Two-Photon-Exchange Effects and $\Delta(1232)$ Deformation

TL;DR

This paper calculates the two-photon-exchange effects in pion electroproduction near the Delta resonance, showing small corrections to some form factor ratios but significant impact on the scalar ratio at small epsilon, crucial for accurate data interpretation.

Contribution

It provides a detailed estimation of TPE effects on electromagnetic transition form factors using a hadronic model and phenomenological inputs, highlighting their importance in experimental analyses.

Findings

TPE effects cause about -10% correction to R_{SM} at small epsilon.

TPE contributions are insensitive to the choice of phenomenological models (MAID or SAID).

Corrections to R_{EM} are small, but significant for R_{SM} at certain kinematics.

Abstract

The two-photon-exchange (TPE) contribution in $ep\rightarrow ep\pi ^0$ with $W=M_{\Delta}$ and small $Q^2$ is calculated and its corrections to the ratios of electromagnetic transition form factors $R_{EM} = E_{1+}^{(3/2)}/M_{1+}^{(3/2)} $ and $R_{SM} = S_{1+}^{(3/2)}/M_{1+}^{(3/2)}$, are analysed. A simple hadronic model is used to estimate the TPE amplitude. Two phenomenological models, MAID2007 and SAID, are used to approximate the full $ep\rightarrow ep\pi ^0$ cross sections which contain both the TPE and the one-photon-exchange (OPE) contributions. The genuine the OPE amplitude is then extracted from an integral equation by iteration. We find that the TPE contribution is not sensitive to whether MAID or SAID is used as input in the region with $Q^2<2$ GeV$^2$. It gives small correction to $R_{EM}$ while for $R_{SM}$, the correction is about -10\% at small $\epsilon$ and about $1\%$ at large $\epsilon$ for $Q^2\approx2.5$ GeV$^2$. The large correction from TPE at small $\epsilon$ must be included in the analysis to get a reliable extraction of $R_{SM}$.