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Some empirical parametrizations of the $\gamma^\ast N \to N(1535)$ transitionamplitudes violates the Siegert's theorem, that relates the longitudinal andthe transverse amplitudes, in the pseudo-threshold limit (nucleon and resonanceat 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 issometimes expressed by the relation $|{\bf q}| A_{1/2}= \lambda S_{1/2}$ in thepseudo-threshold limit, when the photon momentum $|{\bf q}|$ vanishes, and$\lambda = \sqrt{2} (M_R -M)$. In this article, we argue that the Siegert'stheorem should be expressed by the relation $A_{1/2} = \lambda \frac{S_{1/2}}{|{\bf q}|}$, in the limit $|{\bf q}| \to 0$. This result is a consequence ofthe relation $S_{1/2} \propto |{\bf q}|$, when $|{\bf q}| \to 0$, as suggestedby the analysis of the transition form factors and by the orthogonality betweenthe nucleon and $N(1535)$ states. We propose then new empiricalparametrizations for the $\gamma^\ast N \to N(1535)$ helicity amplitudes, thatare consistent with the data and the Siegert's theorem. The proposedparametrization follow closely the MAID2007 parametrization, except for a smalldeviation in the amplitudes $A_{1/2}$ and $S_{1/2}$ when $Q^2 < 1.5$ GeV$^2$.

Improved empirical parametrizations of the $\gamma^\ast N \to N(1535)$ transition amplitudes and the Siegert's theorem