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

TL;DR

This paper refutes a recent claim that the quarkonium interpretation of the sigma meson predicts a much smaller two-photon decay width, showing that experimental data aligns with the quark-antiquark model when meson loops are included.

Contribution

The authors demonstrate that the experimental two-photon decay width of the sigma meson is compatible with a quark-antiquark structure within the Quark-Level Linear Sigma Model, countering recent claims.

Findings

Experimental decay width is consistent with q̄q model.

Meson loops are crucial for accurate decay width predictions.

Claims of smaller decay width due to gauge invariance are incorrect.

Abstract

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.