Backward Compton scattering sum rule and the &#960;<SUP>0</SUP>&#8594;2&#947;,&#951;<SUP>0</SUP>&#8594;2&#947; decay rates

We use the superconvergence of certain Compton scattering (s-channel) helicity amplitudes for fixed s and large t, to derive a sum rule for t- and u-channel processes. The u-channel (&#947;N&#8594;&#947;N) contribution contains the well-known nucleon pole terms and the continuum, which we replace by just the &#960;-N intermediate states; we then feed in photoproduction data. The t-channel (&#947;&#947;&#8594;NN&#x0305;) contribution consists of the &#960;, &#951; poles and the continuum. We choose a suitable combination of superconvergent amplitudes such that the effects of 0+, 2+, and 1+ resonances in the t channel are eliminated. Assuming that this takes care of most of the t-channel continuum, we get a sum rule for the &#960;0&#8594;2&#947; and &#951;0&#8594;2&#947; widths, or alternatively, by using the experimental widths, we can check the consistency of the superconvergence in question. A brief comparison is made with related work by Goldberger and Abarbanel, and by Pagels