New low-Q2 measurements of the Coulomb quadrupole form factor, pion cloud parametrizations and Siegert’s theorem

G. Ramalho

doi:10.1140/epja/i2018-12514-6

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Hadrons and Nuclei

Eur. Phys. J. A (2018) 54: 75
https://doi.org/10.1140/epja/i2018-12514-6

Regular Article - Theoretical Physics

New low-Q² measurements of the $\gamma^{\ast}N\rightarrow\Delta (1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert’s theorem

G. Ramalho^*

Laboratório de Física Teórica e Computacional - LFTC, Universidade Cruzeiro do Sul, 01506-000, São Paulo, SP, Brazil

^* e-mail: gilberto.ramalho@cruzeirodosul.edu.br

Received: 19 February 2018
Accepted: 17 April 2018
Published online: 14 May 2018

Abstract

The novel measurements of the $\gamma^{\ast} N \rightarrow \Delta(1232)$ Coulomb quadrupole form factor in the range $Q^{2}=0.04-0.13$ GeV² changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in remarkable agreement with estimates of the pion cloud contributions to the quadrupole form factors at low $Q^{2}$ . The pion cloud contributions to the electric and Coulomb form factors can be parametrized by the relations $G_{E} \propto G_{En}/(1 + \frac{Q^{2}}{2M_{\Delta}(M_{\Delta}-M)})$ and $G_{C} \propto G_{En}$ , where $G_{En}$ is the neutron electric form factor, and M, $M_{\Delta}$ are the nucleon and $\Delta$ masses, respectively. Those parametrizations are in full agreement with Siegert’s theorem, which states that $G_{E}= \frac{M_{\Delta}-M}{2M_{\Delta}} G_{C}$ at the pseudothreshold, when $Q^{2}=-(M_{\Delta} -M)^{2}$ , and improve previous parametrizations. Also a small valence quark component estimated by a covariant quark model contributes to this agreement. The combination of the new data with the new parametrization for $G_{E}$ concludes an intense period of studying the $\gamma^{\ast} N \rightarrow \Delta(1232)$ quadrupole form factors at low $Q^{2}$ , with the agreement between theory and data.