Some Features of the Single Pion Photoproduction Amplitudes Constructed from Resonances

Abstract

The behaviour of the amplitudes which are constructed from resonances in the single pion photoproduction processes is shown for each t-channel isospin state. The contributions of the unnatural-parity meson exchange are also shown. Among various scattering processes, two of the best analyzed are rc (K) N ->rc(K)N and rN->rcN. The latter gives information on properties of the double helicity fltp amplitude and contributions of the unnatural-parity meson exchange. It is one of the most important problems to study the properties of these contributions and to find the relation between s-channel resonances and t-channel Regge poles. Unfortunately we have scarcely data on the region between 2 Ge V and 3 Ge V which is considered to be a very important region of transition from resonance to Regge. In this paper we investigate the behaviour of the amplitudes constructed from s-channel resonances in the single pion photoproductions and look for the relation mentioned above. The resonance parameters in the single pion photoproduction processes have been extensively investigated by many authors, 1l and are well confirmed for dominant resonances. The couplings for the resonances including non-dominant ones with the mass below 2.2 Ge V have recently been obtained by Devenish, Lyth and Rankin (D.L.R.) .2l In the analyses, their fundamental assumption is that the imaginary parts of the amplitudes may be resonance-saturated, and this is requested from duality ideas. 3l The resonances with their parameters are shown in Fig. 1 and Table. I. These parameters offered us facilities for seeing the characteristic features of the resonance region, at least up to 2 Ge V in the lab. photon energy. We decompose the resonance amplitudes into t-channel isospin states and investigate the properties of the imaginary parts of the photo­ production amplitudes. In our calculation, the resonance amplitude for each process is evaluated by the use of a Breit-Wigner form with resonance parame­ ters obtained by Devenish et al_2l As for real parts of the amplitudes, an exact answer is much dependent on the estimation of the so-called electric Born term, 4l so at present we leave the problem unsolved as a future one.