Empirical parametrizations of the resonance amplitudes based on the Siegert's theorem

TL;DR

This paper develops empirical parametrizations for specific nucleon resonance transition amplitudes that adhere to Siegert's theorem and fit experimental data, improving the modeling of these electromagnetic processes.

Contribution

It introduces new parametrizations of resonance transition amplitudes that are consistent with Siegert's theorem and align with experimental observations.

Findings

Parametrizations satisfy analytic constraints at the pseudothreshold.

The models provide a good fit to experimental data.

Adjustments to pion cloud contributions are discussed for the Δ(1232) transition.

Abstract

We present parametrizations of the $\gamma^\ast N \to N(1535)1/2^-$, $\gamma^\ast N \to N(1520)3/2^-$ and $\gamma^\ast N \to \Delta(1232)3/2^+$ transition amplitudes that are compatible with the analytic constraints at the pseudothreshold (Siegert's theorem). The presented parametrizations also provide a fair description of the experimental data. For the case of the $\gamma^\ast N \to \Delta(1232)3/2^+$ transition, we discuss how the pion cloud parametrizations of the electric and the Coulomb quadrupole form factors can be adjusted according to the Siegert's theorem.