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

摘要

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 M R ), the Siegert's theorem is sometimes expressed by the relation | q | A 1 / 2 = λ S 1 / 2 in the pseudo-threshold limit, when the photon momentum | q | vanishes, and λ = 2 ( M R ? M ) . In this article, we argue that the Siegert's theorem should be expressed by the relation A 1 / 2 = λ S 1 / 2 / | q | , in the limit | q | → 0 . This result is a consequence of the relation S 1 / 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 A 1 / 2 and S 1 / 2 when Q 2 1.5 ? GeV 2 .