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\begin {document}

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\begin{center}

{\Huge A Run-Group Proposal Submitted to PAC 45}

\vspace*{25pt}

{\LARGE\bf
Measurement of Deep Exclusive $\mathrm\pi^-$ Production
using a Transversely Polarized $\mathrm{^{3}He}$ Target
and the SoLID Spectrometer}

\vspace*{3ex}
\today

\vspace*{30pt}

J. Arrington, K. Hafidi, M. Hattawy, P. Reimer, S. Riordan, Z. Ye$^\ast$ \\
{\it Argonne National Laboratory, Physics Division, Argonne, IL, USA}
\vspace*{15pt}

Z. Ahmed$^\ast$, G.R. Ambrose, S. Basnet, R.S. Evans, G.M. Huber$^\dagger$,
W. Li, D. Paudyal, Z. Papandreou\\
{\it University of Regina, Regina, SK, Canada}
\vspace*{15pt}

H. Gao, X. Li, T. Liu, C. Peng, W. Xiong, X.F. Yan, Z. Zhao\\
{\it Duke University, Durham, NC, USA}
\vspace*{15pt}

A. Camsonne,  J-P. Chen, S. Covrig-Dusa, D. Gaskell\\
{\it  Jefferson Lab, Newport News, VA, USA}
\vspace*{15pt}

T. Brecelj, M. Mihovilovi\v{c}, S. \v{S}irca, S. \v{S}tajner\\
{\it Jo\v{z}ef Stefan Institute and University of Ljubljana, Slovenia}
\vspace*{15pt}

K. Aniol\\
{\it California State University -- Los Angeles, Los Angeles, CA, USA}
\vspace*{15pt}

M. Boer\\
{\it Los Alamos National Laboratory, Physics Division, Los Alamos, NM, USA}
\vspace*{15pt}

D. Dutta, L. Ye\\
{\it Mississippi State University, Mississippi State, MS, USA}
\vspace*{15pt}

C. E. Hyde, F.R. Wesselmann \\
{\it Old Dominion University, Norfolk, VA, USA}
\vspace*{15pt}

P. Markowitz\\
{\it Florida International University, Miami, FL, USA}
\vspace*{15pt}

\clearpage
V. Sulkosky  \\
{\it University of Virginia, Charlottesville, VA, USA}
\vspace*{15pt}

E. Voutier\\
{\it Institut de Physique Nucl\'eaire IN2P3/CNRS, Universit\'e Paris Sud, 
Orsay, France}
\vspace*{15pt}

\end{center}

$^\dagger$ Contact person , $^\ast$ Spokesperson

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\begin{abstract}

We propose to measure the transverse nucleon, single-spin asymmetries
$A_{UT}(\phi,\phi_S)$ in the exclusive $\vec{n}(e,e'\pi^-)p$ reaction,
during the transversely polarized $^3$He target SIDIS experiment (i.e.
E12-10-006~\cite{solid:e12-10-006}) with SoLID~\cite{solid_pcdr}.  In
principle, as many as six azimuthal modulations of the form
$A_{UT}^{\sin(\mu\phi+\lambda\phi_S)}$ contribute (where $\mu$ and $\lambda$
are integers) \cite{Di05}, but four of these modulations are small and the
physics interest is concentrated in the largest two.

Our primarily goal is the measurement of $A_{UT}^{\sin(\phi-\phi_S)}$.  This
polarization observable has been noted as being sensitive to the spin-flip
generalized parton distribution (GPD) $\tilde{E}$, and factorization studies
have indicated that precocious scaling is likely to set in at moderate $Q^2\sim
2-4$ GeV$^2$, as opposed to the absolute cross section, where scaling is not
expected until $Q^2>10$ GeV$^2$.  Furthermore, this observable has been noted
as being important for the reliable extraction of the charged pion form factor
from pion electroproduction.  Our secondary goal is the measurement of the
$A_{UT}^{\sin(\phi_s)}$ asymmetry, which is sensitive to the higher twist
transversity GPDs, and provides valuable information on transverse photon
contributions at small $-t$.  Both asymmetry datasets are projected to be of
much higher quality than a pioneering measurement by HERMES \cite{hermes10}.
The remaining four $A_{UT}^{\sin(\mu\phi+\lambda\phi_S)}$ modulations will also
be measured, but are expected to be small.

This measurement is complementary to a proposal reviewed by PAC39 \cite{atpi39}
for the SHMS+HMS in Hall C.  The asymmetry that is most sensitive to
$\tilde{E}$ is the longitudinal photon, transverse nucleon, single-spin
asymmetry $A_L^{\perp}(\sin(\phi-\phi_S))$ in exclusive charged pion
electroproduction.  The SHMS+HMS allow the L--T separation needed to reliably
measure this quantity.  However, the limited detector acceptance and the
error-magnification inherent in an L--T separation necessitates the use of a
next generation, externally polarized, continuous flow, high luminosity
$\mathrm{\vec{^3He}}$ target based on a large volume polarizer and compressor
being developed at the University of New Hampshire.

A wide $-t$ coverage is needed to obtain a good understanding of the
asymmetries.  Thus, it has always been intended to complement the SHMS+HMS
$A_L^{\perp}(\sin(\phi-\phi_S))$ measurement with an unseparated
$A_{UT}^{\sin(\phi-\phi_s)}$ measurement using a large solid angle detector.
The high luminosity capabilities of SoLID make it well-suited for this
measurement.  Since an L--T separation is not possible with SoLID, the observed
asymmetry is expected to be diluted by the ratio of the longitudinal cross
section to the unseparated cross section.  This was also true for the
pioneering HERMES measurements, which provided a valuable constraint to models
for the $\tilde{E}$ GPD.  In order to assure a clean measurement of exclusive
$\pi^-$ production, it is required to detect the recoil proton from the
$\vec{n}(e,e'\pi^-)p$ reaction.  We propose to analyze the E12-10-006 event
files off-line to look for $e-\pi^--p$ triple coincidence events in SoLID for
the case where the proton is emitted $8^o<\theta<24^o$.  This has no impact
upon E12-01-006 whatsoever, and yields valuable unseparated asymmetry data.

% $(b)$ the improved asymmetry data that could be obtained over a broader
%kinematic range if a proton recoil detector (PRD) could be constructed to
%detect those additional protons emitted $24^o<\theta<50^o$.  Here, we are
%seeking PAC approval for scenario $(a)$, as well as advice on whether we
%should pursue the design and prototyping of the PRD to enable scenario $(b)$
%under the proviso that  it have minimal impact upon the running of E12-10-006.

\end{abstract}

\newpage

\tableofcontents
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\newpage
\input{motivation.tex}

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\input{setup.tex}

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\input{projection.tex}

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\input{responses.tex}

%\newpage
\section{Summary}
The $A_{UT}^{\sin(\phi-\phi_S)}$ transverse single-spin asymmetry in the
exclusive $\vec{n}(e,e'\pi^-)p$ reaction has been noted as being especially
sensitive to the spin-flip generalized parton distribution (GPD) $\tilde{E}$.
Factorization studies have indicated that precocious scaling is likely to set
in at moderate $Q^2\sim 2-4$ GeV$^2$, as opposed to the absolute cross section,
where scaling is not expected until $Q^2>10$ GeV$^2$.
%Furthermore, this observable has been noted as being important for the reliable
%extraction of the charged pion form factor from pion electroproduction.
This relatively low value of $Q^2$ for the expected onset of precocious scaling
is important, because it is experimentally accessible at Jefferson Lab.
As we have shown through a detailed UML analysis, the $A_{UT}^{\sin(\phi_S)}$
asymmetry can also be extracted from the same data, providing powerful
additional GPD model constraints and insight into the role of transverse photon
contributions at small $-t$.

This measurement is complementary to a proposal to measure the longitudinal
photon, transverse nucleon, single-spin asymmetry $A_L^{\perp}$ with the
SHMS+HMS in Hall C \cite{atpi39}.  The good resolution and reproducible
systematic uncertainties of the SHMS+HMS setup allow the L--T separation needed
to reliably measure this quantity.  However, a wide $-t$ coverage is needed to
obtain a good understanding of the asymmetry, and it always been intended to
complement the SHMS+HMS $A_L^{\perp}$ measurement with an unseparated
$A_{UT}^{sin(\phi-\phi_s)}$ measurement using a large solid angle detector.
The high luminosity capabilities of SoLID make it well-suited for this
measurement.  Since an L--T separation is not possible with SoLID, the observed
asymmetry is expected to be diluted by the ratio of the longitudinal cross
section to the unseparated cross section.  This was also true for the
pioneering HERMES measurements, which provided valuable constraints to models
for the $\tilde{E}$, $\tilde{H}$, and $H_T$ GPDs.

In our proposal, we will analyze the E12-10-006 event files off-line to look
for $e-\pi^--p$ triple coincidence events in SoLID for the case where the
recoil proton is emitted $8^o<\theta<24^o$.  To be conservative, we assume only
that the recoil proton is identified, and its' momentum is not used to further
reduce the SIDIS background.  This study yields data that are a considerable
advance over the HERMES measurement in terms of kinematic coverage and
statistical precision.  This measurement is also important preparatory work for
future measurements at the EIC, which will allow $A_{UT}^{sin(\phi-\phi_s)}$ to
be directly compared for the $\vec{n}(e,e'\pi^-)p$ and $\vec{p}(e,e'\pi^+)n$
reactions over a broad kinematic range.

%This proposal presents two scenarios: $(a)$ analyze the E12-10-006 event files
%off-line to look for $e-\pi^--p$ triple coincidence events in SoLID for the
%case where the recoil proton is emitted $8^o<\theta<24^o$.  This mode yields
%data that are a considerable advance over the HERMES measurement in terms of
%kinematic coverage and statistical precision.  $(b)$ the improved asymmetry
%data that could be obtained over a broader kinematic range if a proton recoil
%detector (PRD) is constructed to detect those additional protons emitted
%$24^o<\theta<50^o$.  Here, we are seeking PAC approval for scenario $(a)$, as
%well as advice on whether we should pursue the PRD to enable scenario $(b)$
%under the proviso that it have minimal impact upon the running of E12-10-006.

\newpage
\appendix
\input{demp_parameterization.tex}
%\input{proton_detector.tex}
%\newpage
%\begin{thebibliography}{99}
\input{prop_bib.tex}
%\end{thebibliography}

\end{document}
