Exploration of Two-Photon Exchange in proton Form Factors at BESIII

Abstract: The proton and neutron make up over 99.9\% of visible matter in the universe. The internal structure of protons, governed by ElectroMagnetic Form Factors (EMFFs), has been probed in both space-like (SL) and time-like (TL) regions. The BESIII experiment has achieved the most precise TL proton FF measurements to date, providing new insights into proton structure. However, higher-order effects in EMFFs, especially the impact of Two-Photon Exchange (TPE), remain poorly understood due to experimental challenges in $e^{+}e^{-}$ annihilation. In this work, we analyze high-statistics BESIII data across a wide c.m. energy range and observe, for the first time, a significant angular asymmetry (8.6$\sigma$) in proton production. We demonstrate that this asymmetry arises from TPE, using a Born-like event selection, and extract the corresponding TPE-related EMFF properties. The observed interference between two-photon and one-photon exchanges (OPE$\otimes$TPE) is consistent with expectations at the level of the fine-structure constant relative to the OPE.