Parametrizations of the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors and Siegert's theorem

Abstract

The large $N_c$ limit provides relations that can be used to calculate the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors at low and intermediate $Q^2$ under the assumption of the pion cloud dominance. There are two limitations in those parametrizations. First, the parametrization of the Coulomb quadrupole form factor underestimate the low $Q^2$ data. Second, when extrapolated for the timelike region, the form factors violate Siegert's theorem by terms of the order $1/N_c^2$. We propose here corrections to the parametrization of the electric quadrupole form factor, which violate Siegert's theorem only by terms of the order $1/N_c^4$. Combining the improved large $N_c$ pion cloud parametrizations with the valence quark contributions based on a covariant quark model for the quadrupole transition form factors, we obtain an extrapolation to the timelike region consistent with Siegert's theorem, and accomplish also a very good description of the data.

Published version. Extended version with new title. 6 pages, 4 figures

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• New low-$Q^2$ measurements of the ${\gamma }^{\ast }N\to \Delta (1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert's theorem
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• Electroweak form factors of baryons in dense nuclear matter
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• Quark model calculations of transition form factors at high photon virtualities
• A Relativistic Model for the Electromagnetic Structure of Baryons from the 3rd Resonance Region
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