LOCATION, CORRELATION, RADIATION: WHERE IS THE σ, WHAT IS ITS STRUCTURE, AND WHAT IS ITS COUPLING TO PHOTONS?

Abstract

Scalar mesons are a key expression of the infrared regime of QCD. The lightest of these is the σ. Now that its pole in the complex energy plane has been precisely located, we can ask whether this state is transiently [Formula: see text] or [Formula: see text] or a multi-meson molecule or largely glue? The two-photon decay of the σ can, in principle, discriminate between these possibilities. We review here how the γγ → π+π-, π0π0 cross-sections can be accurately computed. The result not only agrees with experiment, but definitively fixes the radiative coupling of the σ. This equates to a two-photon width of (4.1 ± 0.3) keV, which accords with the simple nonrelativistic quark model expectation for a [Formula: see text], [Formula: see text] 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 γγ coupling.