Location, correlation, radiation: where is the $\sigma$, what is its structure and what is its coupling to photons?

TL;DR

This paper investigates the nature of the sigma meson in QCD by analyzing its two-photon decay, providing precise experimental and theoretical insights into its structure and coupling to photons.

Contribution

It accurately computes the sigma meson's two-photon decay width and compares it with experimental data, offering constraints on its internal structure.

Findings

The sigma meson has a two-photon width of (4.1 ± 0.3) keV.

Computed cross-sections agree with experimental measurements.

Results support a quark-antiquark composition for the sigma meson.

Abstract

Scalar mesons are a key expression of the infrared regime of QCD. The lightest of these is the $\sigma$. Now that its pole in the complex energy plane has been precisely located, we can ask whether this state is transiently ${\bar q}q$ or ${\bar {qq}} qq$ or a multi-meson molecule or largely glue? The two photon decay of the $\sigma$ can, in principle, discriminate between these possibilities. We review here how the $\gamma\gamma\to\pi^+\pi^-$, $\pi^0\pi^0$ cross-sections can be accurately computed. The result not only agrees with experiment, but definitively fixes the radiative coupling of the $\sigma$. This equates to a two photon width of $(4.1 \pm 0.3)$ keV, which accords with the simple non-relativistic quark model expectation for a ${\bar u}u, {\bar d}d$ scalar. Nevertheless, robust predictions from relativistic strong coupling QCD are required for each of the possible compositions before we can be sure which one really delivers the determined $\gamma\gamma$ coupling.