The $f_0(1790)$ and $a_0(1950)$ Resonances as Excited $\bar{q}q$ States in the Extended Linear Sigma Model

Abstract

A decade ago, BES Collaboration reported the discovery of a new scalar isosinglet resonance denoted as $f_0(1790)$. The finding was subsequently confirmed by LHCb. Recently, the existence of the corresponding isotriplet state -- the $a_0(1950)$ resonance -- has been claimed by BABAR. We investigate whether these resonances can be described as excited $\bar{q}q$ states. To this end, a comprehensive Lagrangian containing ground-state $\bar{q}q$ mesons as well as their first excitations is constructed in accordance with symmetries of the strong interaction. Both $f_0(1790)$ and $a_0(1950)$ emerge as compatible with $\bar{q}q$ excitations; however, tension appears to arise between the simultaneous interpretation of $f_0(1790)$/$a_0(1950)$ and pseudoscalar mesons $\eta(1295)$, $\pi(1300)$, $\eta(1440)$ and $K(1460)$ as excited $\bar{q}q$ states.