Towards a model-independent determination of the φ -> γ f₀ coupling

Abstract

A guide to the composition of the enigmatic f0(980) and a0(980) states is their formation in φ-radiative decays. Precision data are becoming available from the KLOE experiment at the DAΦNE machine at Frascati, as well as results from SND and CMD-2 at VEPP-2M at Novosibirsk. We show how the coupling of the f0(980) to this channel can be extracted from these, independently of the background provided by σ production. To do this we use the fact that the behaviour of both the f0(980) and σ cannot be determined by these data alone, but is strongly constrained by experimental results from other hadronic processes as required by unitarity. We find that the resulting coupling for the φ → γf0(980) is ∼ 10−4 GeV with a background that is quite unlike that assumed if unitarity is neglected. This provides an object lesson in how unitarity teaches us to add resonances. Not surprisingly the result is crucially dependent on the pole position of the f0(980), for which there are still sizeable uncertainties. At present this leads to an uncertainty in the φ → γf0 branching ratio which can only be fixed by further precision data on the f0(980). Nevertheless, the BR(φ → γf0) is now the same order of magnitude as the experimental BR(φ → γa0).