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

Understand

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.