Measurement of the Beam-Helicity Asymmetry in the $\mathit{p}(\overrightarrow{\mathit{e}},{\mathit{e}}^{\prime }\mathit{p}){\pi }^0$ Reaction at the Energy of the $\Delta \left(1232\right)$ Resonance

In a $p\left(\overrightarrow{e}{,e}^{\prime }p\right){\pi }^0$ out-of-plane coincidence experiment at the three-spectrometer setup of the Mainz Microtron MAMI, the beam-helicity asymmetry has been precisely measured around the energy of the $\Delta \left(1232\right)$ resonance and $Q^2=0.2\mathrm{}(\mathrm{GeV}/c{)}^2$. The results are in disagreement with three up-to-date model calculations. This is interpreted as a lack of understanding of the nonresonant background, which in dynamical models is related to the pion cloud.