Transition form factors: γ * + p → Δ ( 1232 ) , Δ ( 1600 )
We report that electroproduction form factors describing the γ * p → 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 * p → Δ + ( 1232 ) transition already exist on 0 ≤ Q 2 ≲ 8 GeV 2 , and the calculated results compare favorably with the data outside the meson-cloud domain. The predictions for the γ * p → 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 ≈ 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, while the γ * p → Δ + ( 1232 ) transition form factors are larger in magnitude than those for γ * p → Δ + ( 1600 ) in some neighborhood of the real photon point, this ordering is reversed on Q 2 ≳ 2 m p 2 , suggesting that the γ * p → Δ + ( 1600 ) transition is more localized in configuration space.