Two-photon Exchange Corrections at Large Momentum Transfer Revised

Motivated by experimental data at large momentum transfer, we update the analysis of the two-photon exchange effect in the electron–nucleon scattering using the effective field theory formalism. Our approach is suitable for describing the hard \(s\sim |t|\sim |u|\gg \mit {\Lambda }^2\) region, where the hadronic model calculations are not accurate enough. We improve the estimates of various long-range matrix elements and discuss the obtained numerical effects for the unpolarised elastic cross section. Assuming a linear behaviour of the reduced cross section with respect to the photon polarisation, we show that the obtained description allows us to resolve the form factor discrepancy for \(Q^2=2.5\)–3.5 GeV\(^2\). However, the effect obtained is quite small for higher values of \(Q^2\). It is possible that nonlinear effects may be important in understanding the discrepancy in this region. Estimates of the elastic electron–neutron cross section in the region of \(Q^2=2.5\)–3.5 GeV\(^2\) are also performed. The obtained TPE effects are sufficiently large and must be taken into account. Abstract Published by the Jagiellonian University 2025 authors