Improved empirical parametrizations of the transition amplitudes and the Siegert's theorem
Some empirical parametrizations of the transition amplitudes violates the Siegert's theorem, that relates the longitudinal and the transverse amplitudes, in the pseudo-threshold limit (nucleon and resonance at rest). In the case of the electromagnetic transition from the nucleon (mass ) to the resonance (mass ), the Siegert's theorem is sometimes expressed by the relation in the pseudo-threshold limit, when the photon momentum vanishes, and . In this article, we argue that the Siegert's theorem should be expressed by the relation , in the limit . This result is a consequence of the relation , when , as suggested by the analysis of the transition form factors and by the orthogonality between the nucleon and states. We propose then new empirical parametrizations for the helicity amplitudes, that are consistent with the data and the Siegert's theorem. The proposed parametrization follow closely the MAID2007 parametrization, except for a small deviation in the amplitudes and when GeV.