Mixing of the $f_0$ and $a_0$ scalar mesons in threshold photoproduction

We examine the photoproduction of the light scalar mesons $f_0$-$a_0 (980)$ with emphasis on isospin-violating $f_0$ and $a_0$ mixing due to the mass difference between neutral and charged kaons. General forms for the invariant amplitude for scalar meson photoproduction are derived, which yield expressions for the invariant mass distribution of the final meson pairs. A final state interaction form factor is obtained which incorporates $f_0$ and $a_0$ mesons, $K\bar K$ threshold effects, and $f_0-a_0$ mixing. This form factor is applied to predict the effective mass distribution of the $\pi\pi$ and $K\bar K$ pairs in the vicinity of the $K\bar K$ threshold. An estimate of the role of isospin mixing near threshold is provided. The potential role of polarized photons and protons is also discussed.