Dissecting nucleon transition electromagnetic form factors

In Poincaré-covariant continuum treatments of the three valence-quark bound-state problem, the force behind dynamical chiral symmetry breaking also generates nonpointlike interacting diquark correlations in the nucleon and its resonances. We detail the impact of these correlations on the electromagnetically induced nucleon-$\mathrm{\Delta }$ and nucleon-Roper transitions, providing a flavor separation of the latter and associated predictions that can be tested at modern facilities.

Figure 1

$\gamma p\to {\mathrm{\Delta }}^{+}$ magnetic dipole form factor $G_M^{*}$, computed as described in Ref. [19] (solid black curve). The mismatch at small $x$ between data [26, 27, 28, 29, 30] and prediction is explained by meson-cloud effects [19, 33, 34, 35]. Upper panel—diquark dissection: T1B (dot-dashed green curve): pseudovector diquark in both $p,{\mathrm{\Delta }}^{+}$; T1C (dotted blue curve): scalar diquark in $p$, and pseudovector diquark in ${\mathrm{\Delta }}^{+}$. Lower panel—scatterer dissection: T2A (red dashed curve): photon strikes an uncorrelated dressed quark; T2B (dot-dashed green curve): photon strikes a diquark; and T2C (dotted blue curve): diquark breakup contributions, including a photon striking exchanged dressed quark.

Figure 2

$\gamma p\to {\mathrm{\Delta }}^{+}$ electric quadrupole form factor $G_E^{*}$, computed as described in Ref. [19] (solid black curve). The data are drawn from the dynamical coupled-channel analysis in Ref. [34]: circles, complete result; and triangles, an estimate of $G_E^{*}$ as it would appear in the absence of MB FSIs. The legend is otherwise as it appears in Fig. 1.

Figure 3

$\gamma p\to {\mathrm{\Delta }}^{+}$ Coulomb quadrupole form factor $G_C^{*}$, computed as described in Ref. [19] (solid black curve). The legend is as it appears in Fig. 2, with the results from Ref. [34] multiplied by “$-1$” in order to match our conventions for this form factor.

Figure 4

$\gamma p\to R^{+}$ Dirac transition form factor $F_{1,p}^{*}$ as a function of $x=Q^2/m_N^2$, computed as described in Ref. [20] (solid black curve). Data: circles (blue) [30] and squares (purple) [44]. Upper panel—diquark breakdown: T1A (dashed red curve), scalar diquark in both $p,R^{+}$; T1B (dot-dashed green), pseudovector diquark in both $p,R^{+}$; T1C (dotted blue curve), scalar diquark in $p$, pseudovector diquark in $R^{+}$, and vice versa. Lower panel—scatterer breakdown: T2A (red dashed curve), photon strikes an uncorrelated dressed quark; T2B (dot-dashed green curve), photon strikes a diquark; and T2C (dotted blue curve), diquark breakup contributions, including a photon striking exchanged dressed quark.

Figure 5

$\gamma p\to R^{+}$ Pauli transition form factor $F_{2,p}^{*}$ as a function of $x=Q^2/m_N^2$, computed as described in Ref. [20] (solid black curve). Data: circles (blue) [30]; squares (purple) [44]; triangle (gold) [61]; and star (green) [65]. Upper panel—diquark breakdown; lower panel—scatterer breakdown; and legend as in Fig. 4.

Figure 6

Flavor separation, $\gamma p\to R^{+}$ transition form factors: $u$ quark, solid black curve: and $d$ quark, dashed blue. Upper panel—Dirac transition form factor. Lower panel—Pauli transition form factor with ${\kappa }_u^{*}=F_{2,u}^{*}\left(0\right)=-0.91,{\kappa }_d^{*}=F_{2,d}^{*}\left(0\right)=0.14$.

Figure 7

$x^2={(Q^2/m_N^2)}^2$-weighted behavior of the flavor-separated $\gamma p\to R^{+}$ transition form factors: $u$ quark, solid black curve; and $d$ quark, dashed blue curve. Upper (lower) panel—Dirac (Pauli) transition form factor.