Excited Scalar and Pseudoscalar Mesons in the Extended Linear Sigma Model

Abstract

We present an in-depth study of masses and decays of excited scalar and pseudoscalar $\bar{q}q$ states in the Extended Linear Sigma Model (eLSM). The model also contains ground-state scalar, pseudoscalar, vector and axial-vector mesons. The main objective is to study the consequences of the hypothesis that the $f_0(1790)$ resonance, observed a decade ago by the BES Collaboration and recently by LHCb, represents an excited scalar quarkonium. In addition we also analyse the possibility that the new $a_0(1950)$ resonance, observed recently by BABAR, may also be an excited scalar state. Both hypotheses receive justification in our approach although there appears to be some tension 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.

Comments: 28 pages, 6 tables, 1 figure. v2 (published version) contains further clarification of the model and results; typos have been corrected and references added