Theoretical support for the $\pi(1300)$ and the recently claimed $f_0(1790)$ as molecular resonances

TL;DR

This paper uses a coupled-channel Faddeev approach based on chiral dynamics to support the existence of the $ ho(1300)$ and a new $f_0(1790)$ scalar resonance as molecular states, distinct from known resonances.

Contribution

It provides a theoretical framework demonstrating the molecular nature of the $ ho(1300)$ and supports the existence of the $f_0(1790)$ as a separate resonance, aligning with experimental claims.

Findings

Identifies a $ ho(1300)$ resonance from $ ext{π}Kar{K}$ and $ ext{π} ext{π} ext{η}$ systems.

Predicts a scalar resonance near 1790 MeV associated with $f_0(980) ext{π} ext{π}$ interactions.

Supports the $f_0(1790)$ as a distinct state from $f_0(1710)$, possibly with a molecular structure.

Abstract

A study of three-pseudoscalar $\pi K \bar{K}$ and $\pi \pi \eta$ coupled system is made by solving the Faddeev equations within an approach based on unitary chiral dynamics. A resonance with total isospin one and spin-parity $J^\pi = 0^-$ is found with mass $\sim$ 1400 MeV when the $K \bar{K}$ system gets reorganized as the $f_0(980)$. This resonance is identified with the $\pi (1300)$ listed by the Particle Data Group. Further, the two-body amplitude which describes the interaction between a $\pi$ and the $f_0(980)$ is extracted from the study of the $\pi K\bar K$ and $\pi\pi\eta$ system and is then employed to study the $f_0(980)\pi \pi $ system. As a result, a scalar resonance is found near 1790 MeV which drives the two $ f_0 (980)\pi$ systems to resonate as the $\pi (1300)$ while the invariant mass of the two pions falls in the mass region of the scalar $\sigma (600)$. These findings support the existence of a new $f_0$ resonance near 1790 MeV, as found by the BES and Crystal Barrel collaborations. Our results show that this $f_0(1790)$ is definitely distinct to $f_0(1710)$, the latter of which seems to possess a glueball structure dominantly.