Single $\pi^{\mathrm{0}}$ Photoproduction off the Deuteron

The quasifree $\gamma $d $\to \pi^{\mathrm{0}}$n(p) photon beam asymmetry,~has been measured at photon energies~from 390 to 610 MeV, corresponding to CM~energies, W, from 1.271 to 1.424 GeV, for the first time. The data was collected in the A2 Hall of the~MAMI electron beam facility with the Crystal Ball and~TAPS calorimeters covering pion CM angles from 48 to 148 degrees.~In these kinematic regions, polarization observables are sensitive to contributions from~the $\Delta $(1232) and N$^{\mathrm{\ast }}$(1440) resonances. The extracted values of $\Sigma $ have been compared to predictions based~on~PWAs of the existing pion-photoproduction database. We include the SAID, MAID,~and Bonn-Gatchina analyses; while a revised SAID fit,~including the new $\Sigma $ measurements, has also been performed. In addition, isospin symmetry is examined as a~way to predict $\pi ^{\mathrm{0}}$n photoproduction observables, based~on fits to~published~data in the channels $\pi^{\mathrm{0}}$p, $\pi ^{\mathrm{+}}$n, and $\pi^{\mathrm{-}}$p.