Coupled-channels Faddeev AGS calculation of K-ppn and K-ppp quasi-bound states

S. Marri; S. Z. Kalantari

doi:10.1140/epja/i2016-16282-y

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2023 Impact factor 2.6

Hadrons and Nuclei

Eur. Phys. J. A (2016) 52: 282
https://doi.org/10.1140/epja/i2016-16282-y

Regular Article - Theoretical Physics

Coupled-channels Faddeev AGS calculation of K^-ppn and K^-ppp quasi-bound states

S. Marri^* and S. Z. Kalantari

Department of Physics, Isfahan University of Technology, 84156-83111, Isfahan, Iran

^* e-mail: s.marri@ph.iut.ac.ir

Received: 17 May 2016
Accepted: 2 August 2016
Published online: 14 September 2016

Abstract

Using separable $\bar{K}N$ - $\pi\Sigma$ potentials in the Faddeev equations, we calculated the binding energies and widths of the $K^{-}pp$ , $K^{-}ppn$ and $K^{-}ppp$ quasi-bound states on the basis of three- and four-body Alt-Grassberger-Sandhas equations in the momentum representation. One- and two-pole version of $\bar{K}N$ - $\pi\Sigma$ interaction are considered and the dependence of the resulting few-body energy on the two-body $\bar{K}N$ - $\pi$ $\Sigma$ potential was investigated. The s -wave [3 + 1] and [2 + 2] sub-amplitudes are obtained by using the Hilbert-Schmidt expansion procedure for the integral kernels. As a result, we found a four-body resonance of the K ^- ppn and $K^{-}ppp$ quasi-bound states with a binding energy in the range $B_{K^{-}ppn} \sim$ 55-70 and $B_{K^{-}ppp} \sim$ 90-100 MeV, respectively. The calculations yielded full width of $\Gamma_{K^{-}ppn} \sim$ 16-20 and $\Gamma_{K^{-}ppp} \sim$ 7-20 MeV.