Faddeev fixed-center approximation to the $N\bar{K}K$ system and the signature of a $N^*(1920)(1/2^+)$ state

TL;DR

This paper uses the fixed center approximation to Faddeev equations with chiral unitary interactions to explore the $Nar{K}K$ system, providing evidence for a new $N^*(1920)$ resonance with $J^P=1/2^+$.

Contribution

It introduces a novel application of the fixed center approximation to the $Nar{K}K$ system, supporting the existence of a related $N^*$ resonance and validating the method's effectiveness.

Findings

Resonant structures indicate a possible $Nar{K}K$ hadron state.

Results support the existence of an $N^*(1920)$ resonance with $J^P=1/2^+$.

The fixed center approximation proves effective for three-hadron systems.

Abstract

We perform a calculation for the three body $N \bar{K} K$ scattering amplitude by using the fixed center approximation to the Faddeev equations, taking the interaction between $N$ and $\bar{K}$, $N$ and $K$, and $\bar{K}$ and $K$ from the chiral unitary approach. The resonant structures show up in the modulus squared of the three body scattering amplitude and suggest that a $N\bar{K}K$ hadron state can be formed. Our results are in agreement with others obtained in previous theoretical works, which claim a new $N^*$ resonance around 1920 MeV with spin-parity $J^P=1/2^+$. The existence of these previous works allows us to test the accuracy of the fixed center approximation in the present problem and sets the grounds for possible application in similar problems, as an explorative tool to determine bound or quasibound three hadron systems.