Transition form factors: γ*+p→Δ(1232) , Δ(1600)

Abstract

Electroproduction form factors describing the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1232)$, ${\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ transitions are computed using a fully dynamical diquark-quark approximation to the Poincar\'e-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the $\mathrm{\ensuremath{\Delta}}(1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $\mathrm{\ensuremath{\Delta}}(1232)$. Precise measurements of the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1232)$ transition already exist on $0\ensuremath{\le}{Q}^{2}\ensuremath{\lesssim}8\text{ }\text{ }{\mathrm{GeV}}^{2}$, and the calculated results compare favorably with the data outside the meson-cloud domain. The predictions for the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to ${Q}^{2}\ensuremath{\approx}6{m}_{p}^{2}$, enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the $\mathrm{\ensuremath{\Delta}}$-baryons. Interestingly, while the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1232)$ transition form factors are larger in magnitude than those for ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ in some neighborhood of the real photon point, this ordering is reversed on ${Q}^{2}\ensuremath{\gtrsim}2{m}_{p}^{2}$, suggesting that the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ transition is more localized in configuration space.