Revisiting the three-kaon interaction and its relation with $K(1460)$

TL;DR

This paper investigates whether the $K(1460)$ resonance can be understood as a hadronic molecule formed by three kaons, using a coupled-channel three-body approach that accounts for complex threshold effects.

Contribution

It introduces a comprehensive coupled-channel three-body analysis of $K Kar K$, $K o o ext{pions and etas}$ systems to explore the nature of $K(1460)$, including effects of complex thresholds and singularities.

Findings

Previous results with simplified models are reproduced.

Complex coupled-channel effects modify the resonance signals.

Threshold effects and singularities influence the resonance interpretation.

Abstract

We test the hypothesis of $K(1460)$ being a hadronic $J^P=0^-$ molecule through nonperturbative $S$-wave $K K\bar K$, $K\pi\pi$, $K\pi\eta$ coupled-channel dynamics in a three-body unitary isobar approach. The scalar two-body coupled-channel resonances $f_0(500)$, $f_0(980)$, $a_0(980)$ and $K^*_0(700)$ are generated in the subsytems in amplitudes that match phase shifts from experiment. In a first step, previous results in the limit of mass-degenerate, stable $f_0$ and $a_0$ isobars are reproduced. Once the full seven-coupled channel model is switched on, other $S$-matrix effects obscure and modify the resonance signal, including complex thresholds, a two-body cusp, and a triangle singularity at threshold.