Improved empirical parametrizations of the γ⁎N → N(1535) transition amplitudes and the Siegert's theorem

Some empirical parametrizations of the γ⁎N→N(1535) transition amplitudes violate 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 M) to the resonance N(1525) (mass MR), the Siegert's theorem is sometimes expressed by the relation |q|A1/2=λS1/2 in the pseudo-threshold limit, when the photon momentum |q| vanishes, and λ=2(MR−M). In this article, we argue that the Siegert's theorem should be expressed by the relation A1/2=λS1/2/|q|, in the limit |q|→0. This result is a consequence of the relation S1/2∝|q|, when |q|→0, as suggested by the analysis of the transition form factors and by the orthogonality between the nucleon and N(1535) states. We propose then new empirical parametrizations for the γ⁎N→N(1535) helicity amplitudes, that are consistent with the data and the Siegert's theorem. The proposed parametrizations follow closely the MAID2007 parametrization, except for a small deviation in the amplitudes A1/2 and S1/2 when Q2<1.5GeV2.