Faddeev fixed-center approximation to the $\eta K^*\bar{K}^*$, $\pi K^*\bar{K}^*$ and $KK^*\bar{K}^*$ systems

TL;DR

This paper studies three-body meson systems using fixed-center approximation to Faddeev equations, predicting bound states and resonances that could correspond to known mesons like eta(2100).

Contribution

It introduces a novel application of fixed-center approximation to three-meson systems involving K* and eta/pi, predicting new bound states and resonances.

Findings

Identified a bound state around 2054 MeV with quantum numbers 0^+(0^{-+})

Predicted a bump structure around 1900-2000 MeV with quantum numbers 1^-(0^{-+})

Found a stable structure around 2130 MeV in the K K* ar{K}^* system.

Abstract

The three-body $\eta K^*\bar{K}^*$, $\pi K^*\bar{K}^*$ and $KK^*\bar{K}^*$ systems are investigated within the framework of fixed-center approximation to the Faddeev equations, where $K^*\bar{K}^*$ is treated as the scalar meson $f_0(1710)$. The interactions between $\pi$, $\eta$, $K$ and $K^*$ are taking from the chiral unitary approach. By scattering the $\eta$ meson on the clusterized $(K^*\bar{K}^*)_{f_0(1710)}$ system, we find a peak in the modulus squared of the three-body scattering amplitude and it can be associated as a bound state with quantum numbers $I^G(J^{PC})=0^+(0^{-+})$. Its mass and width are around 2054 MeV and 60 MeV, respectively. This state could be associated to the $\eta(2100)$ meson. For the $\pi (K^*\bar{K}^*)_{f_0(1710)}$ scattering, we find a bump structure around 1900-2000 MeV with quantum numbers $1^-({0^{-+}})$. While for the $K K^* \bar{K}^*)_{f_0(1710)}$ system, there are three structures. One of them is much stable and its mass is about 2130 MeV. It is expected that these theoretical predictions here could be tested by future experimental measurements, such as by the BESIII, BelleII and LHCb collaborations.