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

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 Poincaré-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 $0\le Q^2\lesssim 8$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 $Q^2\approx 6m_p^2$, 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 $Q^2\gtrsim 2m_p^2$, suggesting that the ${\gamma }^{\ast }p\to {\Delta }^{+}(1600)$ transition is more localised in configuration space.

Comments: 13 pages, 8 figures, 2 tables