Figure 1

One-loop diagrams in the $N\to \Delta$ vertex. The single line is the dressed-quark propagator, $S\left(p\right)$; the double line is the diquark propagator; vertices are, respectively, the incoming nucleon, ${\Psi }_i$, and the outgoing $\Delta$, ${\Psi }_f$. From top to bottom, the diagrams describe the photon coupling: directly to a dressed quark; to a diquark, in an elastic scattering event; or inducing a transition between scalar and axial-vector diquarks. The $\Delta$ resonance contains only axial-vector diquark correlations so here only such diquarks appear in the top and middle diagrams. In the general case, there are three more diagrams, described in detail elsewhere [24]. They represent two-loop integrals.Reuse & Permissions

Figure 2

${\mu }_n{G}_M^{*p}/{\mu }_p^{*}{G}_M^n$ as a function of $x=Q^2/m_{\rho }^2$ (solid curve) and ${\mu }_n{G}_M^{*n}/{\mu }_n^{*}{G}_M^n$ (filled circles). For $N=p,n$, ${\mu }_N^{*}=G_M^{*N}(Q^2=0)$ and ${\mu }_n=G_M^n(Q^2=0)$. The elastic form factor results are those presented in Ref. [20], so that the comparison is internally consistent.Reuse & Permissions

Figure 3

Upper panel: $G_M^{*}\left(Q^2\right)$: contact-interaction result (solid curve); ameliorated result (dashed curve), explained around Eq. (9); SL-model dressed-quark-core result [27] (dot-dashed curve); and data from Refs. [4, 33, 34, 35, 36, 37], whose errors are commensurate with the point size. (Our formulation of the contact interaction produces Faddeev amplitudes that are independent of relative momentum; hence $G_M^{*}\left(Q^2\right)$ is hard.) Lower panel: ${\mu }_n{G}_{M,\mathrm{Ash}}^{*}\left(Q^2\right)/N\left(Q^2\right)$: contact-interaction (solid curve) and ameliorated result (dashed curve), both obtained with $N\left(Q^2\right)=G_M^n\left(Q^2\right)$. Also shown are empirical results [37] for $G_{M,\mathrm{Ash}}^{*}/N_D\left(Q^2\right)$, where $1/N_D\left(Q^2\right)={[1+Q^2/{\Lambda }^2]}^2$ and $\Lambda =0.71$ GeV, and the SL-model's dressed-quark-core result for this ratio [27] (dot-dashed curve).Reuse & Permissions

Figure 4

Ratios in Eq. (11): contact-interaction result (solid curves); ameliorated result (dashed curves), discussed around Eq. (9); and data [35, 36, 37, 40, 41, 42]. The dash-dot curve in the upper panel is representative of the computation in Ref. [32]. ($G_E^{*}$ and $G_C^{*}$ are small, so Ref. [27] could not reliably separate meson-cloud and dressed-quark core contributions to these ratios.)Reuse & Permissions

Figure 5

$R_{\mathrm{EM}}$ (solid curve) and $R_{\mathrm{SM}}$ (dashed curve) in Eq. (11), computed using the ameliorated contact interaction, discussed in connection with Eq. (9).Reuse & Permissions