Two-photon exchange corrections to ${\gamma }^{\ast }N\Delta$ form factors for $Q^2\le 4$ (Gev/$c$)${}^2$

Abstract

We evaluate the corrections of the two-photon exchange (TPE) process on the ${\gamma }^{\ast }N\Delta$ transition form factors. The contributions of the TPE process to the $eN\to e\Delta (1232)\to eN\pi$ are calculated in a hadronic model with the inclusion of only the elastic nucleon intermediate states, to estimate its effects on the multipoles $M_{1^{+}}^{(3/2)},E_{1^{+}}^{(3/2)},S_{1^{+}}^{(3/2)}$ at the $\Delta$ peak. We find that TPE effects on $G_M^{\ast }$ is very small. $G_E^{\ast },$ and $G_C^{\ast }$ are also little affected at small $Q^2$. For $G_E^{\ast }$, the TPE effects reach about $3-8\%$ near $Q^2\sim 4$ GeV${}^2$, depending on the model, MAID or SAID, used to emulate the data. For $G_C^{\ast }$, the TPE effects decrease rapidly with increasing $ϵ$ while growing with increasing $Q^2$ to reach $\sim 6-15\%$ with $Q^2\sim 4$ GeV${}^2$ at $ϵ=0.2$. Sizeable TPE corrections to $G_E^{\ast }$ and $G_C^{\ast }$ found here points to the need of including TPE effects in the multipole analysis in the region of high $Q^2$ and small $ϵ$. The TPE corrections to $R_{EM}$ and $R_{SM}$ obtained in our hadronic calculation are compared with those obtained in a partonic calculation for moderate momentum transfer of $2<Q^2<4$ GeV${}^2$.

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