Sadiq Thesis Latex

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Introduction

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\section{Positron Beam}

Positrons have many potentials in many discipline of science, like chemistry, physics, material science, surface science, biology and nanoscience~\cite{Chemerisov:2009zz} There are many different ways to generate positrons, and the main challenge is increasing the intensity (or current) of the positron beam.

\section{Motivation} The nucleon electromagnetic form factors are fundamental quantities that related to the charge and magnetization distribution in the nucleon. Conventionally, the nucleon form factors are measured using Rosenbluth Technique (RT)~\cite{Rosenbluth1950}. The form factor scaling ratio,\begin{math}R=\mu _p G_{Ep} / G_{Mp}\end{math}, measured using this technique is around unity as shown in the figure below~\cite{PhysRevD.49.5671}. Since nighties, a technique using elastic electron-proton polarization transfer to measurement this ratio have been developed~\cite{PhysRevD.49.5671, PhysRevC.68.034325, WalkerThesis1989}. In this technique, form factor scaling ratio linearly decreases as the the \begin{math}Q^2\end{math} increases, as shown in the Fig.~\ref{rosen-com-RPT}.

\begin{figure}[htb] \centering \includegraphics[scale=0.70]{1-Introduction/Figures/Sadiq_thesis_mot_RT_RPT_1.png} \caption{Form factor ratio, obtained by Rosenbluth Technique (hollow square) and results from Recoil Polarization Technique~\cite{PhysRevC.68.034325}.} \label{rosen-com-RPT} \end{figure}

The disagreement could arise from the fact the Rosenbluth Techqniue assumes that One Photon Exchange (OPE) during the scattering while the two–photon exchange (TPE), which depends weakly on \begin{math}Q^2\end{math}, could also become considerable with increasing \begin{math}Q^2\end{math} ~\cite{PhysRevC.68.034325}. The contribution of TPE can be obtained by comparing the ratio of \begin{math}e^+~p\end{math} to \begin{math}e^-~p\end{math} ratio. The interference of OPE and TPE can also be studied in the process \begin{math}e^+e^- \rightarrow p\bar p\end{math}

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