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Nucleon and \({\Delta}\) Elastic and Transition Form Factors

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Abstract

We present a unified study of nucleon and \({\Delta}\) elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector \({\otimes}\) vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: \({G_{E}^{p}(Q^{2})/G_{M}^{p}(Q^{2})}\) possesses a zero at Q 2 = 9.5 GeV2; any change in the interaction which shifts a zero in the proton ratio to larger Q 2 relocates a zero in \({G_{E}^{n}(Q^{2})/G_M^{n}(Q^{2})}\) to smaller Q 2; there is likely a value of momentum transfer above which \({G_{E}^{n} > G_{E}^{p}}\); and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the \({\Delta(1232)}\)-baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the \({\Delta(1232)}\) Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the \({N \to \Delta}\) transition, the momentum-dependence of the magnetic transition form factor, \({G_{M}^{*}}\), matches that of \({G_{M}^{n}}\) once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities.

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Authors and Affiliations

  1. Physics Division, Argonne National Laboratory, Argonne, IL, 60439, USA

    Jorge Segovia, Ian C. Cloët & Craig D. Roberts

  2. Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany

    Sebastian M. Schmidt

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  1. Jorge Segovia
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  2. Ian C. Cloët
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Correspondence to Craig D. Roberts.

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Segovia, J., Cloët, I.C., Roberts, C.D. et al. Nucleon and \({\Delta}\) Elastic and Transition Form Factors. Few-Body Syst 55, 1185–1222 (2014). https://doi.org/10.1007/s00601-014-0907-2

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