Gauge Invariant Two-Photon-Exchange Contributions in $e^-\pi^+ \rightarrow e^-\pi^+$

TL;DR

This paper investigates gauge invariant two-photon exchange contributions in electron-pion scattering, comparing two methods for maintaining gauge invariance, and finds their results are nearly identical, with implications for more complex processes.

Contribution

It introduces and compares two methods for ensuring gauge invariance in TPE calculations in hadronic processes, favoring the gauge invariant Lagrangian approach for complex systems.

Findings

TPE corrections are similar across both methods

The gauge invariant Lagrangian approach is preferable for complex processes

Results support consistent TPE calculations in hadronic physics

Abstract

The gauge invariant two-photon exchange (TPE) contributions in $e^-\pi^+ \rightarrow e^-\pi^+$ 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 point-like particles scattering amplitude and another is to construct a gauge invariant Lagangian. The practical calculations show the TPE corrections 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 $ep \rightarrow en\pi^+$.