Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved empirical parametrizations of the $\gamma^\ast N \to
  \Delta(1232)$ and $\gamma^\ast N \to N(1520)$ helicity amplitudes and the
  Siegert's theorem   In the nucleon electroexcitation reactions, $\gamma^\ast N \to R$, where $R$
is a nucleon resonance ($N^\ast$), the electric amplitude $E$, and the
longitudinal amplitude $S_{1/2}$, are related by $E \propto \frac{\omega}{|{\bf
q}|}S_{1/2}$, at the pseudo-threshold limit ($|{\bf q}| \to 0$), where $\omega$
and $|{\bf q}|$ are respectively the energy and the magnitude of three-momentum
of the photon. The previous relation is usually refereed as the Siegert's
theorem. The form of the electric amplitude, defined in terms of the transverse
amplitudes $A_{1/2}$ and $A_{3/2}$, and the explicit coefficients of the
relation, depend on the angular momentum and parity ($J^P$) of the resonance
$R$. The Siegert's theorem is the consequence of the structure of the
electromagnetic transition current, which induces constraints between the
electromagnetic form factors in the pseudo-threshold limit. In the present
work, we study the implications of the Siegert's theorem for the $\gamma^\ast N
\to \Delta(1232)$ and $\gamma^\ast N \to N(1520)$ transitions. For the
$\gamma^\ast N \to N(1520)$ transition, in addition to the relation between
electric amplitude and longitudinal amplitude, we obtain also a relation
between the two transverse amplitudes: $A_{1/2}= A_{3/2} /\sqrt{3}$, at the
pseudo-threshold. % The constraints at the pseudo-threshold are tested for the
MAID2007 parametrizations of the reactions under discussion. New
parametrizations for the amplitudes $A_{1/2}$, $A_{3/2}$ and $S_{1/2}$, for the
$\gamma^\ast N \to \Delta(1232)$ and $\gamma^\ast N \to N(1520)$ transitions,
valid for small and large $Q^2$, are proposed. The new parametrizations are
consistent with both: the pseudo-threshold constraints (Siegert's theorem) and
the empirical data.

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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat