\subsection{Detector Systems}

\subsubsection{Simulation and Analysis Work towards RDR}
\label{sec:detector_RDR}
While there has been considerable progress in the definition of a
baseline detector configuration, including an improved analysis of
MIND and defining the specifications of the near detector, there is
still a significant amount of work that needs to be performed before
the performance of the near and far detectors at the Neutrino Factory
can be finalised for the Reference Design Report (RDR).
 
The efficiency of identification of $\nu_\mu$ and $\overline{\nu}_\mu$
CC interactions, along with the associated backgrounds, has been
studied for MIND. 
All efficiencies and backgrounds have been calculated using full
pattern recognition and reconstruction of neutrino events, that now
include QEL and RES events, in addition to DIS events. 
As a consequence, the efficiencies obtained demonstrate an extension
of the performance of MIND at low energies that allows the oscillation
maximum to be within the efficiency plateau, while maintaining backgrounds
at the $10^{-4}$ level. 
The systematic error on the signal efficiencies obtained is about
$\sim 1\%$ over the whole neutrino-energy range. 
However, there are still a number of simplifications that have been
carried out in the MIND simulations that need to be addressed before
we can quote a final sensitivity for the RDR. 

Similarly, the requirements of the near detector have been identified,
but we have yet to perform a full near detector simulation and
analysis to determine the realistic prospects to measure the flux over
the full energy range, to measure cross-sections, to measure the
divergence of the neutrino beam, to measure charm production and to
search for NSI from tau events.  
We will itemise the next steps needed to complete these and other
studies in time for the RDR in the following sections.

\paragraph{Steps towards RDR for MIND analysis}  
\subparagraph*{Multi-variate likelihood analysis}

A number of additional steps will be required to fully benchmark the
performance of MIND. 
This section presents some possible improvements to the analysis which
have not yet been fully exploited. 
As mentioned in section~\ref{subpar:NCrej}, two energy-deposit based
parameters used by MINOS were studied but not included in the analysis
presented here. 
The extra parameters include the total energy in the candidate and the
mean deposit per plane of the candidate. 
The distributions of these variables for a test set of neutral-current
and charged-current events were used to form PDFs, named $l_{frac}$
and $l_{mean}$ respectively, shown in figure \ref{fig:NCpdfs_2}. 
Samples are taken from the NC and CC PDFs to form the four
log-likelihood rejection parameters:
\begin{eqnarray}
  \label{eq:lik21}
  \mathcal{L}_1 &= &\log \left( \frac{l_{hit}^{CC}}{l_{hit}^{NC}} \right)\\
  \label{eq:lik22}
  \mathcal{L}_2 &= &\log \left( \frac{l_{hit}^{CC}\times l_{frac}^{CC}}{l_{hit}^{NC}\times l_{frac}^{NC}} \right)\\
  \label{eq:lik23}
  \mathcal{L}_3 &= &\log \left( \frac{l_{hit}^{CC}\times l_{mean}^{CC}}{l_{hit}^{NC}\times l_{mean}^{NC}} \right)\\
    \label{eq:lik24}
    \mathcal{L}_4 &= &\log \left( \frac{l_{hit}^{CC}\times l_{frac}^{CC}\times l_{mean}^{CC}}{l_{hit}^{NC}\times l_{frac}^{NC}\times l_{mean}^{NC}} \right)
\end{eqnarray}

\begin{figure}
  \begin{center}$
    \begin{array}{cc}
      \includegraphics[width=8.5cm, height=6.5cm]{03-DetWG/figures/Fig143a} &
      \includegraphics[width=8.5cm, height=6.5cm]{03-DetWG/figures/Fig143b}
    \end{array}$
  \end{center} 
  \caption{Additional PDFs for the NC rejection parameters. (left) fraction of visible energy in candidate and (right) candidate mean deposit per plane. CC in black and NC in red.}
  \label{fig:NCpdfs_2}
\end{figure}

An analysis using the likelihood functions described in equations~\ref{eq:lik21}~--~\ref{eq:lik24} was implemented but no improvement in performance was obtained with respect to using $\mathcal{L}_1$. Distributions of these functions for a test statistic are shown in figure \ref{fig:an2logs}. There is significant correlation between these parameters. Development of a multivariate analysis or neural net based on these variables, which take their correlations into account, will be studied for future analyses.

\begin{figure}
  \begin{center}$
    \begin{array}{cc}
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/Fig144a} &
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/Fig144b} \\
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/Fig144c} &
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/Fig144d}
    \end{array}$
  \end{center} 
  \caption{Log likelihood distributions for the four possible scenarios. (top left) $\mathcal{L}_1$, (top right) $\mathcal{L}_2$, (bottom left) $\mathcal{L}_3$ and (bottom right) $\mathcal{L}_4$}
  \label{fig:an2logs}
\end{figure}

\subparagraph*{Muon momentum measurement by range}

Measurement of the muon momentum using the range of the candidate in
the detector was shown to improve resolution, particularly at low
momenta, by MINOS~\cite{Adamson:2007gu}. 
An independent measure of the momentum could aid in the MIND
analysis. 
The cuts currently implemented via equations~\ref{eq:dispMom}
and~\ref{eq:dispMom2} are highly correlated with the range of the muon
and their power to remove background is likely to be improved with the
inclusion of the muon range measurement. 

\subparagraph*{Hadronic reconstruction}

The studies presented use parameterisations based on results presented
by Monolith and MINOS to estimate the quality of reconstruction of the
hadronic energy and direction.  
These parameters are important both for the reconstruction of neutrino
energy and for the formation of the kinematic cuts. 
In the ultimate analysis, reconstruction will be performed on an
event-by-event basis using deposited charge and distribution
information from that part of the event not associated to the
candidate muon. 

A dedicated study will be required to understand fully the best method
to perform the hadronic reconstruction. 
Using the observable quantities from the event, we could form a seed
for a jet fitting algorithm which could reconstruct both the energy
and momentum of the hadronic shower. 
Using the known structure of neutrino interactions, we can also use
the combination of the muon momentum and hadronic energy to calibrate
the total energy of the neutrino interaction.  

\subparagraph*{Cosmic backgrounds}

The background from cosmic rays and cosmic neutrinos has not been
studied yet. 
This will be important to determine the final detector design and its
location, either in an underground laboratory or in a green field site
on the surface with minimal overburden. 
While understanding the timing of the accelerator system and
directional arguments will enable the rejection of many of these
events it is clear that some level of rock overburden or active
vetoing will be required, especially when considering the surface area
of a 50--100\,kTon MIND. 
The expected Neutrino Factory duty cycle---the proportional time
window when beam related interactions are possible---of $\sim$10\%
will need to be taken into account to determine the level of
overburden that will be required.  

\subparagraph*{Tau background}

Another important study that is required is the determination of the
contribution to the reconstructed spectrum from $\nu_e \rightarrow
\nu_\tau~(\overline{\nu}_e \rightarrow \overline{\nu}_\tau)$
interactions. 
This oscillation channel would be expected to produce a similar
absolute flux of $\nu_\tau~(\overline{\nu}_\tau)$ to that produced by
the golden channel $\nu_\mu~(\overline{\nu}_\mu)$ oscillation
\cite{Indumathi:2009hg}. 
While the high interaction threshold for these species means that
fewer interactions will take place in the detector, tau interactions
become significant above $\sim$8\,GeV. 
Since the $\tau$ produced in CC interactions will decay promptly and
has a branching fraction for $\mu$ containing channels of (17.36 $\pm$
0.05)\%~\cite{Amsler20081} it is possible that a significant fraction
of these events may survive the analysis. 
However, understanding this background, if treated with care, can
contribute information to the fit instead of detracting from
it~\cite{Donini:2010xk}. 
The distortion caused is highly sensitive to the oscillation
parameters so fitting for this distortion could help in the removal of
ambiguities in the determination of $\theta_{13}$ and $\delta_{CP}$. 
To include this study in the full simulation of MIND, we will need to
migrate from NUANCE to GENIE, as NUANCE does not contain tau
production and decays. 
Migration of the full simulation to GENIE has already commenced.

\subparagraph*{Realistic MIND Geometry with Toroidal Magnetic Field Map}

The MIND simulation described in section~\ref{sec:MIND} includes an
idealised geometry with square iron plates 14\,m$\times$14\,m and
3\,cm thick, with two layers of scintillator, each of 1~cm thickness. 
The magnetic field assumed was a simple uniform dipole field of 1~T. 
However, a design that can be realised in practice, with achievable
engineering constraints consisting of octagonal plates of
14\,m$\times$14\,m and with a toroidal field map between 1\,T and
2.2\,T, was presented in \ref{sec:MIND_conceptual_design}. 
While we do not expect that the change in geometry will affect the
MIND performance significantly, it is necessary to perform a new
simulation with these new parameters. 
These changes will be carried out for the RDR.

\paragraph{Steps towards RDR for Near Detector}

We have two options for the near detector baseline: one with a
scintillating-fibre tracker and the other with a straw-tube tracker. 
These detectors need to be immersed in a magnetic field to be able to
take full advantage of the detector resolution to measure the momentum
of the particles produced in the neutrino interaction. 
Either option would have to be followed by a muon spectrometer, which
could be a smaller version of MIND. 
We need to benchmark both of these options and determine which of the
detectors provides  better performance. 
Additionally, upstream of the near detector, we would place a high
resolution charm and tau detector. 
We need to establish whether an emulsion detector is feasible at a
Neutrino Factory or whether the only way we can measure charm and tau
events is using a silicon vertex detector.  

We also need to determine for the RDR whether we need four near
detectors or whether two detectors will suffice (for example, this
could be achieved if the near detector were on rails, and it could be
moved to either of the straight sections of the storage ring,
depending on the charge of the muon). 
Moreover, we need to determine the optimum distance from the near
detector to the end of the decay straight and what shielding is
required. 
All of these considerations need to be resolved through detailed
simulations before the publication of the RDR. 
Full response matrices, similar to those that have been prepared for
the MIND (see Appendix \ref{app:response}), for signal and background
at the final near detector configuration, will also need to be
determined so that the physics performance may be quantified. 

To achieve these goals, the following simulations still need to be carried out:
\begin{itemize}
\item Neutrino electron scattering: Simulations for Inverse Muon Decay
  (IMD) have already been produced as a way of calibrating the
  neutrino flux (section~\ref{sec:ND_performance}). 
  However, IMD has a threshold of 11~GeV, and we need a method of
  determining the flux at lower energies as well. 
  Neutrino-electron $\nu_e e^- \rightarrow \nu_e e^-$ and
  $\overline{\nu}_e e^- \rightarrow \overline{\nu}_e e^-$ elastic
  scattering can provide such a flux measurement over the whole
  neutrino energy range and can be used to cross-check the IMD
  results;
\item Flux extrapolation from near to far detector: Preliminary
  results on the flux extrapolation method have been presented in
  section~\ref{sec:ND_performance}. 
  A method to deduce and take into account the systematic errors from
  the near detector data storage must be developed;
\item Tau and charm analysis: A full
  simulation with a silicon vertex detector and an emulsion detector
  needs to be carried out to determine the tau and charm detection
  efficiency and relevant backgrounds of the tau/charm detector at a
  neutrino factory;
\item Near detector shielding: This is an important topic that needs
  to be addressed at the interface between the storage ring and the
  near detector. 
  From the accelerator end, we need to understand potential muon
  losses in the storage ring and photon contamination from radiative
  decays. 
  From the near detector point of view, we need to ascertain the
  impact of these backgrounds and what type of shielding can be
  tolerated. 
  The flux of neutrino induced muons from the shielding itself will
  also need to be calculated; and
\item Performance of near detector for neutrino scattering physics
  topics: Once the near detector facility has been defined, the
  performance of a near detector to determine neutrino cross-sections,
  parton distribution functions and other topics in neutrino
  scattering physics will be carried out.    
\end{itemize}

\subsubsection{Detector R\&D Plan}

\paragraph{Magnetisation}

\subparagraph{STL optimisation for MIND}

Since the STL implementation we envision for MIND is essentially
identical to that planned for the VLHC and what was actually
prototyped during the R\&D program for the VLHC, there is a relatively
small amount of work that needs to be done prior to developing the
engineering design document for MIND.  
The one area of investigation would be to use multiple superconductor
loops within the STL cryostat.  
The overall size of the STL would remain the same, the total amount of
the superconductor would remain the same, the forces would be
essentially the same, but now the external excitation current would be
reduced from 90-100kA to that number divided by the number of separate
circuits in the STL.  
Configurations with between 5 and 10 circuits will be investigated.  
This makes the external power supply and the room temperature current
leads much more straightforward.

\paragraph{Photo-detectors}

Given the enormous amount of R\&D currently underway in Europe, the
United States, Russia and  Japan on various Geiger-mode, multi-pixel
avalanche photo-diodes (and the rapid progress on performance and
cost), we do not plan to initiate any separate R\&D in this area.  
We will monitor the progress on these types of devices world wide and
stay abreast of advances by communicating with our
colleagues actively working in the field and by staying current with
the literature on the devices. 

\paragraph{Scintillator}

Extruded scintillator is an advanced and mature technology. 
There are a number of areas that we will devote R\&D to, however.
These are summarised below.


\subparagraph*{Specify final extrusion profile through simulation (square or triangle)}

Simulation studies will advise us on the relative merits of square
versus triangle cross-section extrusions.  
These studies will lead to a final choice regarding the scintillator
cross section and dimensions.  
Once the extrusion profile design is finalised, we will initiate discussions with extrusion die manufacturers to optimise the die design for:
\begin{itemize}
  \item Part uniformity;
  \item Production speed; and
  \item Tooling lifetime.
\end{itemize}

\subparagraph*{Engineer detector plane mechanics}

The iron plate design currently is quite mature.  
R\&D will be needed to integrate the detector planes with the steel.  
We will start with the concepts that were used by MINOS and then
extend them to address the larger cross section of the MIND and the
fact that the photo-detectors will be mounted directly on the
scintillator extrusions, thus eliminating the need for fibre
manifolds.  
This simplifies the detector plane tremendously and also allows for
the additional bolts needed for the iron plate support.  
The work will include 2D and 3D modelling with associated ANSYS
analyses. 

 \subparagraph*{Investigate the possibility of co-extruding the fibre with the scintillator.}

Possibly the most manpower-intensive step in the detector plane
fabrication is the insertion (and gluing) of the WLS fibre into the
scintillator extrusion.  
Preliminary investigations have been done at Fermilab to develop
extrusion die tooling that would allow commercial WLS fibre (from
Kuraray most likely) to be co-extruded with the scintillator (inserted
into the hot melt zone and pulled along with the polymer flow).  
Although this is a very tricky process, initial studies were
successful with post-cladding Kuraray WLS fibre with various thin (few
hundred micron) layers of polyethylene, Kapton and Kynar.  
Industrial experts in this field have been contacted and believe it is
possible to develop the process tooling to accomplish this.  
We will work with the Fermilab Scintillator Detector group and outside
vendors to develop process die tooling for this application. 

\subparagraph*{Alternate detector plane possibility}

Although we believe that solid scintillator is the optimum choice for
the detection planes, we will monitor the progress the INO
collaboration is making with RPC R\&D and production for their
detector.  
INO is a candidate far detector for a Neutrino Factory located in
Europe or Japan.

\paragraph{Fibre}

Although we do not feel that R\&D is needed to improve the performance
of the best available wavelength shifting (WLS) fibre that is 
currently available, this product only comes from a single-source
supplier, Kuraray.  
We will investigate with university groups versed in polymer science
and optical-fibre fabrication to see if an alternate technology base
can be developed that could be transferred to industry in order to
present experimenters with a choice of vendors.  
This could also have a positive impact on cost.

\paragraph{Prototyping}

Prototyping a scale version of MIND will allow the technical
feasibility of the MIND design, including the use of extruded
scintillator and SiPM readout options. 
There will be an added benefit that this prototype can be exposed to a
test beam to validate the performance of the detector under realistic
conditions. 

AIDA (Advanced European Infrastructures for Detectors at Accelerators)
\cite{AIDA} is a European project to develop infrastructures for
particle physics detector R\&D. 
As part of this project, a MIND prototype will be assembled and placed
at the end of the H8 beam-line by a consortium of European
institutions. 
The main purpose will be to benchmark and validate simulations to
determine the muon charge identification performance, but also to
measure hadron energy reconstruction and test different reconstruction
algorithms. 
After studying its performance the module will be available as a muon
spectrometer for future users of the beam. 
Also, as part of AIDA, a small Totally Active Scintillating Detector
(TASD) will be constructed and placed inside the Morpurgo magnet of
the H8 beam line. 
The device will be used to measure the electron charge identification
efficiency in a test beam with a realistic detector.  

\paragraph{Detailed Costing and time-line for the RDR}

For the RDR, we will provide a detailed costing for MIND.  
We will start with the WBS structure for MINOS and then develop our
own costing model based on the MIND components, fabrication techniques
and siting issues.  
At present, we do not see any big unknowns that would
result in large cost uncertainties.
An approximate time-line for the completion of the near and far detector
tasks that are required to deliver the RDR is shown in figure
\ref{Fig:DetRDRPlan}. 
\begin{figure}
  \includegraphics[width=\linewidth]{04-RandD-plan/RDR-det-Timeline-110111}
  \caption{
    Approximate time-line for completing important near and far 
    detector tasks needed for the RDR.
  }
  \label{Fig:DetRDRPlan}
\end{figure}
