Measurement of Spin-Density Matrix Elements in ${\mathrm{\Delta }}^{++}(1232)$ photoproduction

We measure the spin-density matrix elements (SDMEs) of the ${\mathrm{\Delta }}^{++}(1232)$ in the photoproduction reaction $\gamma p\to {\pi }^{-}{\mathrm{\Delta }}^{++}(1232)$ with the GlueX experiment in Hall D at Jefferson Lab. The measurement uses a linearly–polarized photon beam with energies from $8.2$ to $8.8$~GeV and the statistical precision of the SDMEs exceeds the previous measurement by three orders of magnitude for the momentum transfer squared region below $1.4$ GeV${}^2$. The data are sensitive to the previously undetermined relative sign between couplings in existing Regge-exchange models. Linear combinations of the extracted SDMEs allow for a decomposition into natural and unnatural–exchange amplitudes. We find that the unnatural exchange plays an important role in the low momentum transfer region.