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

A study of three-pseudoscalar $πK \bar{K}$ and $ππη$ 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 $J^π= 0^-$ 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 $π(1300)$ listed by the Particle Data Group. Further, the two-body amplitude which describes the interaction between a $π$ and the $f_0(980)$ is extracted from the study of the $πK\bar K$ and $ππη$ system and is then employed to study the $f_0(980)ππ$ system. As a result, a scalar resonance is found near 1790 MeV which drives the two $ f_0 (980)π$ systems to resonate as the $π(1300)$ while the invariant mass of the two pions falls in the mass region of the scalar $σ(600)$. 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.