Reconciling φ radiative decays with other data for a0(980), f0(980), ππ→KK and ππ→ηη

Data for φ→γ(ηπ⁰) are analysed using the KK loop model and compared with parameters of a₀(980) derived from Crystal Barrel data. The ηπ mass spectrum agrees closely and the absolute normalisation lies just within errors. However, BES parameters for f₀(980) predict a normalisation for φ→γ(π⁰π⁰) at least a factor 2 lower than is observed. This discrepancy may be eliminated by including constructive interference between f₀(980) and σ. The magnitude required for σ→KK is consistent with data on ππ→KK. A dispersion relation analysis by Büttiker, Descotes-Genon and Moussallam of ππ→KK leads to a similar conclusion. Data on ππ→ηη also require decays of σ to ηη. Four sets of ππ→KK data all require a small but definite f₀(1370) signal. PACS 13.25.Gv; 14.40.Gx; 13.40.Hq