# Transition form factors: $\gamma^\ast + p \to \Delta(1232)$, $\Delta(1600)$

## TL;DR

This paper calculates the transition form factors for gamma-star p to Delta(1232) and Delta(1600) using a relativistic diquark-quark model, providing predictions that align with existing data and extend to higher momentum transfers.

## Contribution

It introduces a fully-dynamical relativistic model for computing transition form factors of Delta resonances, including the first predictions for the Delta(1600) transition form factors.

## Key findings

- Calculated form factors agree with data for Delta(1232) outside meson-cloud domain.
- Predicted form factors for Delta(1600) match empirical values at the real photon point.
- The electric quadrupole form factor indicates deformation of Delta baryons.

## Abstract

Electroproduction form factors describing the $\gamma^\ast p \to \Delta^+(1232), \Delta^+(1600)$ 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 $\Delta(1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $\Delta(1232)$. Precise measurements of the $\gamma^\ast p \to \Delta^+(1232)$ 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 $\gamma^\ast p \to \Delta^+(1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to $Q^2 \approx 6 m_p^2$, 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 $\Delta$-baryons. Interestingly, whilst the $\gamma^\ast p \to \Delta^+(1232)$ transition form factors are larger in magnitude than those for $\gamma^\ast p \to \Delta^+(1600)$ in some neighbourhood of the real photon point, this ordering is reversed on $Q^2 \gtrsim 2 m_p^2$, suggesting that the $\gamma^\ast p \to \Delta^+(1600)$ transition is more localised in configuration space.