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In this work, the two-photon-exchange (TPE) effects in the unpolarized $\mup$ scattering are discussed within the hadronic model where the intermediatestates $N,\Delta$ and $\sigma$ are considered. The contribution from the $N$intermediate is close to the results given by Ref. \cite{Tomalak2014} at thesmall $Q$ and there is a sizeable difference when $Q>0.25$GeV (where $Q^2$ isthe four momentum transfer). The contributions from the $\Delta$ and the$\sigma$ intermediate states are much smaller than that from the $N$intermediate at the small $Q$. In the kinematic region with $k_i\subseteq[0.01,0.3]$ GeV and $Q \leq0.4$GeV (where $k_i$ is the three momentum ofinitial muon at Lab frame), a naive expression for the TPE contributions isgiven, which can be used directly for other analysis.

Two-photon-exchange effects in the unpolarized $\mu p$ scattering within the hadronic model