\newcommand{\GeV}{\,\mathrm{GeV}}
\newcommand{\MeV}{\,\mathrm{MeV}}

\subsection{C12-10-009}
\label{sec:e99999}

\begin{center}

{\bf An Electron Fixed-Target Experiment to Search for \\ a New Vector Boson
$A'$ Decaying to $e^+e^-$} \\
\vskip .25in
Rouven Essig, Philip Schuster, Natalia Toro, Bogdan Wojtsekhowski \\
and  the Hall A Collaboration\\
\end{center}

\subsubsection{Introduction}\label{sec:introduction}
The development of the Standard Model of particle interactions is the culmination of a century of searches and
analyses with fixed-target and colliding-beam experiments. Interactions with new forces beyond the Standard Model
are currently limited by well-tested gauge symmetries to a handful of possibilities. One of the few remaining ways
for interactions with new sub-GeV vector-like forces to arise is for charged particles to
acquire millicharges, $\epsilon e$, under these forces. This occurs through a simple and generic mechanism
proposed by Holdom \cite{Holdom:1985ag}, in which a new vector particle $A_\mu^\prime$ mixes via
quantum loops with the Standard Model photon. MeV--GeV masses for the $A'$
gauge boson are particularly well-motivated in this context. Such sub-GeV forces are a common feature of
extensions of the Standard Model, but existing constraints are surprisingly weak, with limits at
$\epsilon e\lesssim (0.3-1) \times 10^{-2}e$.

Fixed-target experiments with high-intensity electron beams and existing precision spectrometers are ideally 
suited to explore sub-GeV forces by probing reactions in which a new $A'$ vector
particle is produced by radiation off an electron beam
\cite{Bjorken:2009mm,Reece:2009un}.  
The $A'$ can decay to an electron and positron pair and appears as a narrow resonance of small magnitude
in the invariant mass spectrum.  
In \cite{Bjorken:2009mm}, several fixed-target experimental strategies
were outlined to search for new sub-GeV vector interactions.

The C12-10-009 experiment is a concrete plan for an $A'$ search using
the CEBAF accelerator and the High Resolution Spectrometers (HRS) in Hall A \cite{APEX_proposal}.
This experiment, the \emph{$A'$ Experiment} (APEX), can probe charged particle
couplings with new forces as small as
$3\times 10^{-4} e$ and masses between $65~\MeV$ and $525~\MeV$ --- an improvement
by more than two orders of magnitude in cross section sensitivity over all previous experiments.

Fixed-target experiments of this form are particularly timely in light
of a series of recent anomalies from terrestrial, balloon-borne, and satellite experiments that suggest that
dark matter interacts with Standard Model particles. 
Much of this data hints that dark matter is directly charged
under a new force mediated by an $A'$ and not described by the Standard Model. 
Theoretical as well as phenomenological expectations suggest an $A'$
mass $m_{A'}\lesssim 1 \GeV$ and $\epsilon e \lesssim 10^{-2} e$.

\subsubsection{Expected reach and impact}
APEX will be sensitive to new gauge bosons with couplings as small as
$\epsilon^2 \equiv \alpha'/\alpha \sim 9\times 10^{-8} $ and masses in the range $65-525 \MeV$ (here 
$\alpha$ ($\alpha'$) is the coupling of the photon ($A'$) to electrically charged matter).
This is about a factor of $3-35$ times lower in $\epsilon$ than
existing constraints (which assume that the $A'$ couples also to muons), and corresponds to
$\sim 10-1000$ times smaller cross sections.

The precise mass range probed by this type of experiment can be varied by changing
the spectrometer angular settings and/or the beam energies, see the APEX
plan in Fig.~\ref{fig:APEXreach}.
The parameter range probed by APEX is interesting for several reasons.
This region of mass and coupling is compatible
with $A'$'s explaining the annual modulation signal seen by the dark matter direct detection
experiment DAMA/LIBRA, and also with dark matter annihilating into $A'$s, which explains
a myriad of recent cosmic-ray and other astrophysical anomalies.  
In addition, and independently of any connection to dark matter,
the APEX experiment would be the
first to probe $A'$s of mass $\gtrsim 50 \MeV$ with gauge kinetic mixing below
$\epsilon \sim 10^{-3}$, the range most compatible
if the Standard Model hypercharge gauge force is part of a Grand Unified Theory.

\begin{figure}[t]
\centerline{
\includegraphics[width=0.8\textwidth, angle = 0.]{APEX/APEX_reach.eps}}
\caption[The reach of the APEX experiment, the APEX test run and existing constraints.]{{The reach of the APEX experiment (blue contour), the APEX test run (red hatched region) and existing constraints (gray shaded regions).}}
\label{fig:APEXreach}
\end{figure}

The importance for fundamental physics of precision searching
for new forces near the GeV scale cannot be overstated.

\subsubsection{Concept}\label{sec:concept}

In the APEX experiment, we are interested in collecting as many true
$e^+e^-$ coincidence events as possible, since the $A'$ is expected to
decay to $e^+e^-$ pairs.  A large background of such true coincidence
events is expected from Standard Model QED Bethe-Heitler and
radiative trident processes, but the $A'$ would appear as a narrow
spike on top of this large Standard Model background.  A further
background is caused by accidental $e^+e^-$ coincidences from two
distinct scattering events, in which an electron scatters into the
L-HRS from one event, while a positron scatters into the R-HRS in a
second event within the timing window of the trigger.  Lastly, there
are both true and accidental $e^-\pi^+$ coincidence events.  Rejection
of these two backgrounds is key to the $A'$ search and is achieved by
means of a short trigger timing window and good particle
identification (PID).

The other crucial factor in determining the sensitivity of this
experiment is the optics, which determines the ultimate mass
resolution of the experiment.  Since we are looking for a narrow spike
on top of a large, smooth QED background, excellent mass resolution is
essential to achieve the best possible sensitivity to an $A'$.
In the APEX experiment it is crucial to take into account all above considerations. 

Figure~\ref{fig:APEXlayout} shows the lay-out of the APEX experiment.
The central momenta of both spectrometers are set to half
the beam energy.
At such a setting the background rates are minimized, while 
at the same time most of $A'$ events will be detected in spite
of the small momentum bite of the HRSs.
\begin{figure}[t]
\centerline{
\includegraphics[width=0.75\textwidth, angle = 0.]{APEX/APEX_layout.eps}}
\caption{{The lay-out of the APEX experimental setup.}}
\label{fig:APEXlayout}
\end{figure}

Our \emph{coincidence trigger} is defined as a signal in the S2m of both the left HRS
\emph{and} the right HRS, \emph{and} a signal in the Gas Cherenkov
counters of the right HRS.  
The coincidence trigger based on these three signals allows us to
collect true coincidence events with high efficiency and acceptable DAQ dead time.  
Such events are candidates for true coincident $e^+e^-$ signal events.  

The design of the target for the APEX experiment shown in
Fig.~\ref{fig:APEXtarget} has a number of interesting
ideas including the concept of narrow ribbons, a tension mechanism,
and alignment and calibration target sets. 
\begin{figure}[t]
\centerline{
\includegraphics[width=0.75\textwidth, angle = 0.]{APEX/APEX_target.eps}}
\caption{{The components of the target for the APEX experiment.}}
\label{fig:APEXtarget}
\end{figure}


\subsubsection{PAC35 report and concerns}\label{sec:PAC}

PAC35 conditionally approved the APEX experiment (proposal PR12-10-009). 
The APEX collaboration was given a test run to address some of the PAC concerns:

\begin{enumerate}
\item Run with the zig-zag mesh design of the tungsten target and
  prove that it allows the requested vertex resolution.
\item Prove that it is possible to reach the uncertainty of 0.1~mrad
  in determining the central scattering angle between the two spectrometers.
\item Prove that it is possible to use the gas Cherenkov counters in
  the trigger to help clean up pions. In fact, the TAC report claims that
  this would not be possible with total rates/PMT at the level of a few
  hundred Hz to MHz. Also prove that an off-line rejection of 10,000:1 can be achieved.
\item Provide a detailed description of the different contributions to background
  and their importance (how assumptions and/or approximations can
  influence the predictions) and a comparison with measurement.
\item Prove that a 20~ns (S0-S0) and 40~ns (S0-S0-C) timing window can be achieved.
\item Prove that the vertical drift chambers (VDCs) can operate at a
  rate higher than 20~kHz/wire (that, according to the TAC report, is 
the maximum Hall A has operated until now).
\item If possible, set the septum magnets at higher fields 
to prove that also at energies higher than 2~GeV the field uniformity 
requested for the experiment can be achieved).
\end{enumerate}


\subsubsection{The results of the test run and the future plans}

The test run suggested by the PAC35 report was prepared and realized after the PREX
experiment in June 2010.
The detectors were tested in all the extreme conditions expected during the APEX 
production run.
The data were analyzed and preliminary results were presented at the $A'$-boson
workshop~\cite{APEX_Workshop} at JLab in September 2010. 
Its web page has the reports on each subsystem of the experiment and the
data analysis.
The observed detector performance was found to be in compliance with 
the APEX requirements.
Several results of general interest for the Hall A collaboration are: 
a 15~ns coincidence time window, a 5~MHz rate capability of the VDC
chambers,  a target with a set of narrow ribbons for reduction of the 
multiple scattering,  and an observation that pion rate for small
angle configuration with 2.2~GeV beam is
much lower than one could calculate using the commonly used code by Wiser.

The updated proposal was resubmitted to PAC37 on December 1, 2010.
The $e^+e^-$ data collected during the test run will be analyzed for a 
possible signal of the $A'$ boson in the mass range 170-240 MeV.  The sensitivity of this test run 
data goes well beyond the currently existing constraints in this mass range, but is well below 
that achievable in the full APEX experiment and, of course, also covers a much smaller mass range.  

\begin{thebibliography}{9}

\bibitem{Holdom:1985ag}
B.~Holdom,  Phys. Lett.  {\bf B166} (1986) 196.

\bibitem{Bjorken:2009mm}
J.~D. Bjorken, R.~Essig, P.~Schuster, and N.~Toro, Phys. Rev. {\bf D80}
  (2009) 075018, [\href{http://xxx.lanl.gov/abs/0906.0580}{{\tt 0906.0580}}].

\bibitem{Reece:2009un}
M.~Reece and L.-T. Wang, {\it {Searching for the light dark gauge boson in
  GeV-scale experiments}},
[\href{http://xxx.lanl.gov/abs/0904.1743}{{\tt 0904.1743}}].

\bibitem{APEX_proposal}
{A New Proposal to Jefferson Lab PAC35: {\it {Search for a New Vector Boson $A'$
  Decaying to $e^+e^-$}}},
  ``{http://hallaweb.jlab.org/collab/PAC/PAC35/PR-10-009-Dark-Matter-Search.pdf}.''

\bibitem{APEX_Workshop} {The Workshop  ''Searching for a New Gauge Boson at JLab''},
September 20-21, 2010,``{http://conferences.jlab.org/boson2010/index.html}.''

\end{thebibliography}
