscalar meson is exchanged, namely σ, ω. We further consider the Kbar exchange.

6. Considering that the parity of the Λ* is odd, the Λ*KbarN coupling is a scalar type. So the Kbar exchanged potential is essentially same as the scalar exchange in the NN potential, but it depends on the total spin S. Kaon exchange 1 – spin dependence Exchange factor Attractive for S=0 Repulsive for S=1

7. Kaon exchange 2 - effective Kaon mass In the Kaon propagator, since the energy transfer is not zero, we use the effective Kaon mass. It becomes smaller as the resonance energy is close to the KbarN threshold. Namely, in the upper energy state, Kaon exchange is stronger than the.

8. Coupling constants in our potential Coupling constants in our potential are classified into three types. Coupling constants determined by the chiral unitary approach are complex value, so we take its absolute value. : Chiral : Juelich : Unknown The unknown coupling constant is estimated by using the Λ* structure from chiral unitary approach analysis.

9. Estimation of the Λ*Λ*N(X=σ, ω) coupling By chiral dynamics, exchanged meson couples to the constituent baryon or meson in the. So the coupling constants can be estimated by summing up the microscopic contribution. : Chiral : Juelich ππσ is determined by σ decay : KKbarσ is assumed to be 0 Estimated coupling constants are complex. To obtain real value, we take their absolute value. We deal only dominant components, KbarN and πΣ.

10. potentials III. Results

11. Bulk property of the potential To study the bulk property of the potential, we calculate the volume integral of the potential. This results show that The potential is attractive(repulsive) for S=0(S=1). The potential is stronger than the, because of the stronger coupling constants and the lighter effective Kaon mass.

12. With mixing Bound states of the system With no mixing S=0: More bounds S=1: No bound states S=0: Only bounds

13. Wave function We obtain the wave function of the bound state for each. Each state is peaking at ～ 0.5 fm. The state is dominant, but the state is also important.

14. Decay width : B → πΣN We consider the case that the in the bound state decays with the nucleon being a spectator. The coupling constant is given by the chiral unitary approach.

15. *As the strangeness S=-1, the baryon number B=2 Λ*-hypernuclei system, the Λ*N bound state is studied. *The Λ*N one-boson-exchange potential is constructed by extending the Juelich potential. *The unknown coupling constant is estimated by using the information of the Λ* structure obtained from chiral unitary approach. *Solving the Schrödinger eq, we obtain the bound state solution for S=0 ; Summary

16. Backup slides

17. Decay width If there exists the bound states, we can estimate the decay width with obtained wave function.

18. Cut-off mass The coupling strength depends on the exchanged meson momentum. This effect is taken into account as monopole type form factor. For vertices NNX(X=σ, ω), cut-off is given by Juelich potential. But, cut-off masses concerning the Λ* is unknown. We take into account the size of the Λ* and nucleon as parameter “c”. The unknown cut-off can be written with “c”. Considering the size of the Λ* [5], “c” is assumed to be 1.5.

19. c dependence Binding energies and decay width depend on the size of the Λ*, parameter c. *Small “c “ leads to shallow bound. *πΣN decay is dominated by kinematics.

20. 1. Other decay modes 2. Extension of our model 3. Few body calculations Future plans

21. Other diagrams B → ΛNB → ΣN B → πΛNB → πΣN Non-mesonic decay Mesonic decay Using obtained wave function, other decay width, Non- mesonic decay, ΛN,ΣN and mesonic decay πΛN, πΣN, can be estimated.

22. Extension of our model Including complexness Energy dependence : Chiral: Juelich: Estimated The Λ* energy dependence in the Λ*Λ*X and Λ*KbarN vertices should be taken into account, when the Λ*N system bounds deeply. Several parameters concerning the Λ* are complex value. So, our model needs an extension. To include the information of the Λ* given by chiral dynamics more directly, we need model improvement. Complex Λ*N potential

23. Few body calculation Other channel contribution Other two-body channels, the ΣN and ΛN contribution can be included within our model. Extension to few body studies, the Λ*NN and Λ*NNN can be calculated, using the Λ*N potential.