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The existence of the quasi-bound state in \(K{\bar{K}}NN\) four-body system

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Abstract

The possible existence of quasi-bound state in \(K{\bar{K}}NN\) with quantum numbers \(J=0\) and \(I=0\) on the basis of four-body Alt-Grassberger-Sandhas equations in the momentum representation was investigated. We constructed a separable representation for the subamplitudes in the [3+1] and [2+2] partitions. The separable expansion for the integral kernels in the three- and four-body equations was obtained by using the method of the energy-dependent pole expansion (EDPE). Different separable phenomenological and chiral SU(3) based potentials having the one- and two-pole structure of the \(\varLambda (1405)\) resonance were used to study the dependence of the results on \({\bar{K}}N-\pi \varSigma \) interaction. It was shown that the four-body \(K{\bar{K}}NN\) system is bound with a binding energy of \(B_{K{\bar{K}}NN}\sim \) 38–78 MeV and width of \(\varGamma _{K{\bar{K}}NN}=46-118\) MeV.

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Data Availability

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and there are no experimental data. All model parameters are given in the text and in the tables.]

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Acknowledgements

The authors would like to thank the University of Isfahan for the supporting of the postdoctoral project of the first author (contract No 136/99).

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Authors and Affiliations

  1. Faculty of Physics, University of Isfahan, 81746-73441, Isfahan, Iran

    Sajjad Marri & Mehdi Nasri Nasrabadi

Authors
  1. Sajjad Marri
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  2. Mehdi Nasri Nasrabadi
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Correspondence to Sajjad Marri.

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Communicated by Eulogio Oset.

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Marri, S., Nasrabadi, M.N. The existence of the quasi-bound state in \(K{\bar{K}}NN\) four-body system. Eur. Phys. J. A 58, 130 (2022). https://doi.org/10.1140/epja/s10050-022-00788-6

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