\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 we can finalise the performance of the near and far detectors at a Neutrino Factory 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 background 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 allow the oscillation maximum to be in 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 charge 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/fracpdf.eps} &
      \includegraphics[width=8.5cm, height=6.5cm]{03-DetWG/figures/meanpdf.eps}
    \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/an2hits.eps} &
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/an2frachit.eps} \\
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/an2hitmean.eps} &
      \includegraphics[width=7.5cm, height=5.5cm]{03-DetWG/figures/an2all3.eps}
    \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 depositted charge and distribution information from that part of the event not associated to the candidate muon.

A dedicated study will be required to fully understand 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~ktonne 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 required is 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 through a silicon vertex detector. 

We also need to determine for the RDR whether we need four detectors or we can have two detectors only (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 the MIND one (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 wa 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 \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.
\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{Photodetectors}

Given the enormous amount of R\&D currently underway in Europe, the United States, Russia and  Japan on various Geiger-mode, multi-pixel avalanche photodiodes (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 advance as they develop 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.

  \subparagraph*{Specify final extrusion profile through simulation (square or triangle)}
	
	Simulation studies will advise us on the relative merits of square vs. 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 finalized, we will initiate discussions with extrusion die manufacturers to optimize the die design for:
	\begin{itemize}
	\item Part uniformity
	\item Production speed
	\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 sectionof the MIND and the fact that the photodetectors 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 modeling 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 the 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 to demonstrate 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 beamline 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 timeline for the RDR}

For the RDR, we will provide a detailed costing exercise 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 this point in time, we do not see any big unknowns that would result in large cost uncertainties and the subsequent need for large amounts of contingency.  An approximate timeline for the completion of the near and far detctor 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.eps}
  \caption{
    Approximate timeline for completing important near and far 
    detector tasks needed for the RDR.
  }
  \label{Fig:DetRDRPlan}
\end{figure}
