Two-Photon-Exchange effects in $ep\rightarrow en\pi^+$ and their corrections to separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$ at small $-t$

TL;DR

This paper investigates two-photon-exchange effects in the $ep ightarrow en ext{ extpi}^+$ reaction at small momentum transfer, quantifying their impact on cross sections and emphasizing their importance for accurate experimental extraction of form factors.

Contribution

The study provides a hadronic model calculation of TPE effects on separated cross sections in $ep ightarrow en ext{ extpi}^+$, highlighting their significance in experimental analyses.

Findings

TPE corrections to unpolarized cross sections range from -4% to -20%.

Corrections to $\sigma_L$ are about -10% to -30%.

Corrections to $\sigma_T$ are around 20%.

Abstract

In this work, the two-photon-exchange (TPE) effects in $ep\rightarrow en\pi^+$ at small $-t$ are discussed within a hadronic model. Under the pion dominance approximation the TPE contribution to the amplitude can be described by a scalar function in the limit $m_e\rightarrow 0$. The TPE contributions to the amplitude and the unpolarized differential cross section are both estimated when only the elastic intermediate state is considered. We find that the TPE corrections to the unpolarized differential cross section are about from $-4\%$ to $-20\%$ at $Q^2=1$--$ 1.6$ GeV$^2$. After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$. We find that the TPE corrections (at $Q^2=1$--$1.6$ GeV$^2$) to $\sigma_{\textrm{L}}$ are about from $-10\%$ to $-30\%$, to $\sigma_{\textrm{T}}$ are about $20\%$, and to $\sigma_{\textrm{LT,TT}}$ are much larger. By these analysis, we conclude that the TPE contributions in $ep\rightarrow en\pi^+$ at small $-t$ are important to extract the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$ and the electromagnetic magnetic form factor of $\pi^+$ in the experimental analysis.