Determination of Radiative Widths of Scalar Mesons from Experimental Results on γγ → ππ

The scalar mesons in the 1 GeV region constitute the Higgs sector of the strong interactions. They are responsible for the masses of all light flavour hadrons. However, the composition of these scalar states is far from clear, despite decades of experimental effort. The two photon couplings of the f 0 's are a guide to their structure. Two photon results from Mark II, Crystal Ball and CELLO prompt a new Amplitude Analysis of γγ → π + π − , π 0 π 0 cross-sections. Despite their currently limited angular coverage and lack of polarized photons, we use a methodology that provides the nearest one can presently achieve to a model-independent partial wave separation. We find two distinct classes of solutions. Both have very similar two photon couplings for the f 0 (980) and f 0 (400 − 1200). Hopefully these definitive results will be a spur to dynamical calculations that will bring us a better understanding of these important states. 1 1 Introduction Two photon processes are a remarkably useful tool for studying the structure of matter and determining the composition of hadrons [1]. Photons clearly couple to charged objects and the observed cross-sections are directly related to these charges. Thus, for example, in the reaction γγ → ππ, the shape of the integrated cross-sections perfectly illustrates this dynamics. At low energies, the photon sees the pion as a whole entity and couples to its charge. Consequently, the cross-section for γγ → π + π − is large at threshold, whereas the γγ → π 0 π 0 cross-section is very small [2]. When the energy increases, the shortening of its wavelength enables the photon to see the individual constituents of the pion, couples to their charges and causes them to resonate (see, for instance, [3]). Both the charged and neutral cross-sections are then dominated by the Breit-Wigner peak corresponding to the f 2 (1270) resonance, with several underlying f 0 states. The coupling of each of these to γγ is a measure of the charges of their constituents (to the fourth power) and so helps to build up a picture of the inner nature of these mesons. But how do we determine their γγ couplings from experimental data ? In an ideal world, with complete information on all the possible angular correlations between the initial and final state directions and spins, we could decompose the cross-sections into …