The N Delta form factors: from the real photon to pseudothreshold

Abstract

We study the extrapolation of the electromagnetic N Delta transition form factors in the time-like region, from the real photon point to zero CM momentum (pseudothreshold), where the transition moments can be compared with quark model predictions. Our method consists of calculating the long-range contributions to the form factors due to the Delta -excitation by a 'quasi-real' pion photoproduced through the background. These long-range dispersive effects are of the order of 30% for the magnetic dipole and of 100% for the two electric quadrupoles. In particular, they account for the presently accepted experimental E2/M1 ratio and predict a large difference, for real photons, between the transverse and the longitudinal quadrupole moments. The imaginary parts are also investigated and found to be different from zero, through very small, only near pseudothreshold. As regards the k2 dependence, it is found that these contributions yield for the magnetic form factor a faster decrease than the dipole in the space-like region, as expected, but essentially the same for time-like photons. For the quadrupole moments, the extrapolation to pseudothreshold yields a vanishingly small value as foreseen by the naive quark model.