\subsection{Near detectors}

\subsubsection{Introduction}

As mentioned in section~\ref{sec:Baseline_near}, the baseline is to
have four near detectors, one each at the end of each of the four
straights of the two storage rings. 
This allows the measurement of the neutrino flux of each neutrino
beam and reduces the systematic error in the oscillation parameters
\cite{Tang:2009na}. 
Apart from the flux measurement, the near detector will also be able
to perform precision measurements of neutrino-nucleon,
neutrino-electron, and charm-production cross-sections.
Each of these measurments is necessary to reduce the systematic errros
of the neutrino oscillation analysis. 
Additionally, the near detector will embark on an extended programme
of precision neutrino physics and searches for Non Standard
Interactions (NSI). 

Section~\ref{sec:ND_performance} describes the performance required of
a near detector at a Neutrino Factory. 
It includes an analysis using neutrino-electron scattering to extract
the neutrino flux with a near detector, a description of how the near
detector flux measurement can be used to extrapolate to the far
detector to constrain the parameters of the neutrino oscillation
signal, a description of the neutrino scattering physics that can be
achieved with a near detector (including cross-sections, QCD and other
electroweak physics topics) and finally a section on the measurement
of charm production from neutrino interactions (one of the dominant
backgrounds in the oscillation signal in the far detector) and the tau
search, which can be used to constrain NSI.  

Section~\ref{sec:ND_design} describes the requirements of the near
detector to achieve the above physics goals, including two possible
options that are being considered, one with a scintillating fibre
tracker and the other using a high resolution straw-tube tracker.
In addition, two other options will be considered to perform the
charm and tau measurements; one of which includes an emulsion
detector, the other a silicon vertex detector.

\subsubsection{Performance requirements}
\label{sec:ND_performance}

\paragraph{Neutrino flux measurement; inverse muon decay}

\subparagraph*{Introduction \\}

In order to perform measurements of neutrino oscillations at a
neutrino facility, it is necessary to establish the rate of neutrino
interactions. 
The aim of the near detector of the Neutrino Factory is to
measure precisely the absolute neutrino flux, the neutrino cross
sections, and to estimate the backgrounds in the far detector. 
Hence, careful design of a near detector is crucial for the reduction
of systematic uncertainties in the long-baseline neutrino-oscillation
experiment. 
The paragraphs which follow demonstrate that quasi-elastic
neutrino-electron scattering can be used to measure the neutrino flux
coming from the Neutrino Factory storage ring with a systematic
uncertainty of $ \sim 1 \%$. 

\subparagraph*{Quasi-Elastic scattering off electrons in the near detector \\}

The quasi-elastic neutrino-electron scattering is suitable for the measurement of the neutrino flux because its absolute cross-section can be calculated theoretically with enough confidence. The two processes of interest for neutrinos from $\mu^-$ decays are:
\begin{eqnarray}
 \nu_{\mu} + e^{-} & \rightarrow & \nu_{e} + \mu^{-} \, ; 
   {\rm and}  \label{p1} \\
 \bar{ \nu_{e} } + e^{-} & \rightarrow & \bar{ \nu_{\mu} } + \mu^{-} \, .
   \label{p2}
\end{eqnarray}
For the processes in equation \ref{p1}, also known as inverse muon
decay, the differential cross section is isotropic in the
centre-of-mass system. The total cross section is given by:  
\begin{equation}
\sigma=\frac{G^2_F}{\pi}\frac{ (s - m^2_{\mu})^{2} }{s} \, .
\end{equation}
For the process in equation \ref{p2}, also known as muon production
through annihilation, the differential cross section in the
centre-of-mass system is given by:
\begin{equation}
 \frac{d\sigma}{dcos\theta}=\frac{G^2_F}{\pi}\frac{(s-m^2_{\mu})^{2}}{s} \times 
\left(1+\frac{s-m^2_{\mu}}{s+m^2_{\mu}}cos\theta\right)\left(1+\frac{s-m^2_{e}}{s+m^2_{e}}cos\theta\right) \, ;
\end{equation}
and the total cross section is:
\begin{equation}
 \sigma=\frac{G^2_F}{\pi}\frac{ (s - m^2_{\mu})^{2} }{s^2}(E_{e}E_{\mu}+\frac{1}{3}E_{\nu 1}E_{\nu 2}) \, ;
\end{equation}
where $E_{\nu 1}$ and $E_{\nu 2}$ are the energies of the neutrinos. $E_{\nu 1}$ and $E_{\nu 2}$ depend, in turn, only on  $s$. Both processes have a threshold at $\sim 11$~GeV.

\subparagraph*{Simulation of the near detector \\}

A Monte Carlo simulation of muon decay in flight along the 600 m long straight section of the decay ring has been developed. The two leptonic processes in equations \ref{p1} and \ref{p2} have been simulated in turn in order to determine the detector requirements and to select the best criteria for the suppression of the background. After this, the GENIE \cite{Andreopoulos:2009zz} event generator and the GEANT4 simulation tool were used to simulate the entire spectrum of neutrino interactions and the response of the detector.

\subparagraph*{Near detector requirements \\}

If we want to measure the neutrino flux by using the quasi-elastic neutrino-electron scattering for earlier measurements of these processes see \cite{Vilain:1996yf,Mishra:1990yf}), the detector has to be able to distinguish between the leptonic events and inclusive charged current (CC) neutrino-nucleon scattering:
\begin{equation}
 \nu_{\mu} + N \rightarrow \mu^{-} + X \, ;
 \label{p3}
\end{equation}
which has a cross section a few orders of magnitude larger. Some of the events from the charged-current processes (equation \ref{p3}) can mimic leptonic events from quasi-elastic neutrino-electron scattering, but instead of a single muon in the final state there will be also a hadronic system $X$. The measured recoil energy of this hadronic system can be used as a good criterion for the suppression of the background.

The energy spectrum of the beam neutrinos on the plane perpendicular to the straight section and 100~m away from its end are shown in figure \ref{NuE}, where the threshold for the two processes of interest is shown with a dotted line.
\begin{figure}
\begin{center}
  \includegraphics[width=0.5\textwidth]{03-DetWG/figures/EnuPol0.eps}
\end{center}
\caption{Distributions over the neutrino energy on the plane perpendicular to the straight section and 
100~m away from its end. Dotted lines indicate the threshold for the process of quasi-elastic scattering off electrons.}
\label{NuE}
\end{figure}

Figure \ref{Mu_Th_E} shows the distributions over the energy and the
polar angle of the muons from quasi-elastic neutrino-electron
scattering at that plane. One can see that all these muons have very
small polar angles $\theta_{\mu} < 5$~mrad. This angular spread comes
mainly from the muon beam divergence as the intrinsic scattering angle
in processes \ref{p1} and \ref{p2} is much smaller.  
We use this as another criterion for suppression of the background.
\begin{figure}
\begin{center}
  \includegraphics[width=.49\textwidth]{03-DetWG/figures/EmuPol0.eps} 
  \includegraphics[width=.49\textwidth]{03-DetWG/figures/ThetamuPol0.eps}
\end{center}
  \caption{
    The energy distributions (left) and the polar angle distributions
    (right) of the muons generated in the detector by the reactions
    $\nu_{\mu} + e^{-} \rightarrow \nu_{e} + \mu^{-}$ and
    $\bar{\nu}_{e}  + e^{-} \rightarrow \bar{\nu}_{\mu} + \mu^{-}$.
  }
  \label{Mu_Th_E}
\end{figure}

The properties of the quasi-elastic scattering off electrons described
above impose specific requirements on the near detector. 
The detector has to provide an interaction rate sufficient for the
measurement despite the very small cross sections of the leptonic
processes, $\sim  4\times 10^{-41}$~cm$^2$ at 15~GeV (for comparison,
the total $\nu_{\mu}N$ CC cross section is  $\sim 10^{-37}$~cm$^2$ at
this energy). 
This requires a solid detector. 
Also, the detector must be able to reconstruct the polar angle of the
scattered muon with maximum precision. 
This requires a low-$Z$ tracker. 
At the same time, the near detector has to be able to measure the
hadronic-recoil energy in the background events down to values of
several MeV. 
This requires a precise calorimeter.

\subparagraph*{Neutrino event generation \\}

In order to test different criteria for the suppression of the background from CC reactions and to determine the strict requirements for the near detector we make use of the neutrino event generator GENIE \cite{RefGenie1,Andreopoulos:2009rq} to simulate the interactions of the neutrinos with a detector made of polystyrene ($\rho = 1.032$~g/cm$^3$). The GENIE simulation uses as an input the neutrino flux created by the simulation of muon decay in flight.

The following neutrino interaction processes are included in the GENIE event generator:
\begin{itemize}
 \item Quasi-elastic scattering;
 \item Elastic NC scattering;
 \item Baryon resonance production in charged and neutral current interactions;
 \item Coherent neutrino-nucleus scattering;
 \item Non-resonant deep inelastic scattering (DIS);
 \item Quasi-elastic charm production;
 \item Deep-inelastic charm production;
 \item Neutrino-electron elastic scattering; and
 \item Inverse muon decay.
\end{itemize}
The process  $\bar{\nu}_{e}  + e^{-} \rightarrow \bar{\nu}_{\mu} +
\mu^{-}$ is not included in GENIE. This is not crucial for our
simulation since, for unpolarised muons, it has a rate that is $\sim
10$ times less than that of inverse muon decay.

\subparagraph*{GEANT4 simulation of the near detector \\}

In the GENIE data files all final state particles are recorded using the GHEP library. These particles are then read through an interface by the GEANT4 simulation and treated as primary particles for tracking through the volume of the detector.

The detector that has been simulated is a low-$Z$, high-resolution scintillating-fibre tracker. It consists of consecutive modules placed perpendicular to the beam axis. Each module consists of five planes made of plastic-scintillator slabs 1~cm thick and a fibre station. The scintillator slabs serve to absorb and measure the energy of recoil particles in the interaction. The fibre station consists of four layers of fibres with horizontal orientation and four layers with vertical orientation. Signals from individual fibres are used to construct space points (hits) from charged particles crossing the station. 
 

Three different fibre-station conceptual designs have been simulated. 
The first option is a station made of cylindrical fibres with radius
of 0.5\,mm.
For this design, the position of the fibre centres in a given layer is
shifted by 0.25\,mm with respect to centres of the fibres in the
neighbouring layer (figure \ref{fibres1} - left). 
The other two options consider a station made of square fibres with
0.5\,mm side  and displacement between the neighbouring layers of
0.25\,mm and 0.125~mm, respectively (figure \ref{fibres1} - right). 
In each design the station thickness is 4~mm. 
\begin{figure}
\begin{center}
 \includegraphics[width=.45\textwidth]{03-DetWG/figures/round-1.eps}
%\end{center}
%\vspace{5mm}
%\begin{center}
 \includegraphics[width=.45\textwidth]{03-DetWG/figures/square-1.eps}
\end{center}
\caption{Schematic drawing of a fibre station made of cylindrical (left) and squared (right) fibres.}
\label{fibres1}
\end{figure}

The overall dimensions of the detector are $1.5 \times 1.5 \times
1.08$~m$^3$ which corresponds to a mass of $\sim 2.5$~Ton. 
A sketch of the detector with a $\nu_{\mu}N$ interaction in its second
module is shown in figure \ref{detector}.
\begin{figure}
\begin{center}
  \includegraphics[width=.6\textwidth]{03-DetWG/figures/event1.eps}
\end{center}
\caption{Schematic drawing of the detector with a $\nu_{\mu}N$ interaction in its second module.}
\label{detector}
\end{figure}

\subparagraph*{Digitisation \\}  

The fibre signal is taken to be proportional to the energy deposition in the corresponding fibre. It is then corrected for the attenuation of the light in its path between the hit and the fibre end. The signal is then smeared with a Gaussian with $\sigma /E = 25\% $. 
A simplified parametrisation is used for the absorber blocks. The signal in a given slab is taken to be proportional to the total energy deposition and is smeared with a Gaussian with $\sigma /E = 5\%$.

\subparagraph*{Reconstruction and analysis \\}

\emph{\noindent Reconstruction of the muon track}

For the purpose of these studies a simplified reconstruction of the events has been used.  No pattern recognition is implemented and we simply use hits in the fibres belonging to the muon track.
A space point measurement is then created for each fibre station. Its $x$ and $y$ coordinates are calculated independently as the weighted average of the coordinates of the centres of the hit fibres. The weights are proportional to the digitised signals. The space points obtained this way are used to reconstruct the muon track via the Kalman filter (e.g. taking multiple scattering into account).

The difference between the reconstructed polar angle of the muon and its true value from the simulation is used to measure the resolution. Figure \ref{resol} shows the distributions over this difference for the three different conceptual designs of the fibre stations. It is seen that the resolution is $\sim0.5$~mrad in all three cases.

\begin{figure}
\begin{center}
 \includegraphics[width=.49\textwidth]{03-DetWG/figures/res-ro.eps}
 \includegraphics[width=.49\textwidth]{03-DetWG/figures/res-sq2.eps}
 \includegraphics[width=.49\textwidth]{03-DetWG/figures/res-sq4.eps}
\end{center}
\caption{The difference between the reconstructed polar angle of the muons and its true value  from the simulation for a fibre station made of cylindrical staggered fibres (top left), squared fibres staggered by 0.25~mm (top right) and squared  fibres staggered by 0.125~mm  (bottom). Gaussians are fitted to all distributions.}
\label{resol}
\end{figure}


\emph{\noindent Background rejection exploiting energy deposition in the absorber blocks}

We propose to use the total energy deposition in the first illuminated detector module as a first tool to reject background events.
Figure \ref{fit1} shows the energy deposition in the first illuminated detector module plotted as a function of the reconstructed-muon scattering angle. It is seen that the leptonic events and the CC background are well
separated. Fig \ref{fit2} shows the distributions of the outgoing muons over the reconstructed polar angle $\theta_{\mu}$
and the variable $\theta^2_{\mu} \times E$. The variable $\theta^2_{\mu} \times E$ is proportional to the event inelasticity $1-y = E_{had}/E_{\nu}$. Only events with a total energy
deposition in the first illuminated absorber block less than 15~MeV are selected. A linear
extrapolation of the CC background toward $\theta_{\mu} = 0$ is used to evaluate the number of
background events under the leptonic peak.
\begin{figure}
\begin{center}
 \includegraphics[width=.6\textwidth]{03-DetWG/figures/Edep.eps} 
\end{center}
\caption{Energy deposition in the first illuminated scintillating slab compared to the reconstructed muon scattering angle.}
\label{fit1}
\end{figure}
\begin{figure}
\begin{center}
 \includegraphics[width=.49\textwidth]{03-DetWG/figures/thetaCut.eps}
 \includegraphics[width=.49\textwidth]{03-DetWG/figures/thetaECut.eps}
\end{center}
\caption{Distributions over the reconstructed polar angle $\theta_{\mu}$ (left) and the \emph{inelasticity} $\theta^2_{\mu}E$ (right) of the outgoing muons. The leptonic events are filled with grey, the hadronic events are plotted in blue and the total spectrum is in black. The cut value is denoted by a black inverted triangle. The red lines indicate the background extrapolation.}
\label{fit2}
\end{figure}



The results obtained exploiting both suppression variables are summarised in Table \ref{ND_IMB_results}.
It is seen that by imposing a suitable cut on the recoil energy and subtracting the fitted inclusive background with a muon in the final state under the leptonic peak, it is possible to evaluate statistically the number of events due to pure leptonic scattering with a precision of $\sim 1\%$. Both variables ${\theta}_{\mu}$ and $\theta^2_{\mu} \times E$ may be used for this task.
\begin{table}
\caption{Results for background extrapolation exploiting two different suppression variables. The true number of leptonic events is 6632.}
\label{ND_IMB_results}
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
{\bf Cut on} & {\bf All events} & {\bf Bkgr events} & {\bf Bkgr events}  & {\bf Simulated} & {\bf Leptonic}    \\
             & {\bf below the}  & {\bf below the}   & {\bf from the fit} & {\bf leptonic}  & {\bf events}        \\
             & {\bf cut}        & {\bf cut}         &                    & {\bf events}    & {\bf from the fit}  \\
\hline
${\theta}_{\mu}$                            & 9450        & 2860           & $ 2865 \pm 57 $  & 6632     & $6585 \pm 57$ \\
$\theta^2_{\mu} \times E$ & 9284       & 2666           & $ 2596 \pm 74 $  & 6632     & $6688 \pm 74$ \\
\hline
\end{tabular}
\end{center}
\end{table}

\subparagraph*{Conclusions \\}

The quasi-elastic neutrino-electron scattering can be used to measure
the neutrino flux coming from the Neutrino Factory storage ring. 
The angle ${\theta}_{\mu}$ and the \emph{inelasticity} 
$1-y \sim \theta^2_{\mu} \times E$ have similar discriminating power. 
The latter variable seems to have a flatter distribution when
${\theta}_{\mu}\rightarrow 0$. 

\paragraph{Neutrino flux measurement; neutral current elastic
  neutrino-electron scattering}

The experimental determination of the absolute neutrino flux below
11~GeV will rely upon the measurement of neutral current elastic
scattering off electrons: $\nu e^- \rightarrow \nu e^-$. 
The total cross section for NC elastic scattering off electrons is
given by~\cite{Marciano:2003eq}: 
\begin{eqnarray}
\sigma (\nu_l e \to \nu_l e) & = & \frac{G_\mu^2 m_e E_\nu}{2\pi} \left[ 1 -4 \sin^2 \theta_W + \frac{16}{3} \sin^4 \theta_W \right] \\
\sigma (\bar{\nu}_l e \to \bar{\nu}_l e) & = & \frac{G_\mu^2 m_e E_\nu}{2\pi} \left[ \frac{1}{3} -\frac{4}{3} \sin^2 \theta_W + \frac{16}{3} \sin^4 \theta_W \right]
\end{eqnarray}
where $\theta_W$ is the weak mixing angle. 
For $\sin^2 \theta_W \simeq~0.23$ the above cross sections are very
small $\sim 10^{-42} (E_\nu/\gev)~cm^2$. 
The NC elastic scattering off electrons can be used to determine the
absolute flux normalization since the cross sections only depend upon
the the knowledge of $\sin^2 \theta_W$. 
The value of $\sin^2 \theta_W$ at the average momentum transfer
expected at Neutrino Factory near detector $Q\sim 0.07 \gev$ can be extrapolated down from the
LEP/SLC measurements with a precision of $\sim 0.2\%$ within the
Standard Model (SM). 
However, in order to take into account potential deviations from the
SM predictions, in the flux extraction we must initially consider a
theoretical uncertainty $\leq 1\%$, obtained from direct measurements
of $\sin^2 \theta_W$ at momentum scales comparable to the Neutrino Factory near detector momenta. 
As discussed in Section~\ref{SBL:sec:sin2thetaW}, precision
electroweak measurements with the ND data at a Neutrino Factory near detector can determine the
value of $\sin^2 \theta_W$ to better than 0.3\%. 
The theoretical uncertainty on the absolute flux normalization can
therefore be improved substantially by a combined analysis with the
electroweak measurements. 

\begin{figure}[ht]
\centering\includegraphics[width=.85\textwidth]{03-DetWG/figures/SBL_NCnuel}
\caption{Distributions of the angle of the electron with respect to the beam direction
(left) and of the discriminating variable $P(1 -\cos \theta)$ (right) for NC elastic
scattering off electrons and for the corresponding backgrounds in the ND.
%[figure to be finalized, space holder]
}
\label{fig:NCnu-e}
\end{figure}

The signature of the process $\nu_l (\bar{\nu}_l) e \rightarrow \nu_l (\bar{\nu}_l) e$ is a single
electron in the final state, emitted almost collinearly with the beam direction
($\theta \sim $ mrad). The dominant backgrounds are given by NC $\pi^0$ production and
single photon production, in which one photon fakes a single electron. A smaller
background contribution is given by $\nu_e$ quasi-elastic scattering events in which the
proton is not visible. This measurement
requires a detector which can efficiently distinguish photons from electrons.
The low density magnetized tracker proposed for the Neutrino Factory near detector can identify electrons and positrons
and reconstruct the corresponding track parameters, allowing a background rejection
$\leq 10^{-6}$ .
Figure~\ref{fig:NCnu-e} shows the distributions of kinematic variables for signal
and background.
It is thus possible to select a sample of NC elastic scattering events off electrons
with small background in the Neutrino Factory near detector. The main limitation of such a measurement
is the statistics of the selected sample, which, for the Neutrino Factory  near detector will not be a problem.
It must be noted that in a low density magnetized design the background is originated
from asymmetric $\gamma$ conversions in which the positron is not reconstructed.
This type of background is expected to be charge-symmetric and this fact gives a
powerful tool to calibrate the $\pi^0/\gamma$ background in-situ.

\paragraph{Effects of High $\Delta m^2$ Oscillations on the Flux Extraction}
\label{SBL:sec:fluxosc}

The results described in the previous sections were obtained under the
assumption that the events observed in the ND are originated by the same
(anti)-neutrino flux produced by the decay of the parent muons.  
The recent results from the MiniBooNE experiment might suggest the
possibility of relatively high $\Delta m^2$ anti-neutrino oscillations
consistent with the LSND signal. 
This effect, if confirmed, seems to indicate a different behavior
between neutrinos and anti-neutrinos, which would imply CP or CPT
violation. 
The MINOS experiment also reported different oscillation parameters
between $\nu_\mu$ and $\bar{\nu}_\mu$ from the disappearance analysis,
although this result is as yet not statistically compelling.

The presence of high $\Delta m^2$ oscillations with characteristic oscillation length
comparable with the ND baseline at the Neutrino Factory energies, would imply that the spectra
observed in the ND could be already distorted by neutrino oscillations.
The main effect expected on the flux extraction from a MiniBooNE/LSND oscillation is that a deficit is induced in the $\bar{\nu}_\mu$ CC spectrum from a significant disappearance rate.

Any in situ determination of the fluxes would then require the unfolding of the oscillation
effect from the measured spectra. The measurement
strategy in the ND should necessarily include a combined oscillation and flux analysis.
Since the ND cannot be easily moved, different complementary measurements are needed.

Several follow-up experiments have been proposed to investigate the MiniBooNE/LSND
effects: move MiniBooNE to a near detector location, OscSNS at the ORNL
neutron spallation source or a two-detector LAr experiment at the CERN PS.
All of them are expected to cover the region in the oscillation parameters
consistent with MiniBooNE/LSND data, so that by the time the Neutrino Factory experiments will take data
we might have a confirmation or disprove of the high $\Delta m^2$
oscillation hypothesis. However, the precision which will be ultimately achieved
in the determination of the fluxes at Neutrino Factory near detector is directly connected to the high
$\Delta m^2$ oscillation parameters.
If the oscillation is confirmed, we will then need dedicated precision measurements
in the ND at the Neutrino Factory.



\paragraph{Influence of near detector flux data on far detector sensitivities}

Any neutrino near detector facility will have many possible functions. Among these will be the measurement of the absolute flux in the direction of the far detectors. There is the possibility that this measurement could be used, in addition to the determination of the absolute normalisation, to project a non-oscillation flux prediction to the far detector site to be used in the determination of the oscillation parameters. This would require the reconstruction of the whole flux spectrum at the near detector so that the projection could be carried out reliably. The initial studies of the power of a technique for the projection of the near detector flux spectrum as a means of extracting oscillation parameters are described in the paragraphs which follow.

\subparagraph*{Flux measurement \\}
\label{subSec:Flux}

Comparison of the neutrino flux at the near and far sites is problematic for various reasons. However small, a detector within $\sim$1~km of the beam pipe subtends a far greater beam solid angle than a large scale detector positioned thousands of kilometres from the source. Additionally, the solid angle subtended by the near detector as seen from different parts of the decay pipe varies considerably. Considering a 1~m radius near detector placed 100~m from the end of a 600~m long straight decay length and the $14\times 14$~m$^2$ cross section MIND at 4\,000~km from the same decay pipe it can be seen that the solid angle of the near detector as seen from the two ends of the decay pipe ranges from $6.4\times 10^{-6}-3.1\times 10^{-4}$~sr, a range of two orders of magnitude, whereas for the far detector the solid angle ranges between $1.22-1.23\times 10^{-11}$~sr, up to 7 orders of magnitude smaller and varying by only 1\% of the larger value. As can be seen in figure \ref{fig:NDNFflux}, this results in a different energy spectrum for near detector distances up to a distance of $\sim$1~km. Due to the steep angle of the beam direction, positioning the near detector facility at 1~km would be restrictively expensive, as well as problematic from an engineering standpoint. As such, one of the main focuses of this study must be to determine whether it is still possible to extract a prediction for the far detector flux, even if the near detector flux differs considerably from the far detector spectrum, when the near detector is positioned close to the end of the decay straight.
\begin{figure}
  \begin{center}$
    \begin{array}{cc}
      \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/PlotNDFluxE.eps} &
      \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/PlotFDFluxE.eps}\\
      \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/PlotNDFluxMu.eps} &
      \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/PlotFDFluxMu.eps}\\
    \end{array}$
  \end{center}
  \caption{Difference in expected fluxes at near and far sites: (top) $\nu_e$ flux through a 1~m radius detector 100~m and 1~km from a 600~m decay straight (left) and at a 7~m radius detector 4000~km from the Neutrino Factory; (bottom) $\nu_\mu$ flux for the same detectors (using unpolarised muon expectation).}
  \label{fig:NDNFflux}
\end{figure}

Direct comparison of the expected fluxes at the two sites allows for a clear determination of the expected reduction in certain energy bins. This technique would require any near detector to have excellent energy resolution to reduce the errors in the determination of the near detector flux before projection. However, the proximity of the detector to the beam source means that a large mass is not a requirement from a statistical point of view and hence a high resolution detector constructed of multiple sub-detectors could be built with designs based on upgrades to the NOMAD~\cite{Barichello:2003gu} or Minerva~\cite{Kafka:2010zza} detectors as possible candidates. The studies described below focus on the determination of oscillation parameters via the Neutrino Factory golden channel using a matrix representation of all aspects of the set-up and is inspired by the technique used by the MINOS collaboration~\cite{Michael:2006rx}.

\subparagraph*{Flux projection for non-oscillation prediction \\}
\label{sec:matMeth}

The technique essentially involves three matrices describing the set-up: near detector response, flux projection and far detector response; in addition to cross-section matrices for the relevant processes and a parametrisation of the oscillation probability which is ultimately used in the determination of the sensitivity to oscillation parameters. Through purely mathematical arguments one can prove that the oscillation probability is related to the two observed signals via the relationship:
\begin{equation}
  \label{eq:OscProbNeFa}
  P_{osc} = M_{FD}^{-1}M_{dat}M_{ND}M_{nOsc}^{-1} \, ;
\end{equation}
where $M_{FD}$ and $M_{ND}$ are matrices representing the combination of cross-section and response for $\nu_\mu~(\overline{\nu}_\mu)$ at the far detector and $\nu_e~(\overline{\nu}_e)$ at the near detector respectively, $M_{nOsc}$ relates the expected far detector $\nu_e~(\overline{\nu}_e)$ flux without oscillations to the expected $\nu_e~(\overline{\nu}_e)$ flux at the near detector and $M_{dat}$ is the ratio of the observed $\nu_\mu~(\overline{\nu}_\mu)$ interaction spectrum at the far detector to the observed $\nu_e~(\overline{\nu}_e)$ interaction spectrum at the near detector. The extracted function would then be fit to the oscillation probability formulae to find the best fit values of the $\theta_{13}$ and $\delta$. This technique formed the basis of the first basic study of the matrix method which was presented in~\cite{Laing:2008zzb}.

There are, however, a number of problems with this direct method. The finite resolution of both detectors would mean the direct ratio of observed signals could not be used without some correction but, more importantly, fitting such a complex function as the oscillation formula, particularly in the low energy region, can be problematic. Inversion of the response of a detector, particularly a coarse grained calorimeter like the far detector can lead to statistical instabilities or bias in the prediction of the true energy interactions (see~\cite{Cowan:1998ji} for a more detailed discussion of this inverse problem). For these reasons the next step in the study involved a re-definition of the fitted quantity.

This updated method attempts to fit the observed far detector spectrum directly by using the projection of the observed near detector spectrum. That is, the predicted spectrum for a given grid point on the ($\theta_{13}$,$\delta$) plane is calculated as:
\begin{equation}
  \label{eq:nf2008}
  N_{FD} = M_{FD}P_{osc}(\theta_{13},\delta)M_{nOsc}M_{ND}^{-1}N_{ND} \, ;
\end{equation}
where $N_{FD}$ and $N_{ND}$ are the observed far and near detector spectra respectively, with other symbols defined as in equation~\ref{eq:OscProbNeFa}. In this way only the higher resolution near-detector response needs to be inverted. The prediction here would, however, use binned data as opposed to using the integration of the flux calculations, so the binning used at the near detector would have to be optimised for the projection. Calculation of the expected appearance spectrum from the no-oscillation flux spectrum is aided by fine binning, however, statistical significance and detector resolution limit how fine the binning can be in reality. An initial study using the golden-channel oscillation without backgrounds was performed and presented in~\cite{Laing:2008zz} using a near detector with $\nu_e~(\overline{\nu}_e)$ detection threshold of 5~GeV and energy resolution of 35\%/$\sqrt{E}$.

In order to predict the interaction spectra at the far detector, the near detector would be required to measure both the $\nu_\mu~(\overline{\nu}_\mu)$ and $\overline{\nu}_e~(\nu_e)$ interaction spectra. The only background to the $\nu_\mu~(\overline{\nu}_\mu)$ measurement is likely to be from neutral current interactions. Using a combination of missing $p_T$ and vertex reconstruction, both of which should be measured with high resolution at a near detector, this could be suppressed to at least the level in the far detector. The $\overline{\nu}_e~(\nu_e)$ measurement would require a more sophisticated analysis to achieve a pure sample. Both channels could benefit from the study of low-rate background processes such as electron scattering but these processes are limited by statistics and take place often in restricted energy ranges and as such could not be used alone to perform this analysis. Any final analysis is likely to use a combination of channels and analyses to maximise statistics and purity.

Projection of the predicted flux is carried out using scaling matrices calculated using a comparison of the true fluxes at the near and far sites. The ultimate analysis would benefit from the use of a Monte Carlo study either to quantify the additional neutrinos expected in the beam from neutral current interactions and the corrections required to take into account the near-detector resolution or to construct a probability matrix relating directly near-detector interactions to unoscillated far-detector interactions, which is the method favoured in the MINOS analysis~\cite{Michael:2006rx}. However, a simple scaling argument allows for the understanding of the near detector effects and can be directly compared to existing studies which do not yet take into account the effect of additional neutrinos scattered into the beam by interactions.

\subparagraph*{Comparison of near detector projection to standard fit method \\}

An initial study of the power of this technique has been carried out
assuming a 100~kg cylindrical detector of 1~m radius placed 100~m from
the end of a 600~m straight decay section. The flux expected at the
near detector site is predicted by randomly generating muon decays
along a straight line with an appropriate beam divergence and
calculating the expected spectrum from the detector acceptance as
calculated for each decay position. The detector is modelled using a
conservative estimate of the $\overline{\nu}_e~(\nu_e)$ energy
resolution of 35\%/$\sqrt{E}$(GeV) with efficiency rising linearly
from 0\% at 0~GeV up to 70\% above 4~GeV. The
$\nu_\mu~(\overline{\nu}_\mu)$ resolution is set at
20\%/$\sqrt{E}$(GeV), with efficiency of 80\% for $\overline{\nu}_\mu$
and 60\% for $\nu_\mu$ above 4~GeV (similar to the far detector). A
full detector simulation is not yet available to test the validity of
these assumptions or  to estimate the background levels, as such the
current basic study assumes the two signals are separated without
background. 

A smear is performed on the calculated interactions at the near detector and the flux and correlation matrices for each channel and the far detector are then projected to the appropriate far detector in bins of width 0.5~GeV. The total integrated interaction spectra expected at a near detector over a data taking run of 5 years allows the flux through the detector to be predicted to a high level of accuracy using the inversion of the response matrices (see figure \ref{fig:predfluxND}). Only slight oscillation of the predicted values is visible at higher energies. However, the quality of the prediction is likely to be worse if the technique was utilised for a limited data-set, or if the efficiencies or energy resolutions were reduced. In the future a more sophisticated unfolding will be developed.
\begin{figure}
  \begin{center}$
    \begin{array}{cc}
    \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/NDRecFluxMuPlus.eps} &
    \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/NDRecFluxMuMinus.eps}\\
    \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/residMuPlus.eps} &
    \includegraphics[height=5.5cm,width=7.5cm]{03-DetWG/figures/residMuMinus.eps}
    \end{array}$
  \end{center}
  \caption{Comparison of predicted to true flux through the ND for stored $\mu^+$ (left) and stored $\mu^-$(right). (top) Actual spectra and (bottom) fractional residuals.}
  \label{fig:predfluxND}
\end{figure}

The far detector spectra are calculated with the non-oscillation predictions from the near detector. The far-detector spectra obtained are then used to perform a fit using the function:
\begin{equation}
  \label{eq:chicorr}
  \chi^2 = \displaystyle\sum_i\sum_j(N_{i,j}-n_{i,j})V^{-1}_{i,j}(N_{i,j}-n_{i,j})^T \, ;
\end{equation}
where $i$ is the detector baseline, $j$ the polarity, $N$ the predicted spectrum, $n$ the data spectrum and $V$ the correlation matrix, composed of the projected matrix of the prediction and the expected errors on the far detector measurement. Figure \ref{fig:NeFfits} shows the results of fits to a range of $\theta_{13}$ and $\delta$ values using this technique (left) compared to similar fits performed in which the neutrino flux is allowed to be part of the fit (right), rather than be constrained by the near-detector data. As can be seen, the resolution of $\theta_{13}$ is as good or better using the projection technique. Resolution of $\delta$ is generally better for large $\theta_{13}$ but reduces to a similar level for $\theta_{13} \leq 1^{\circ}$.
\begin{figure}
  \begin{center}$
    \begin{array}{cc}
    \includegraphics[width=7cm,height=6cm]{03-DetWG/figures/fitsNearFar.eps} &
    \includegraphics[width=7cm,height=6cm]{03-DetWG/figures/compStandNF.eps}
    \end{array}$
  \end{center}
  \caption{Fits to simulated data using the near-far prediction (left) and compared to equivalent fits performed allowing the flux to be determined as part of the fit (right). All fits assume normal hierarchy.}
  \label{fig:NeFfits}
\end{figure}

This tendency is illustrated in figure \ref{fig:projNF} for a set of true values of $\theta_{13} = 1^{\circ}$ and $\delta = 45^{\circ}$ where the minimum $\chi^2$ is projected onto each axis in turn.
\begin{figure}
  \begin{center}$
    \begin{array}{cc}
    \includegraphics[width=7.5cm,height=6cm]{03-DetWG/figures/thetaProf1_45.eps} &
    \includegraphics[width=7.5cm,height=6cm]{03-DetWG/figures/deltaProf1_45.eps}
    \end{array}$
  \end{center}
  \caption{Projection of the minimum $\chi^2$ onto the $\theta_{13}$ axis (left) and the $\delta$ axis (right) for $\theta_{13}=1^\circ$ and $\delta=45^\circ$.}
  \label{fig:projNF}
\end{figure}
At the 1$\sigma$ level ($\chi^2-\chi^2_{min}=1$) the fit to $\theta_{13}$ is very similar for both methods, however, the near-far projection is already better at the 3$\sigma$ level ($\chi^2-\chi^2_{min}=9$). The projection onto the $\delta$ axis for both methods is very similar, although for this example case the true value is a better fit in the case of the near-far-projection method.
\begin{figure}
  \begin{center}$
    \begin{array}{cc}
    \includegraphics[width=7.5cm,height=6cm]{03-DetWG/figures/trendNFTheta.eps} &
    \includegraphics[width=7.5cm,height=6cm]{03-DetWG/figures/trendNFDelta.eps}\\
    \includegraphics[width=7.5cm,height=6cm]{03-DetWG/figures/trendStandTheta.eps} &
    \includegraphics[width=7.5cm,height=6cm]{03-DetWG/figures/trendStandDelta.eps}
    \end{array}$
  \end{center}
  \caption{Quality of fit to $\theta_{13}$ (left) and $\delta$ (right) for a range of values. Using the near-far projection method (top) and a method in which the neutrino flux is part of the fit (bottom).}
  \label{fig:trendNF}
\end{figure}

Figure \ref{fig:trendNF} shows the trend for the measurement of the oscillation parameters for both the near-far projection method and the fitted-flux method. In both cases, 1$\sigma$ errors are garnered from the projection of the minimum $\chi^2$ onto the appropriate axis and $\theta_{13}$ is determined very precisely, with the true value being the best fit value in most cases. Determination of $\delta$ is not as precise, with the precision of the near-far projection method being somewhat better. Considering the deviation of the best fit delta value from the true value, it can be seen that the mean difference for the standard method is $\sim0.9\sigma$ whereas for the projection method it is $\sim0.6\sigma$.

\subparagraph*{Conclusions \\}

A basic method for the projection of the observed near detector spectrum at a Neutrino Factory to the far-detector sites has been developed. Under the assumption of pure near detector signals it has been shown that this projection can be used to predict accurately the far detector spectrum in the absence of oscillations. While in its current form this method has no clear advantage at the $1\sigma$ level over a method in which the flux is extracted from the fit directly, there seems to be evidence of improved sensitivity at $3\sigma$.  These preliminary results show the potential for a high-resolution near detector to improve the precision with which the oscillation parameters can be measured.


\paragraph{Study of neutrino interactions}
\label{SBL:sec:nuint}

The unprecedented neutrino fluxes available for the Neutrino
Factory program will allow the collection of a large number of
inclusive neutrino charged current (CC) interactions. 
As discussed above, the reduction of systematic uncertainties for the
neutrino oscillation program requires a highly segmented near
detector, thus providing excellent resolution in the reconstruction of
neutrino events. 
The combination of this substantial flux with a finely segmented near
detector offers a unique opportunity to produce a range of neutrino
scattering physics measurements, in addition to those needed by the
long base line oscillation program. 
The combined statistics and precision expected in the ND will allow
precise tests of fundamental interactions and better understanding of
the structure of matter. 
Given the broad energy range of the beam, a diverse range of physics
measurements is possible in the Neutrino Factory near detector.
To provide a flavour for the outstanding physics potential, we give a
short description of the studies that can be performed at a Neutrino
Factory near detector for a few selected topics. 
A more detailed and complete discussion of the short baseline physics
potential will appear in a separate physics working group paper and in
subsequent Neutrino Factory reports. 

\subparagraph*{Electroweak Physics}
\label{SBL:sec:sin2thetaW}

Neutrinos are a natural probe for the investigation of
electroweak physics.  Interest in a precise determination of the weak mixing angle ($\sin^2 \theta_W$)
at Neutrino Factory energies via neutrino scattering is twofold: a) it provides a direct measurement of
neutrino couplings to the $Z$ boson and b) it probes a different scale of momentum transfer
than LEP by virtue of not being on the $Z$ pole. The weak mixing angle can be extracted
experimentally from three main NC physics processes:
\begin{enumerate}
\item Deep Inelastic Scattering off quarks inside nucleons: $\nu N \to \nu X$;
\item Elastic Scattering off electrons: $\nu e^- \to \nu e^-$; and
\item Elastic Scattering off protons: $\nu p \to \nu p$.
\end{enumerate}


The most precise measurement of $\sin^2 \theta_W$ in neutrino deep
inelastic scattering (DIS) comes from the NuTeV experiment, which
reported a value that is $3\sigma$ from the Standard
Model~\cite{Zeller:2001hh}.
The Neutrino Factory near detector can perform a similar analysis in
the DIS channel by measuring the ratio of NC and CC interactions
induced by neutrinos: 
\begin{equation}
{\cal R}^\nu \equiv \frac{\sigma^\nu_{\rm NC}}{\sigma^\nu_{\rm CC}}
 \simeq \rho^2 \left( \frac{1}{2} - \sin^2 \theta_W +\frac{5}{9} \left(1 + r \right) \sin^4 \theta_W  \right)
\end{equation}
where $\rho$ is the relative coupling strength of the neutral to charged current interactions
($\rho =1$ at tree level in the Standard Model) and $r$ is the ratio of anti-neutrino to
neutrino cross section ($r \sim 0.5$).

The measurement of $\sin^2 \theta_W$ from DIS interactions can be
performed with a low density magnetized tracker since an accurate
reconstruction of the NC event kinematics and of the $\nu_e$ CC
interactions are crucial to keep the systematic uncertainties on the
event selection under control. 
The analysis selects events in the ND after imposing a cut on the
visible hadronic energy of $E_{\rm had} > 3$ GeV, as in the NOMAD
$\sin^2 \theta_W$ analysis (the CHARM analysis had $E_{\rm had} > 4$
GeV). 

The use of a low density magnetized tracker can substantially reduce systematic uncertainties
with respect to a massive calorimeter. The largest experimental systematic uncertainty in NuTeV is related to the subtraction
of the $\nu_e$ CC contamination from the NC sample. Since the low density tracker at the Neutrino Factory
can efficiently reconstruct the electron tracks, the $\nu_e$ CC interactions can be
identified on an event-by-event basis, reducing the corresponding uncertainty to a
negligible level. Similarly, uncertainties related to the location of the interaction vertex,
noise, counter efficiency etc. are removed by the higher resolution and by the different
analysis selection. 

A second independent measurement of $\sin^2 \theta_W$ can be obtained from NC
$\nu_\mu e$ elastic scattering. This channel has lower systematic uncertainties since it does
not depend upon the knowledge of the structure of nuclei, but has limited statistics
due to its very low cross section. The value of $\sin^2 \theta_W$ can be extracted from
the ratio of neutrino to anti-neutrino interactions~\cite{Marciano:2003eq}:
\begin{equation} \label{eqn:NCel}
{\cal R}_{\nu e} (Q^2) \equiv \frac{\sigma(\bar{\nu}_\mu e \to \bar{\nu}_\mu e)}{\sigma(\nu_\mu e \to \nu_\mu e)} (Q^2)
\simeq \frac{1 - 4 \sin^2 \theta_W + 16 \sin^4 \theta_W}{3 -12 \sin^2 \theta_W + 16 \sin^4 \theta_W}
\end{equation}
in which systematic uncertainties related to the selection and electron identification cancel out.

The extraction of the weak
mixing angle is dominated by the systematic uncertainty on the $\bar{\nu}_\mu / \nu_\mu$
flux ratio, which is entering Equation~(\ref{eqn:NCel}).   At a Neutrino Factory this systematic uncertainty will be considerably reduced over conventional beam facilities used for previous studies.
Together, the DIS and the NC elastic scattering channels
involve substantially different scales of momentum transfer, providing a tool to test the
running of $\sin^2 \theta_W$ in a single experiment. To this end, the study of NC elastic scattering
off protons can provide additional information since it occurs at a momentum scale which is
intermediate between the two other processes. Furthermore, in the two NC elastic processes
off electrons and protons it is possible to reconstruct the $Q^2$ on an event-by-event
basis, providing additional sensitivity. 

\subparagraph*{Strange Content of the Nucleon}
\label{sec:deltas}


The role of the strange quark in the
proton remains a central investigation in hadronic physics. The interesting question is
to what extent the strange quarks contribute substantially to the nucleon vector and axial-vector
currents. A large observed value of the strange quark contribution to the nucleon spin
(axial current), $\Delta s$, would require further theoretical speculations with respect to present
assumptions. The nucleon spin structure also affects the couplings of axions and
supersymmetric particles to dark matter. To better understand this, experiments at
MIT/Bates, Mainz, and Jefferson Lab probed and continue to probe the contribution of
strange quarks to the electromagnetic (vector) current. However, the only reliable
measurement of $\Delta s$ can be obtained from the detection of neutrino-proton NC elastic
scattering, $\nu p \to \nu p$.
In the limit $Q^2 \to 0$, the differential cross section is
proportional to the square of the iso-vector axial-vector form factor plus/minus the strange
axial form factor, $(G_A \pm G_s)^2$, where $G_s^2(Q^2=0) = \Delta s$.
Unfortunately, previous neutrino
scattering experiments have not been precise enough to provide a definitive statement on
the contribution of the strange sea to either the axial or vector form factor.
The Neutrino Factory near detector neutrino beam will be sufficiently intense that
a measurement of NC elastic scattering 
can provide a definitive statement on
the contribution of the strange sea to either the axial or vector form factor.
Systematic uncertainties can be reduced by measuring the NC/CC ratios for both neutrinos and
anti-neutrinos as a function of $Q^2$:
\begin{equation}
{\cal R}_{\nu p} (Q^2) \equiv \frac{\sigma(\nu_\mu p \to \nu_\mu p)}{\sigma(\nu_\mu n \to \mu^- p)}(Q^2); \;\;\;\;\;
{\cal R}_{\bar{\nu} p} (Q^2) \equiv \frac{\sigma(\bar{\nu}_\mu p \to \bar{\nu}_\mu p)}{\sigma(\bar{\nu}_\mu p \to \mu^+ n)}(Q^2)
\end{equation}
 



\subparagraph*{Structure of the Nucleon}
The following have been identified as important physics topics to address the structure of the nucleon at a near detector of a Neutrino Factory:
\begin{itemize}
\item Measurement of Form Factors and Structure Functions;
\item QCD Analysis of Parton Distribution Functions;
\item $d/u$ Parton Distribution Functions at Large $x$;
\item GLS Sum Rule and $\alpha_s$;
\item Non-perturbative Contributions and High Twists;
\item Quark-hadron Duality; and
\item Generalized Parton Distributions.
\end{itemize}


\subparagraph*{Parton Distribution Functions}
\label{SBL:sec:PDFs}


A QCD analysis of the ND data in the framework of global fits to extract
parton distribution functions is a crucial step to constrain systematic uncertainties
on the electroweak measurements.  In addition,
precision measurements of (anti)-neutrino structure functions and differential cross sections
would directly affect the LBL oscillation searches, providing an estimate of all background
processes which are dependent upon the angular distribution of the outgoing particles
in the FD.

For quantitative studies of inclusive deep-inelastic lepton-nucleon
scattering, it is vital to have precise $F_3$ structure functions,
which can only be measured with neutrino and antineutrino beams, as
input into global PDF fits.  Because it depends on weak axial quark
charges, the $F_3$ structure function is unique in its ability to
differentiate between the quark and antiquark content of the nucleon.
On a proton target, for instance, the neutrino and antineutrino $F_3$
structure functions (at leading order in $\alpha_s$) are given by
%
\begin{eqnarray}
xF_3^{\nu p}(x)
&=& 2 x \left( d(x) - \bar u(x) + \bar s(x) + \cdots \right)\, , \\
%
xF_3^{\bar\nu p}(x)
&=& 2 x \left( u(x) - \bar d(x) - \bar s(x) + \cdots \right)\, .
\end{eqnarray}
%
In contrast, electromagnetic probes are sensitive only to a sum of
quark and antiquark PDFs.  Unfortunately, the neutrino scattering
cross sections have considerably larger uncertainties than the
electromagnetic inclusive cross sections at present.
The high intensity Neutrino Factory facility offers
the promise to reduce the gap between the uncertainties on the weak and electromagnetic
structure functions, and would have a major impact on global PDF
analyses.
In addition to data in the DIS region, there is considerable interest
in obtaining data at low $Q^2$ (down to $Q^2 \sim 1$~GeV$^2$) and low
$W$ ($W < 2$~GeV).

Global PDF fits show that at large values of $x$ ($x > 0.5-0.6$) the $d$
quark distribution (or the $d/u$ ratio) is very poorly determined.
The main reason for this is the
absence of free neutron targets.  Because of the larger electric charge
on the $u$ quark than on the $d$, the electromagnetic proton $F_2$
structure function data provide strong constraints on the $u$ quark
distribution, but are relatively insensitive to the $d$ quark distribution.
To constrain the $d$ quark distribution as a function of the hadronic four-momentum
transfer squared, $t$, a precise knowledge
of the corresponding neutron $F_2^n$ structure functions is required, which in
practice is extracted from inclusive deuterium $F_2$ data.
At large values of $x$ the nuclear corrections in deuterium become
large and, more importantly, strongly model dependent, leading to
large uncertainties on the resulting $d$ quark distribution.

Perhaps the cleanest and most direct method to determine the $d/u$
ratio at large $x$ is from neutrino and antineutrino DIS on hydrogen.
Should a hydrogen target at the Neutrino Factory near detector become
available, a new measurement of 
neutrino and antineutrino DIS from {\it hydrogen} would offer significantly
improved uncertainties and could therefore make an important discovery
about the $d/u$ behavior as $x \to 1$. To be competitive with the
proposed JLab 12~GeV experiments, the kinematical reach would need
to be up to $x \sim 0.85$ and with as large a $Q^2$ range as possible
to control the higher twist and other subleading effects in $1/Q^2$.

\subsubsection{Near detector baseline design}
\label{sec:ND_design}

\paragraph{Option A - scintillating fibre tracker}

This option considers a low $Z$, high resolution scintillating fibre
tracker. 
It is composed of consecutive modules placed perpendicular to the beam
axis (figure \ref{fibres2} a). Each module (figure \ref{fibres2} b) has
two volumes: an absorber made of plastic scintillator slabs and a fibre
station made of thin scintillating fibres. The recoil
hadronic energy is measured in the absorber, while the fibre station reconstructs
particle tracks with high angular resolution.  

The overall thickness of the absorber is $5 \ cm$. 
It is subdivided into five layers perpendicular to the beam axis. 
The light attenuation in the material of the slabs introduces a
dependence of the measured signal on the position of the particle
hit, which can be eliminated by reading the signal from the absorber scintillator
slabs at both edges of a slab. 

The fibre station (figure \ref{fibres2} c) consists of 4 layers of
fibres with horizontal orientation and 4 layers of fibres with
vertical orientation. 
Three different conceptual designs for the fibre station are under
consideration. 
The first one is a station made of cylindrical 0.5\,mm thick fibres
(figure \ref{fibres2} c-bottom). 
For this design the position the fibres in a given layer is shifted by
0.25\,mm according to the fibres in the neighbouring one. 
The other two options consider a station made of squared 0.5\,mm thick
fibres with a displacement between neighbouring layers of 0.25\,mm and
0.175\,mm respectively (figure \ref{fibres2} c-top). 
In all three options the fibre station thickness is 4\,mm and the
station consists of  $\sim 12 000 $ fibres. 
\begin{figure}
\begin{center}
 \includegraphics[width=.95\textwidth]{03-DetWG/figures/detscheme2.eps}
\end{center}
\caption{Schematic drawing of the scintillating fibre tracker (a). In each fibre station (b,c) the layers of fibres with horizontal orientation are in blue and the layers with vertical orientation are in green. The absorbers are shown in brown.}
\label{fibres2}
\end{figure}

Our baseline option is a detector made of 20 consecutive
modules. Thus, the overall detector dimensions are 
$1.5 \times 1.5 \times 1.08 \ m^3$ that corresponds to a total mass of
$\sim 2.5$\,Ton.

In order to achieve maximal resolution on the muon scattering angle
the detector volume should be free of magnetic field. 
Such a choice implies an additional magnetised detector, placed
downstream of the scintillating fibre tracker to measure the sign,
momentum and trajectory of the outgoing muons.

\paragraph{Option B - High resolution straw tube tracker}
We propose here a possible high resolution straw tube tracker inspired
by the HiResM$\nu$ near detector \cite{Mishra:2008nx} being considered
for the LBNE project at Fermilab \cite{Fermilab_P5,Fermilab_SG}. 
In this section we describe the detector being considered for LBNE,
which would have identical features to the one at a Neutrino Factory. 

Building upon the NOMAD-experience \cite{Altegoer:1997gv}, we propose
a low-density tracking detector with a fiducial mass of 7.4\,Ton as a
neutrino target. 
The active target tracker will have a factor of two more sampling
points along the $z$-axis ($\nu$ -direction) and a factor of six more
sampling points in the plane transverse to the neutrino compared to
the NOMAD experiment. 
The proposed detector will further enhance the resolving power by
having an order of magnitude more tracking points and coverage for
side-exiting neutrals and muons. 

We are proposing straw-tube trackers (STT) for the active neutrino target, similar to the ATLAS Transition Radiation Tracker \cite{Akesson:2004nj,Akesson:2004nh,Abat:2008zza} and the COMPASS detector \cite{Bychkov:2002xw}. The tracker will be composed of straw tubes with 1 cm diameter, in the vertical ($y$) and horizontal ($x$) direction. In
front of each module a plastic radiator made of many thin foils allows the identification of electrons
through their Transition Radiation. The nominal fiducial volume for CC analysis is:
$350\times 350\times 600$~cm$^3$, corresponding to 7.4 tons of mass with an overall density $\rho < 0.1$~g/cm$^3$.

The STT will be surrounded by an electromagnetic calorimeter (sampling Pb/scintillator) covering
the forward and side regions. Both sub-detectors will be installed inside a dipole magnet providing
a magnetic field of $\sim 0.4$~T. An external muon detector based upon Resistive Plate Chambers (RPC)
will be placed outside of the magnet (see figure~\ref{fig:HiRes}).

\begin{figure}
\begin{center}
 \includegraphics[width=.85\textwidth]{03-DetWG/figures/HIRES.eps}
\end{center}
\caption{Sketch of the proposed HiRes detector showing the inner straw tube tracker (STT), the electromagnetic calorimeter (EM CALO) and the magnet with the muon range detector (MRD). Also shown is one module of the proposed straw tube tracker (STT). Two planes of straw tubes are glued together and held by an aluminium frame.}
\label{fig:HiRes}
\end{figure}

The neutrino target will be mainly composed of carbon, with a radiation length of about
5~m and spacepoint resolution around 200~$\mu$m. The momentum resolution is dominated by multiple scattering for tracks 1 m long ($\Delta p/p = 0.05$), while the measurement error for $p = 1$~GeV tracks would be $\Delta p/p = 0.006$. The proposed
detector will measure track position, $dE/dx$, and transition radiation (with Xe filling) over the
entire instrumented volume. The unconverted photon energy will be measured in the calorimeters
with a target energy resolution of $\sim 10\%/\sqrt{E}$. The detector will provide:
\begin{itemize}
\item Full reconstruction of charged particles and gammas;
\item Identification of electrons, pions, kaons, and protons from $dE/dx$;
\item Electron (positron) identification from Transition Radiation ($\gamma > 1000$);
\item Full reconstruction and identification of protons down to momenta of 250 MeV;
\item Reconstruction of electrons down to momenta of 80 MeV from curvature in the B-field.
\end{itemize}

The proposed near detector will measure the relative abundance, the
energy spectrum, and the detailed topologies for $\nu_\mu$,
$\overline{\nu}_\mu$, $\nu_e$ and $\overline{\nu}_e$ induced
interactions, including the momentum vectors of negative, positive and
neutral ($\pi^0$, $K_s^0$, $\Lambda$ and $\overline{\Lambda}$)
particles composing the hadronic system. 
A NC event candidate in NOMAD, shown in figure~\ref{fig:NC_NOMAD},
gives an idea of the precision with which the charged-particles and
the forward gammas were measured. 
Detailed simulations of this detector have been carried out in the
context of the LBNE proposals \cite{LBNE}. These simulations will be
adapted to the neutrino spectra at a Neutrino Factory to derive the
performance parameters of this detector in this context. We expect
such performance parameters for the Reference Design Report. 
\begin{figure}
\begin{center}
 \includegraphics[width=.80\textwidth]{03-DetWG/figures/NOMAD_NC.eps}
\end{center}
\caption{Candidate NC Event in NOMAD. Tracking charged particles in the HiRes detector
will provide a factor of two higher segmentation along z-axis and a factor of six higher segmentation
in the transverse-plane compared to NOMAD.}
\label{fig:NC_NOMAD}
\end{figure}

\paragraph{Charm and Tau Detector} 
A near detector at a Neutrino Factory needs to  measure the charm
cross-section to validate the size of the charm background in the far
detector, since this is the main background to the wrong-sign muon
signature (see section~\ref{sec:MIND}). The charm cross-section and
branching fractions are poorly known, especially close to threshold,
so a near detector would need to be able to detect charm
particles. Data available for charm cross-sections from neutrino
interactions result from dimuon events in large mass neutrino
experiments or from high resolution emulsion detectors operating at
neutrino beams (for a comprehensive review see~\cite{Lellis:2004yn}
and references therein). Recent results come from the dimuon data
in the CHORUS \cite{:2008xp} (8,910 neutrino induced and 430
antineutrino induced dimuon events) and NOMAD \cite{nomad:2010dimu}
experiments ($\sim 15,000$ dimuon events). The theoretical uncertainty
in the charm cross-section arises from the errors in the strange sea
content of the nucleon, the semi-leptonic charm to muon branching
fraction (with a 10\% relative error) and the longitudinal structure
function ($F_L$) and higher-twist effects. For this reason, it is
paramount to make an independent near detector measurement of the
charm cross-section with of order $10^6$ charm events and make the
error in the charm cross-section negligible in the estimation of the
neutrino oscillation background.

Since tau events have a similar signature to charm events, any
detector that can measure charm should be able to measure taus as
well. This is important to explore couplings of Non Standard
Interactions (NSI) at source $\epsilon_{\tau\mu}^s$, $\epsilon_{\tau
  e}^s$ or detection $\epsilon_{\tau\mu}^d$, $\epsilon_{\tau e}^s$(see
section~\ref{sec:nsi} for a comprehensive treatment). Either an
emulsion based detector or a semiconductor vertex detector for charm
and tau detection could be used for this purpose.  

A near detector at about 100~m from the muon decay ring needs to
operate in a high intensity environment ($\sim 10^9~\nu_\mu$ CC events
per year in a detector of mass 1 ton). The ideal detector to identify
the decay topologies of tau leptons and charmed hadrons should be able
to cope with the neutrino event rate and any background from the
facility. While in principle, the muons are bound inside the storage
ring, a calculation of the expected muon escape probability has not
been performed yet and would likely be due to rare processes (for
example, stray muons either escaping early in one of the arcs or the
early part of the straight section and end up scattered towards the
near detector). 
Should this be a problem, active shielding with
magnetized iron toroids to sweep away stray muons could be
used. Another background problem will be due to photons. Radiative
muon decay (1.4\%) and radiation by the decay electrons could be an
overwhelming background that will likely need shielding with, for
example, a 30-50 $X_0$ high-Z material. However, this shielding will
in turn cause ``neutrino radiation'' from neutrino interactions in the
shielding itself to create a large muon flux upstream of the near
detector. The shielding could be made active and could be used as a
beam profile monitor and, if sufficiently segmented, could be used to
measure the beam divergence. A solution to shielding in the near
detector has not been found yet and will be studied in time for the
Reference Design Report. 


Notwithstanding the above mentioned considerations for background
shielding, the near detector should be able to: 
\begin{itemize}
\item have high resolution to identify the short-lived charm hadrons
  and tau  leptons; 
\item measure the momentum and the charge of decay particles; 
\item perform a complete and accurate kinematical reconstruction of
  neutrino events. 
\end{itemize}
In the next two sections we identify two different ways of achieving
these goals, one with an emulsion based detector and the other with a
silicon vertex detector. 

\subparagraph*{Emulsion Detector}

Nuclear emulsions are a very well proven technology operating on
neutrino and charged-particle beams since the 1950s. 
Emulsion technology, pure nuclear emulsion and Emulsion Cloud Chamber
(ECC) targets, has already demonstrated that it is a superb technique
for the study of decay topologies
\cite{Niu:1971xu,Ushida:1980rr,Ushida:1980rs,Albanese:1985wk,:2007ny,Kodama:2000mp,Agafonova:2010dc}. 
A discussion of the performance that has been achieved in previous
emulsion-based experiments is beyond the scope of this section. 
We recall only the outstanding accuracy of this technology in detecting
short-lived particles with an excellent signal to background ratio. 
For details we refer to \cite{9783642036057,Arrabito:2007td} and
references therein.

So far the largest emulsion film production for a high-energy physics
experiment is the one for the OPERA detector \cite{Nakamura:2006xs}. 
Therefore, in the following we consider the emulsion films used for
the OPERA target \cite{Acquafredda:2009zz}. 
Each film has transverse dimensions $10 \times 13$\,cm$^2$ and
consists of a 44\,$\mu$m thick emulsion layer on both sides of a
205\,$\mu$m thick triacetyl cellulose (TAC) base. 
The radiation length of the nuclear emulsions is 5.5~cm and of the TAC
base 31~cm, while the density is 2.84 g/cm$^3$ and 1.35 g/cm$^3$ respectively.

The possibility of exploiting the emulsion technology for a near
detector has been already discussed in \cite{Abe:2007bi}. 
It was stressed that the main issue is whether it can cope with the
high rate that will be observed at a Neutrino Factory. 
Here we estimate the practical limits and the performance that could
be envisaged for a detector based on the emulsion technology in 
a very intense neutrino beam. 
We consider a pure emulsion target, followed by a magnetic
spectrometer, exploiting nuclear emulsions as a high-precision
(sub-micron) tracker.

The target proposed consists of a sequence of 150 films for a total
length of about 4.6 cm. 
Therefore, the proposed target weight is 1 kg and has a thickness
of about $0.2 X_0$. 
An important issue is the number of interactions
that can be stored in the target whilst preserving the capability of
connecting them unambiguously with the hits recorded by the
electronic detectors. 
Experience with OPERA bricks exposed to a neutrino beam, and
integrating over thousands of interactions, shows that up to 10
neutrino interactions per cm$^3$ can be stored \cite{Aoki:2010zz}.
Therefore, in a target (about 500 cm$^3$ of
nuclear emulsions) we can collect up to 5000 neutrino interactions.

Downstream of the target, we consider a spectrometer: consisting of a
sandwich of nuclear emulsions and very light material that we call a
``spacer''. 
This material provides a long lever arm between two consecutive
emulsions (tracking devices) with a stable mechanical structure. A
Rohacell plate, a few centimetres thick, fulfills this
requirement. The trajectory measured with the emulsions which precede
and follow the spacer provides the measurement of the charge and
momentum of the particle. The total length of the target plus
spectrometer is of the order of 10 cm. 

Emulsion spectrometers have also been exposed to charged particle
beams of 0.5, 1.0 and 2.0\,GeV \cite{Fukushima:2008zzb}. 
The spectrometer was composed of three emulsion sheets interleaved
with two spacers, each of which produces an air gap of 15\,mm, and 
immersed in a dipole magnetic field of 1.06\,T.
The measured momentum resolution in the range 0.5 to 2.0\,GeV is
$13.3\pm 0.3$\%.  

Monte Carlo simulations have been performed in order to compute the
momentum resolution and the charge identification efficiency of the
spectrometer. Depending on the magnetic field, on the relative
alignment of the emulsion plates in the spectrometer and on the
spectrometer geometry, the momentum resolution for a 10 GeV muon is
better than 25\%, with a charge misidentification better than
0.2\%. 
As far as the electrons are concerned, the momentum resolution
is as good as in the muon case, while the charge misidentification is
much worse due to showering. Very preliminary results show that the
electron charge misidentification is of the order of 40\%. However,
further studies are needed before we can draw firm quantitative
conclusions on the electron charge misidentification.

Although it is not the goal of this study, it is worth noting that
downstream of the spectrometer we have to place an electronic detector
with the aim of providing the time stamp for the events. We plan to
perform the scanning of the events without any electronic detector
prediction. Therefore, the time information is mandatory in order to
match the emulsion information to that of the electronic
detector to allow the charged-current to neutral-current
separation. Furthermore, this electronic detector is also needed to
identify primary electrons. Given the expected event density in the
target and its dimension, the electronic detector will be able to
provide the time stamp only if it has a position accuracy of the order
of 50~$\mu$m. Therefore, one could imagine synergy between the
emulsion detector and an electronic detector (either a silicon or
scintillating fibre detector) operating on the same beam-line. 

The final question that needs to be addressed is whether an emulsion
based detector can operate close to the storage ring of a Neutrino
Factory. A dedicated study to asnwer this question will be carried out
in time for the Reference Design Report. 

\subparagraph*{Silicon Vertex Detector\\}

The second possible detector capable of identifying short lived
particles at a near detector of a Neutrino Factory is a silicon vertex
tracker. The advantage of this type of detector is that it is able to
operate at a high event rate and still have very good spatial
resolution. This is necessary to distinguish the primary neutrino
interaction vertex from the secondary vertex due to the short lived
charm hadron or the tau lepton. Downstream of the vertex detector, we
need a tracking detector capable of distinguishing electrons from
muons in a magnetic field. So, a possible configuration could consist
of a silicon strip or pixel detector, followed by either the
scintillating fibre tracker or the straw tube tracker mentioned in the
previous sub-section. 

Such a vertex detector could be similar to the NOMAD--STAR detector
that was installed upstream of the first drift chamber of the NOMAD
neutrino oscillation experiment \cite{Altegoer:1997gv} (see figure
\ref{fig:nomad_star}).
The main aim
of this detector was to test the capabilities of silicon detectors
for short baseline neutrino oscillation searches
\cite{GomezCadenas:1995ij,GomezCadenas:1996jx}. However, this set-up
can mimic a possible design  for a near detector at a Neutrino Factory
\cite{Ellis:2006wj}. It was used to measure the impact parameter and
double vertex resolution to determine the charm detection
efficiency. 
\begin{figure}[htbp]
\begin{center}
  \includegraphics[width=.65\linewidth]{03-DetWG/figures/nomadstar.eps}
  \includegraphics[width=.30\linewidth]{03-DetWG/figures/star_new.eps}
\end{center}
\caption{Left: The NOMAD detector with the Silicon TARget (NOMAD--STAR).Right: Side view of NOMAD-STAR.}
\label{fig:nomad_star}
\end{figure}

%\emph{\noindent NOMAD--STAR at a Neutrino Factory}

The flux of neutrinos at a near detector 80 metres downstream of a
muon storage ring \cite{Tang:2009na} will produce  $2.3\times 10^8
\nu_\mu$~CC events per year in a detector of similar mass as
NOMAD--STAR (50 kg). With the measured efficiencies from the
NOMAD-STAR analysis, this would correspond to about $7\times 10^5$
charm events reconstructed per year. 
This would allow a sensitive measurement of the charm cross-section
close to the charm threshold.

%\emph{Impact parameter detection of taus}

The reconstruction of taus from an impact parameter signature with a
dedicated silicon vertex detector was studied in the NAUSICAA proposal
\cite{GomezCadenas:1995ij}. A  silicon vertex detector with a $B_4 C$
target was proposed as an ideal medium to identify taus. Standard
$\nu_\mu$ CC interactions have an impact parameter resolution of
28~$\mu$m, while tau decays have an impact parameter resolution of
62~$\mu$m. By performing a cut on the impact parameter significance
($\sigma_{IP}/IP$) one can separate  one prong decays of the tau from
the background. For three prong decays of the tau, a double vertex
signature is used to separate signal from background. The total net
efficiency of the tau signal in NAUSICAA was found to be 12\%. With
this efficiency, one could have a sensitivity of  $P_{\mu\tau}<
3\times 10^{-6}$ at 90\% C.L. on the $\mu-\tau$ conversion
probability.  

Another idea proposed in 1996 was to use a hybrid detector
emulsion-silicon tracking to improve the tau detection efficiency
\cite{GomezCadenas:1996jx}. A Letter of Intent (called TOSCA) was
submittd to the CERN SPSC in 1997 \cite{TOSCA} with a detector based
around this idea.  Tau detection efficiencies of 42\%, 10.6\% and 27\%
were determined for the muon, electron and one charged hadron decays
of the tau, yielding a net probability of $P_{\mu\tau}< 0.75\times
10^{-5}$ for the CERN SPS beam at 350 GeV.  

Assuming 12\% efficiency from the NAUSICAA proposal, and assuming that
charm production is about 4\% of the $\nu_\mu$ CC rate between 10 and
30 GeV (CHORUS measured $6.4\pm 1.0\%$ at 27 GeV)
\cite{Lellis:2004yn}, would imply a signal of $1.2\times 10^8$ tau
events (with $P_{\mu\tau}=100\%$ conversion rate) and $4\times 10^7$
charm events. Charm events from anti-neutrinos (for example
$\overline{\nu}_e$) mimic the potential signal. The identification of
the positron can reduce the background, but electron and positron
identification normally has a lower efficiency than muon
identification. It is very important to have a light detector (ie, a
scintillating fibre tracker) behind the vertex detector inside a
magnetic field to identify the positron with high efficiency (in the
best scenarios $\sim 80\%$ would be the maximum achievable). A further
way to separate the charm background from signal is to use the
kinematic techniques of NOMAD. Assuming the NOMAD net efficiency
yields a $P_{\mu\tau}< 2\times 10^{-6}$. These considerations are
preliminary and a full study needs to be carried out to validate these
assumptions.  

