Specific supersimple properties of $e^-e^+\to \gamma H$ at high energy

We study the process $e^-e^+\to \gamma H$, where $H$ represents $H_{SM}$, $h^0$ or $H^0$, which occurs at the one loop level in the standard model (SM) or in the minimal supersymmetric standard model (MSSM). We establish supersimple (sim) high energy expressions for all helicity amplitudes of this process, and we identify their level of accuracy for describing the various polarized and unpolarized observables, and for distinguishing SM from MSSM or another beyond the standard model (BSM). We pay a special attention to transverse electron-positron polarizations and azimuthal dependencies induced by the imaginary parts of the amplitudes, which are relatively important in this process.