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

TL;DR

This paper investigates two-photon exchange effects in unpolarized muon-proton scattering using a hadronic model, highlighting the significance of intermediate states and providing a simplified expression for TPE contributions in specific kinematic regions.

Contribution

The study models TPE effects considering N, Δ, and σ intermediate states, offering new insights into their relative contributions and a practical expression for certain kinematic conditions.

Findings

N intermediate contribution aligns with previous results at small Q

Δ and σ contributions are smaller at low Q

A simplified TPE expression is provided for specific kinematic range

Abstract

In this work, the two-photon-exchange (TPE) effects in the unpolarized $\mu p$ scattering are discussed within the hadronic model where the intermediate states $N,\Delta$ and $\sigma$ are considered. The contribution from the $N$ intermediate is close to the results given by Ref. \cite{Tomalak2014} at the small $Q$ and there is a sizeable difference when $Q>0.25$GeV (where $Q^2$ is the 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 of initial muon at Lab frame), a naive expression for the TPE contributions is given, which can be used directly for other analysis.