Comment on "Two-photon decay of the sigma meson"

We comment on a recent paper by Giacosa, Gutsche, and Lyobovitskij, in which it is argued that a quarkonium interpretation of the $\sigma$ meson should give rise to a much smaller two-photon decay width than commonly assumed. The reason for this claimed discrepancy is a term in the transition amplitude, necessary for gauge invariance, which allegedly is often omitted in the literature, including the work of the present authors. Here we show their claims to be incorrect by demonstrating, in the context of the Quark-Level Linear $\sigma$ Model, that the recently extracted experimental value $\Gamma_{\sigma\to2\gamma}=(4.1\pm0.3)$ keV is compatible with a $q\bar{q}$ assignment for the $\sigma$, provided that meson loops are taken into account as well.