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

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• 作者：G. Ramalho ^{gilberto.ramalho@iip.ufrn.br" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Physics Letters B
• 出版年：2016
• 出版时间：10 August 2016
• 年：2016
• 卷：759
• 期：Complete
• 页码：126-130
• 全文大小：426 K

文摘

Some empirical parametrizations of the k to view the MathML source">γ^⁎N→N(1535)${\gamma }^{⁎}N\to N(1535)$ 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 k to view the MathML source">N(1525)$N(1525)$ (mass k to view the MathML source">M_R$M_R$), the Siegert's theorem is sometimes expressed by the relation k to view the MathML source">|q|A_1/2=λS_1/2$|\mathbf{q}|A_{1/2}=\lambda S_{1/2}$ in the pseudo-threshold limit, when the photon momentum k to view the MathML source">|q|$|\mathbf{q}|$ vanishes, and $\lambda =\sqrt{2}(M_R-M)$. In this article, we argue that the Siegert's theorem should be expressed by the relation k to view the MathML source">A_1/2=λS_1/2/|q|$A_{1/2}=\lambda S_{1/2}/|\mathbf{q}|$, in the limit k to view the MathML source">|q|→0$|\mathbf{q}|\to 0$. This result is a consequence of the relation k to view the MathML source">S_1/2∝|q|$S_{1/2}\propto |\mathbf{q}|$, when k to view the MathML source">|q|→0$|\mathbf{q}|\to 0$, as suggested by the analysis of the transition form factors and by the orthogonality between the nucleon and k to view the MathML source">N(1535)$N(1535)$ states. We propose then new empirical parametrizations for the k to view the MathML source">γ^⁎N→N(1535)${\gamma }^{⁎}N\to N(1535)$ 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 k to view the MathML source">A_1/2$A_{1/2}$ and k to view the MathML source">S_1/2$S_{1/2}$ when k to view the MathML source">Q²<1.5 GeV²$Q^2<1.5{\text{GeV}}^2$.