Theoretical support for theπ(1300)and the recently claimedf0(1790)as molecular resonances

Abstract

A study of three-pseudoscalar $\ensuremath{\pi}K\overline{K}$ and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\eta}$ 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 ${J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$ is found with mass $\ensuremath{\sim}1400\text{ }\text{ }\mathrm{MeV}$ when the $K\overline{K}$ system gets reorganized as the ${f}_{0}(980)$. This resonance is identified with the $\ensuremath{\pi}(1300)$ listed by the Particle Data Group. Further, the two-body amplitude which describes the interaction between a $\ensuremath{\pi}$ and the ${f}_{0}(980)$ is extracted from the study of the $\ensuremath{\pi}K\overline{K}$ and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\eta}$ system and is then employed to study the ${f}_{0}(980)\ensuremath{\pi}\ensuremath{\pi}$ system. As a result, a scalar resonance is found near 1790 MeV which drives the two ${f}_{0}(980)\ensuremath{\pi}$ systems to resonate as the $\ensuremath{\pi}(1300)$ while the invariant mass of the two pions falls in the mass region of the scalar $\ensuremath{\sigma}(600)$. 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.