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\newcommand{\Lumi}{ \mathcal{L}}


\title{Analysis Note on the Deeply Virtual Neutral Pion Production Cross Section Measurement}


\author{Robert Johnston$^1$ \and Sangbaek Lee$^1$
\and Igor Korover$^1$
\and Xiaqing Li$^1$
\and Andrey Kim$^2$
}
\date{%
    $^1$Massachusetts Institute of Technology\\%
    $^2$University of Connecticut\\[2ex]%
    \today
}


\begin{document}

\maketitle
\tableofcontents
\cleardoublepage
% \phantomsection
\addcontentsline{toc}{chapter}{\listfigurename}
\listoffigures

\chapter{Collaborator's Note: Differences Between This and Prior Analysis Note}
For ease of reading by collaborators, here are a listing of differences between this analysis note (for Fall 2022 DNP meeting) and the most recently collaboration approved analysis note (for April 2022 APS meeting):
\begin{itemize}
    \item \textbf{Model Comparison} The large reported change from analysis notes is the inclusion of the Goloskov Kroll Model to compare the preliminary CLAS12 cross section to a theoretical model. This is covered in section \ref{chap:GKmodel}.
    \item \textbf{Exclusivity Cuts and Results} There are small improvements to this text for a more complete description of work accomplished.
\end{itemize}

\chapter{PID}
\input{PID}

\chapter{Exclusive Selection}  
\label{chap:exclusive}
\input{Exclusive}

\chapter{Simulations}
\label{chap:acc}
\input{Simulations}

\chapter{Luminosity and Virtual Photon Flux Factor}
\label{chap:lumi}
\input{Luminosity}

\chapter{Results}
\input{Results}

\chapter{Comparison with Model} 
\label{chap:GKmodel}
\input{model}


\chapter{Acknowledgements}
Acknowledgement should be given to the MIT Milner Hadronic Physics group: Richard Milner, Douglas Hasell, Igor Korover, Xiaqing Li, Patrick Moran, Sangbaek Lee, and Robert Johnston. This work was also facilitated by the use of OSG and MIT Tier 2 computing, so we would like to thank Maurizio Ungaro, Christoph Paus, Ernie Ihloff, Jim Kelsey, and others for their technical support. 

\include{biblio}

\chapter{Appendix}

\iffalse

From paper on understanding pi+ production, we have:

 \begin{equation}\label{xsec}
     \frac{d^4\sigma_{\gamma^*p \rightarrow p'\pi^0}}{dQ^2W^2dtd\phi_{\pi}} =
     \frac{\alpha (W^2-m^2)}{16\pi^2 E^2_L m^2 Q^2 (1-\epsilon)}
     ((\frac{d\sigma_T}{dt}+\epsilon\frac{d\sigma_L}{dt})+
     \epsilon cos(2\phi) \frac{d\sigma_{TT}}{dt} + \sqrt{2\epsilon(1+\epsilon)}cos(\phi)\frac{d\sigma_{LT}}{dt})
\end{equation}

Comparing the two, we have a difference in the prefactor of:



0.3894 * 1E6 * $\frac{1}{16\pi(W^2-m_p^2)\sqrt{W^4 + (Q^2)^2+m_p^4+2W^2Q^2-2W^2m_p^2+2Q^2m_p^2}}$
\fi

\input{Appendix}


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