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

TL;DR

The paper tackles the role of Two-Photon Exchange (TPE) in the time-like proton electromagnetic form factors by analyzing high-statistics BESIII data across a broad center-of-mass energy range. It introduces and employs a charge-asymmetry observable to isolate OPE⊗TPE effects and performs a detailed angular-distribution analysis, extracting interference coefficients that reveal a significant TPE contribution. The study reports the first clear TL observation of TPE in $e^{+}e^{-} \to p\bar p$, with an $8.6\sigma$ angular asymmetry and the most precise TL proton EMFF measurements to date, while validating the interpretation through comparisons with $e^{+}e^{-} \to \mu^{+}\mu^{-}$ and a careful treatment of radiation corrections. The results advance understanding of proton structure in the TL region, highlight the influence of the imaginary part of higher-order form factors such as $F_3$, and provide essential input for theoretical models of EMFFs.

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$σ$) 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.

Figures (3)

• Figure 1: (a) The charge asymmetry in the processes $e^{+}e^{-}\to p\bar{p}$ and $e^{+}e^{-}\to \mu^{+}\mu^{-}$ is depicted by the black dots with error bars and the purple squares with error bars, respectively, with the latter included for comparison. The overall charge asymmetry is represented by a green and red solid line with band, and a red solid line with band at $\sqrt{s}=2.125$ GeV. Both statistical and systematic uncertainties are included in this figure. (b) The overall dependence of $A_{c}$ on $\sqrt{s}$ for the process $e^{+}e^{-}\to p\bar{p}$ (represented by the black dots with error bars) is analyzed and the average is shown in a blue line and band. Both statistical and systematic uncertainties are included in this figure.
• Figure 2: (a) The fit to the corrected proton distribution $\mathrm{d} \sigma_{p\bar{p}}/\mathrm{d}\cos\theta$ at $\sqrt{s}=2.125$ GeV, using a symmetric model [illustrated by the red solid line and band, as equation (\ref{['dsigma']})] and an asymmetric model [illustrated by the blue solid line and band, equations(\ref{['dsigma']})+(\ref{['dint']})]. The red shaded area represents the contribution from symmetry, while the blue shaded portion indicates the asymmetry contribution. Only statistical uncertainties are shown in this figure. (b) The the interference coefficients $b_{1}(q^{2})$, is analyzed and represented by the orange dots with error bars. Both statistical and systematic uncertainties are included in this figure. (c) The the interference coefficients $b_{3}(q^{2})$, is analyzed and represented by the magenta dots with error bars. Both statistical and systematic uncertainties are included in this figure.
• Figure 3: The observed charge asymmetry distributions $\mathrm{d} A_{C}/\mathrm{d}\cos\theta$ before introducing any explicit constraint on $M_{p\bar{p}}$, across two energy intervals: (a) 2.0900-2.1228 GeV/$c^{2}$, and (b) 2.1228-2.1499 GeV/$c^{2}$, are showcased with corrected data points (black dots with error bars) and contrasted with Monte Carlo (MC) simulations (blue triangles with error bars) that incorporate vacuum polarization (VP) and radiation effects. The overall charge asymmetry for each energy intervals, illustrated by the green solid line and band. Both statistical and systematic uncertainties are included in this figure. The results shown are based on a Born-like event selection ($M_{p\bar{p}}>2.1228$ GeV), where TPE contributions are expected to be dominant.