Electromagnetic trace anomaly in a generalized linear sigma model

Abstract

We build the electromagnetic trace anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four quark content. In the leading order of this framework, we study the decays into two photons of the lowest isosinglet scalar mesons. We find that the direct inclusion of underlying mixing among two- and four-quark components in the trace anomaly term is essential in order for the model prediction to agree with the available experimental data on decay width of $f_0(980)$ to two photons. Consequently, this sets a lower bound of 0.5 KeV on the decay with of $f_0(500)$ to two photons.