The analysis of the $\gamma p\to \eta {\pi }^{0}p$ reaction has been performed using data from the GRAAL experiment. The total and differential cross sections and the beam asymmetry have been obtained from threshold up to 1.5 GeV of beam energy. The two resonances $S_{11}(1535)$ and $\Delta (1700)$ are expected to be excited in the intermediate states of this reaction. The results are used to test predictions based on the assumption that both resonances are dynamically generated from the meson-baryon interaction provided by chiral Lagrangians. The term involving the $\Delta (1700)$ excitation, followed by the decay into $\eta \Delta (1232)$, is found to be dominant.

The possibility of anisotropies in the speed of light relative to the limiting speed of electrons is considered. The absence of sidereal variations in the energy of Compton-edge photons at the European Synchrotron Radiation Facility's GRAAL facility constrains such anisotropies representing the first nonthreshold collision-kinematics study of Lorentz violation. When interpreted within the minimal standard-model extension, this result yields the two-sided limit of 1.6\ifmmode\times\else\texttimes\fi{}10-14 at 95% confidence level on a combination of the parity-violating photon and electron coefficients ($\kappa${}\texttildelow{}o+)YZ, ($\kappa${}\texttildelow{}o+)ZX, cTX, and cTY. This new constraint provides an improvement over previous bounds by 1 order of magnitude.