Comparison of Neural Network and Hadronic Model Predictions of Two-Photon Exchange Effect

Abstract

Predictions for the two-photon exchange (TPE) correction to unpolarized $ep$ elastic cross section, obtained within two different approaches, are confronted and discussed in detail. In the first one the TPE correction is extracted from experimental data by applying the Bayesian neural network (BNN) statistical framework. In the other the TPE is given by box diagrams, with the nucleon and the $P_{33}$ resonance as the hadronic intermediate states. Two different form factor parametrizations for both the proton and the $P_{33}$ resonance are taken into consideration. Proton form factors are obtained from the global fit of the full model (with the TPE correction) to the unpolarized cross section data. Predictions of both methods agree well in the intermediate $Q^2$ range, $(1,3)$ GeV${}^2$. Above $Q^2=3$ GeV${}^2$ the agreement is on $2\sigma$ level. Below $Q^2=1$ GeV${}^2$ the consistency between both approaches is broken. The values of the proton radius extracted within both models are given. In both cases predictions for VEPP-3 experiment have been obtained and confronted with the preliminary experimental results.

19 pages, 12 figures, 4 tables. Section 3, dedicated to Bayesian neural networks, has been extended. One new figure (Fig. 2) has been added. Two other figures have been removed. Sect. 5 has been re-edited and also extended

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• A dispersive approach to two-photon exchange in elastic electron-proton scattering
• Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future
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• The Proton Radius from Bayesian Inference
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• Relevance of Two Boson Exchange Effect in Quasi-Elastic Charged Current Neutrino-Nucleon Interaction
• Resonance Contributions to Radiative Corrections in Charged-Current Elastic (Anti)Neutrino-Nucleon Scattering at GeV Energies