Towards a model independent determination of the phi -> f_0 - gamma coupling

Abstract

A guide to the composition of the enigmatic f_0(980) and a_0(980) states is their formation in phi-radiative decays. Precision data are becoming available from the KLOE experiment at the DAPHNE machine at Frascati, as well as results from SND and CMD-2 at VEPP-2M at Novosibirsk. We show how the coupling of the f_0(980) to this channel can be extracted from these, independently of the background provided by sigma production. To do this we use the fact that the behaviour of both the f_0(980) and sigma 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 phi -> gamma f_0(980) is about 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 f_0(980), for which there are still sizeable uncertainties. At present this leads to an uncertainty in the phi -> f_0 gamma branching ratio which can only be fixed by further precision data on the f_0(980).