Table of contents Introduction Model Results

1. Toshitaka Uchino Tetsuo Hyodo, Makoto Oka Tokyo Institute of Technology 6 OCT 2010 Table of contents Introduction Model Results

2. I. Introduction hypernuclei model From several works about Kbar NN system, the state is dominant in the bound state. So we take the viewpoint that KbarNN bound state is regarded as bound state of the ( hypernuclei). There is a previous work by Arai-Oka-Yasui [1].

3. Arai-Oka-Yasui model and our model AOY model is constructed as follows : • s-wave : dominant for the lowest energy state. • Λ* : does not decay. • 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 fundamentally, but Interaction : determined by chiral unitary approach. Purpose : finding possible bound states.

4. hypernuclei model with chiral dynamics 1 In this work, we are going to apply chiral unitary dynamics[2,3] to the hypernuclei model. MB multiple scatterings The coupling constant of the to MB channels are taken from[2,3]. Using this structure, we estimate the unknown interaction.

5. hypernuclei model with chiral dynamics 2 Each Λ* interact with nucleon, whereas the transition between each Λ*N state can take place. Then, we solve the coupled channel Schrödinger Eq. is a superposition of two states

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

7. II. Model The OBEP We construct the potential by extending the Juelich(Model A) potential[4]. It is the simplest one- Boson-exchange potential which includes hyperon. Exchanged mesons are σ, ω, and Kbar, because Isospin of the =0.

8. Kaon exchange 1 – spin dependence Considering that the parity of the is odd, the coupling is 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. Exchange factor Attractive for S=0 Repulsive for S=1

9. 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 threshold. Namely, in the upper energy state , Kaon exchange is stronger than the .

10. Coupling constants in our potential The coupling constants in our potential are classified into three types. : Chiral : Unknown : Juelich

11. Estimation of the (X=σ, ω)coupling constants By chiral dynamics, exchanged meson couples to the constituent meson or baryon in the . So the coupling constants can be estimated by summing up the microscopic contribution. ππσis determined by σ decay : Chiral : KKbarσ is assumed to be 0 : Juelich Estimated coupling constants are complex. To obtain real value, we take their absolute value.

12. 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 is unknown. Considering the size of the [5], we assume them as below. Here, we take c=1.5.

13. III. Results potentials

14. 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.

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

16. 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.

17. Decay width : B → πΣN We consider the case that the in the bound state decays with nucleon spectator. Coupling constant is given by chiral unitary approach.

18. Theoretical uncertainties Our model has several theoretical uncertainties or ambiguities. • Λ* size : parameter “c”. • Input chiral unitary models. • How to obtain real valued couplings. • σKbarK couplings.

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. Comparison with another model

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

22. Future plans Few body calculation In our model, the Λ*Npotential is constructed. Using this potential, we can study the bound state for few body Λ* hypernuclei. Other decay mode Using obtained wave function, other decay width can be estimated. Non-mesonic decay, ΛN ,ΣN and mesonic decay πΛN, πΣN.

23. Other diagrams B → ΛN B → ΣN B → πΛN B → πΣN

24. Thank you

26. Tensor force for s-wave

27. Interaction of each meson exchange Given coupling constants Estimated coupling constants

28. Theory Binding energies of KbarNN

29. Experiments

30. Explicit potential form Notation σ contribution Kbar contribution

31. ω contribution

32. Gaussian Expansion Method Schrödinger eq is changed to matrix eigenvalue problem by GEM.

33. I. Introduction hypernuclei model We take the viewpoint that bound state is regarded as bound state of the ( hypernuclei). There is a previous work by Arai-Oka-Yasui [1].

34. hypernuclei model with chiral dynamics In this work, we are going to apply chiral unitary dynamics[2,3] to the hypernuclei model. 1.MB multiple scatterings The coupling constant of the to MB channels are taken from[2,3]. 2. is a superposition of two states