Location, correlation, radiation: where is the $σ$, what is its structure and what is its coupling to photons?
Abstract
Description
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 ${\bar q}q$ or ${\bar {qq}} qq$ 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 $γγ\toπ^+π^-$, $π^0π^0$ 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 $(4.1 \pm 0.3)$ 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 $γγ$ coupling.
18 pages, 11 figures. To be published in Modern Physics Letters A A number of references updated and three sentences changed in the text to reflect these
18 pages, 11 figures. To be published in Modern Physics Letters A A number of references updated and three sentences changed in the text to reflect these