Gauge invariant two-photon exchange contributions in e−π+→e−π+

The gauge invariant two-photon exchange (TPE) contributions in e−π+→e−π+ are discussed at hadronic level. The contact term is added to keep the full amplitude gauge invariant by two methods: one is to multiply form factors with the amplitude for point-like particles and another is to construct a gauge invariant Lagrangian. The practical calculations show the TPE contributions by these two methods are almost the same, while the later method is favored when extending the discussion to processes including two charged finite-size particles like ep→enπ+.