A measurement of two-photon exchange in Super-Rosenbluth separations with positron beams

The proton electric and magnetic form factors, $G_E$ and $G_M$, are intrinsically connected to the spatial distribution of charge and magnetization in the proton. For decades, Rosenbluth separation measurements of the angular dependence of elastic e$^-$-p scattering were used to extract $G_E$ and $G_M$. More recently, polarized electron scattering measurements, aiming to improve the precision of $G_E$ extractions, showed significant disagreement with Rosenbluth measurements at large momentum transfers ($Q^2$). This discrepancy is generally attributed to neglected two-photon exchange (TPE) corrections. At larger $Q^2$ values, a new `Super-Rosenbluth' technique was used to improve the precision of the Rosenbluth extraction, allowing for a better quantification of the discrepancy, while comparisons of e$^+$-p and e$^-$-p scattering indicated the presence of TPE corrections, but at $Q^2$ values below where a clear discrepancy is observed. In this work, we demonstrate the significant benefits to combining the Super-Rosenbluth technique with positron beam measurements. This approach provides a greater kinematic reach and is insensitive to some of the key systematic uncertainties in previous positron measurements.