Transition form factors: $γ^\ast + p \to Δ(1232)$, $Δ(1600)$

Abstract

Electroproduction form factors describing the $γ^\ast p \to Δ^+(1232), Δ^+(1600)$ transitions are computed using a fully-dynamical diquark-quark approximation to the Poincaré-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the $Δ(1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $Δ(1232)$. Precise measurements of the $γ^\ast p \to Δ^+(1232)$ transition already exist on $0 \leq Q^2 \lesssim 8\,$GeV$^2$ and the calculated results compare favourably with the data outside the meson-cloud domain. The predictions for the $γ^\ast p \to Δ^+(1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to $Q^2 \approx 6 m_p^2$, 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 $Δ$-baryons. Interestingly, whilst the $γ^\ast p \to Δ^+(1232)$ transition form factors are larger in magnitude than those for $γ^\ast p \to Δ^+(1600)$ in some neighbourhood of the real photon point, this ordering is reversed on $Q^2 \gtrsim 2 m_p^2$, suggesting that the $γ^\ast p \to Δ^+(1600)$ transition is more localised in configuration space.