Toshitaka Uchino

T. Hyodo, M. Oka

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We study the strange dibaryon system at the Λ*N viewpoint.

The possible bound state of the Kbar nuclei attracts much attention. Among them, the KbarNN system is actively discussed. From several theoretical works, the KbarNN bound is found to be dominated by the Λ* N bound state.

Bound state

Λ* and N bounds

+ nucleus

Advantage : Few-body calculation (Λ* hypernuclei picture [1]) Estimation of the decay width Λ*N interaction : constructed as a potential.

Λ* hypernuclei

2 [1] A. Arai, M. Oka and S. Yasui, Prog. Theor. Phys. 119, 103 (2008), 0705.3936

The Λ*N system is considered based on the results obtained by the chiral unitary model[2,3].

Couplings constants on Λ* can be obtained.

The two channel coupled Λ*N system.

3 [2] T. Hyodo, S. I. Nam, D. Jido and A. hosaka, Phys. Rev. C68. 018201(2003). [3] T. Hyodo, S. I. Nam, D. Jido and A. Hosaka, Prog. Theor. Phys. 112. 73. (2004).

Relevant couplings can be classified into three types.

: chiral unitary model : Juelich model : need determination

The Λ* N potential is constructed by extending the Juelich One- Boson-Exchange Potential model.

  Isoscalar exchange   Kbar exchange ( S=0 : attractive, S=1 : repulsive )

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・Λ* couplings can be estimated by summing up all microscopic contributions.

・Only dominant components (πΣ, KbarN) are considered.

: Chiral unitary model : Juelich model : Determined by meson decay processes and so on

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S=0 Attractive pocket

S=1 Almost repulsive

Λ*1=1427MeV Λ*2=1400MeV

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λ=1 λ=1/2 λ=0

In the spin S=1 case, we have no resonances. For S=0, possible resonances are searched for by the use of the Real Scaling method with the parameter λ.

The results in the S=0 channel are shown below :

•  Resonance appears around 10 MeV below the KbarNN threshold •  Decay to the Λ*2N system is not so large The quasi-bound state is dominated by the Λ*1N bound state. 7

Resonance ! Λ*1N shallow bound

πΣN Λ*N quasi-bound

ΛN ΣN πΛN

E(MeV)

100

175 240

315

Λ* : decays to only πΣ with 50MeV width Λ*N quasi-bound state : can decay to YN or πYN (Y=Λ or Σ)

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It is important to study the decay properties. Experimental signals were observed in the ΛN spectrum, while it is hard to include the ΛN channel in the theoretical model space.

Decay width can be estimated perturbatively with the wave function of the Λ*1N bound state.

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|B! =! d3p

(2!)3 !̃("p)|!"("p)N(#"p)!

!B!f =!d"|MB!f |2

Y

!!

N

N

M(k)

1 2

Y

!!

N

N

M(k)

1 2

!

!̃("p) =!d3r!("r)ei!p·!r

Invariant scattering amplitudes on πYN and YN decay

!

"!

N

N

1

!B1

!!

B2

N

1 2

B1

!!

B2

N

1 2

!

：Chiral unitary ：Juelich ：Weinberg-Tomozawa

Exchange

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  πΣN decay (fall apart process) is dominant

  Width is close to 50 MeV

Scattering Fall apart

Relevant diagrams

ORB[4] OM[5] BNW[6]

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[5] J. A. Oller and U. G. Meissner, Phys. Lett. B500. 263(2001)

[4] E. Oset, A. Ramos and C. Bennhold, Phys. Lett. B. 527. 99(2002)

[6] B. Borasoy, R. Niessler and W. Weise, Phys. Rev. Lett. 94. 213401(2005)

Properties of the Λ*N system converge qualitatively (shallow bound, dominated by the πΣN decay).

 Λ*N two-body system is studied  Λ*N potential is constructed by extending OBEP

with chiral unitary model  Λ*N quasi-bound state is found slightly below the

KbarNN threshold  Λ*N quasi-bound state almost decays to πΣN

Λ*N quasi-bound

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 Λ*NN three-body system  Modification of the Λ*N potential - resonance poles - couplings from the residue

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