$γ^\ast N \to N(1535)$跃迁振幅的改进经验参数化和Siegert定理
Improved empirical parametrizations of the $γ^\ast N \to N(1535)$ transition amplitudes and the Siegert's theorem
摘要：
$γ^\ast N \to N(1535)$跃迁振幅的一些经验参数化违反了Siegert定理，该定理在赝阈值极限（核子和共振静止）中将纵向振幅和横向振幅联系起来。在从核子（质量为$M$）到共振$N(1525)$（质量为$M_R$）的电磁跃迁的情况下，Siegert定理有时可以表示为在赝阈值极限下的关系式$|{\bf q}| A_{1/2}= λS_{1/2}$（当光子动量$|{\bf q}|$为零时）和$λ= \sqrt{2} (M_R -M)$。本文证明了Siegert定理在极限$|{\bf q}| \to 0$下可用关系式$A_{1/2} = λ\frac{S_{1/2}}{ |{\bf q}|}$表示.这一结果是关系$S_{1/2} \propto |{\bf q}|$的结果，当$|{\bf q}| \to 0$，建议由过渡形状因子的分析和由核子和$N(1535)$状态之间的正交性。然后，我们提出了新的经验参数化的$γ^\ast N \to N(1535)$螺旋振幅，这是一致的数据和Siegert定理。建议的参数化密切遵循MAID 2007参数化，除了在幅度$A_{1/2}$和$S_{1/2}$的小偏差时，$Q^2 < 1.5$ GeV $^2$。
英文摘要：
Some empirical parametrizations of the $γ^\ast N \to N(1535)$ 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 $M$) to the resonance $N(1525)$ (mass $M_R$), the Siegert's theorem is sometimes expressed by the relation $|{\bf q}| A_{1/2}= λS_{1/2}$ in the pseudo-threshold limit, when the photon momentum $|{\bf q}|$ vanishes, and $λ= \sqrt{2} (M_R -M)$. In this article, we argue that the Siegert's theorem should be expressed by the relation $A_{1/2} = λ\frac{S_{1/2}}{ |{\bf q}|}$, in the limit $|{\bf q}| \to 0$. This result is a consequence of the relation $S_{1/2} \propto |{\bf q}|$, when $|{\bf q}| \to 0$, 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 $γ^\ast N \to N(1535)$ 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 $A_{1/2}$ and $S_{1/2}$ when $Q^2 < 1.5$ GeV$^2$.
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