Two-photon-exchange effects in the unpolarized μp scattering within the hadronic model

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In this work, the two-photon-exchange (TPE) effects in the unpolarized μp scattering are discussed within the hadronic model where the intermediate states N,Δ and σ are considered. The contribution from the N intermediate is close to the results given by Ref. Tomalak2014 at the small Q and there is a sizeable difference when Q>0.25GeV (where Q² is the four momentum transfer). The contributions from the Δ and the σ intermediate states are much smaller than that from the N intermediate at the small Q. In the kinematic region with kᵢ [0.01,0.3] GeV and Q ≤0.4GeV (where kᵢ is the three momentum of initial muon at Lab frame), a naive expression for the TPE contributions is given, which can be used directly for other analysis.