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%--------  Executive summary
\section*{Executive summary}

\subsection*{Introduction}

The starting point for the International Design Study for the Neutrino
Factory (the IDS-NF \cite{IDSNFWWWSite}) was the output of the earlier
International Scoping Study for a future Neutrino Factory and
super-beam facility (the ISS)
\cite{Bandyopadhyay:2007kx,Apollonio:2009,Abe:2007bi}.
The accelerator facility described in section \ref{Sect:AccWG}
incorporates the improvements that have been derived from the
substantial amount of work carried out within the Accelerator Working
Group. 
Highlights of these improvements include:
\begin{itemize}
  \item Initial concepts for the implementation of the proton driver
    at each of the three example sites, CERN, FNAL, and RAL;
  \item Detailed studies of the energy deposition in the target area;
  \item A reduction in the length of the muon beam phase-rotation and
    bunching systems;
  \item Detailed analyses of the impact of the risk that stray
    magnetic field in the accelerating cavities in the ionisation
    cooling channel will reduce the maximum operating gradient.
    Several alternative ionisation-cooling lattices have been
    developed as fallback options to mitigate this technical risk;
  \item Studies of particle loss in the muon front-end and the
    development of strategies to mitigate the deleterious effects of
    such losses;
  \item The development of more complete designs for the muon linac and
    re-circulating linacs;
  \item The development of a design for the muon FFAG that
    incorporates insertions for injection and extraction; and 
  \item Detailed studies of diagnostics in the decay ring.
\end{itemize}
Other sub-systems have undergone a more ``incremental'' evolution; an
indication that the design of the Neutrino Factory has achieved a
degree of maturity.
The design of the neutrino detectors described in section
\ref{Sect:DetWG} has been optimised and the Detector Working Group has
made substantial improvements to the simulation and analysis of the
Magnetised Iron Neutrino Detector (MIND) resulting in an improvement
in the overall neutrino-detection efficiency and a reduction in the
neutrino-energy threshold. 
In addition, initial consideration of the engineering of the MIND
has generated a design that is feasible and a finite element analysis
of the toroidal magnetic field to produce a realistic field map has
been carried out.
Section \ref{Sect:DetWG} also contains, for the first time, a
specification for the near-detector systems and demonstration that the
neutrino flux can be determined with a precision of 1\% through
measurements of inverse muon decay at the near detector.

The performance of the facility, the work of the Physics and
Performance Evaluation Group, is described in section
\ref{Sect:PPEG}.
The effect of the improved MIND performance is to deliver a discovery
reach for CP-invariance violation in the lepton sector, the
determination of the mass hierarchy, and of $\theta_{13}$ that extends
down to values of $\sin^2 2 \theta_{13} \sim 5 \times 10^{-5}$ and is
robust against the systematic uncertainties. 
In addition, the improved neutrino-energy threshold has allowed an
indicative analysis of the kind of re-optimisation of the facility
that could be carried out should $\theta_{13}$ be found close to the
current upper bound.
The results presented in section \ref{Sect:PPEG} demonstrate
that the discovery reach as well as the precision with which the
oscillation parameters can be measured at the baseline Neutrino
Factory is superior to that of other proposed facilities for all
possible values of $\sin^2 2 \theta_{13}$.

\subsection*{Motivation}

The phenomenon of neutrino oscillations, arguably the most significant
advance in particle physics over the past decade, has been established
through measurements on neutrinos and anti-neutrinos produced in the
sun, by cosmic-ray interactions in the atmosphere, nuclear reactors,
and beams produced by high-energy particle accelerators
\cite{Amsler:2008zzb}.
In consequence, we know that the Standard Model is incomplete and must
be extended to include neutrino mass, mixing among the three neutrino
flavours, and therefore lepton-flavour non conservation.
These observations have profound implications for the ultimate theory
of particle interactions and for the description of the structure and
evolution of the Universe.  
In particular:
\begin{itemize}
  \item Mixing among the three massive neutrinos admits the
    possibility that the matter-antimatter (CP) symmetry is violated
    via the neutrino-mixing matrix.  
    Such an additional source of CP-invariance violation may hold the
    key to explaining how the antimatter created in the Big Bang
    was removed from the early Universe; 
  \item If a neutrino is to be distinguished from its antineutrino
    counterpart it is necessary to assign a conserved lepton number
    to the neutrino.
    At present there is no theoretical justification for such a
    conserved quantum number.
    If lepton number is not conserved, then a neutrino is
    indistinguishable from an antineutrino, i.e. the neutrino is a
    Majorana particle; a completely new state of matter.
    If this is so, then it is conceivable that the ``see-saw''
    mechanism can give an explanation of why the neutrino mass is tiny
    compared to the other matter fermions and may help to explain why
    the neutrino mixing angles are so large compared to those of the
    quarks; and
  \item The neutrino abundance in the Universe is second only to that
    of the photon and so, even with a tiny mass, the neutrino may make
    a significant contribution to the dark matter which is known to
    exist.
    Therefore, the neutrino may play an important role in determining
    the structure of the Universe.
\end{itemize}
These exciting possibilities justify an energetic and far reaching
programme.

An essential part of such a programme is to make precision
measurements of the oscillation parameters. 
Assuming the three flavours and the unitary neutrino-mixing matrix
that is presently favoured, oscillation measurements can be used to
determine the three mixing angles and the the critical phase parameter
that can provide a new source of CP-invariance violation. 
Neutrino oscilaltion measurements can also be used to determine the
two (signed) mass differences. 
This programme is similar to the long-standing investigations of quark
mixing via the CKM matrix and it would now seem to be clear that an
understanding of the flavour problem will definitely necessitate
precision measurements in both quark and lepton sectors.  

Not all the properties of the neutrino can be determined by
oscillation experiments. 
Equally important is the determination of the Majorana or Dirac nature
of the neutrino which requires a totally different experiment. 
Currently, the search for neutrinoless double beta decay is the most
promising. 
In addition, although oscillation measurements determine the mass
differences, they are insensitive to the absolute mass, $m_1$, of the 
lightest mass state. 
The determination of $m_1$ requires a very precise measurement of the
end-point of the electron spectrum in beta decay.
The mass would also follow from the observation of neutrinoless double
beta decay. 

The Neutrino Factory, described in this report, is capable of
generating intense, high-energy neutrino and anti-neutrino beams which
are required to make the exquisitely sensitive oscillation
measurements. 
\begin{itemize}
  \item The deviation of $\theta_{23}$ from $\pi/4$;
  \item The deviation of $\theta_{13}$ from $0$;
\end{itemize}
and, for $\sin^2 2 \theta_{13} \gtrsim 5 \times 10^{-5}$:
\begin{itemize}
  \item The degree to which CP-invariance is violated in the (Dirac)
    lepton sector; and
  \item The neutrino mass hierarchy.
\end{itemize}
The intense beams will be equally valuable should there be either a
more extended neutrino sector that includes, for example, a fourth
generation or sterile-neutrino state or new non-standard interactions.
The large data sets that will be collected will have a unique
potential to throw light on the physics of flavour and hence the
ultimate theory of particle physics.  

\subsection*{Neutrino oscillations and the Neutrino Factory}

Neutrino oscillations are described by a unitary ``mixing matrix''
that rotates the mass basis into the flavour basis. 
The mixing matrix is parametrised by three mixing angles
($\theta_{12}$, $\theta_{23}$, and $\theta_{13}$) and one phase
parameter ($\delta$)
\cite{Pontecorvo:1957cp,Pontecorvo:1957qd,Maki:1962mu,Bilenky:2001rz}. 
If $\delta$ is non-zero (and not equal to $\pi$), then CP-invariance
violation in the neutrino sector will occur so long as 
$\theta_{13} > 0$.
Measurements of neutrino oscillations in vacuum can be used to
determine the moduli of the mass-squared differences 
$\Delta m^2_{31} = m^2_3 - m^2_1$ and 
$\Delta m^2_{21} = m^2_2 - m^2_1$ (where the $m_i$ are the masses of 
the neutrino mass eigenstates) and, with the aid of interactions with
matter, also the sign. 
The bulk of the measurements of neutrino oscillations to date have
been collected using the dominant, ``disappearance'', channels 
$\nu_e \rightarrow \nu_e$ and $\nu_\mu \rightarrow \nu_\mu$.  
These data have yielded values for two of the three mixing
angles ($\theta_{12}$ and $\theta_{23}$), the magnitude of the
mass-squared differences $\Delta m^2_{31}$ and $\Delta m^2_{21}$, and
that $m_2 > m_1$ (i.e. that $\Delta m^2_{21} > 0$).
The challenge to the neutrino community, therefore, is to determine
the sign of $\Delta m^2_{31}$ (the ``mass hierarchy''), to measure
$\theta_{13}$ and $\delta$, and to improve the accuracy with which
$\theta_{23}$ is known.

Over the next few years, the T2K, NO$\nu$A, Double Chooz,
Daya Bay, and RENO experiments will exploit the sub-leading, 
$\nu_\mu \rightarrow \nu_e$ and  $\bar{\nu}_e \rightarrow \bar{\nu}_x$
channels to improve significantly the precision with which
$\theta_{13}$ is known. 
The NO$\nu$A long-baseline experiment may also be able to determine
the mass hierarchy if $\theta_{13}$ is close to the present upper
limit.
However, it is very unlikely that either T2K or NO$\nu$A will be able
to discover CP-invariance violation, i.e. that $\delta \ne 0,\pi$.

The most effective channel for a precision measurement of
$\theta_{13}$ and the search for CP-invariance violation is the
sub-leading $\nu_e \rightarrow \nu_\mu$ oscillation.
The determination of the mass hierarchy relies on the measurement of
the oscillation frequency of neutrinos passing through the earth,
hence the sensitivity increases as the distance the neutrino beam
propagates through the earth increases.
The best sensitivity to CP-invariance violation is also found at large
source-detector distances as long as the neutrinos have a sufficiently
large energy, $E_\nu$.  
Therefore, optimum sensitivity to the parameters of the Standard
Neutrino Model (S$\nu$M) can be achieved at a facility that provides
intense, high-energy $\nu_e$ and $\bar{\nu}_e$ beams.

In the Neutrino Factory, beams of $\nu_e$ and $\bar{\nu}_\mu$ 
($\bar{\nu}_e$, $\nu_\mu$) are produced from the decays of $\mu^+$
($\mu^-$) circulating in a storage ring.
As the muon charge-to-mass ratio is large the neutrinos carry away
a substantial fraction of the energy of the parent muon, hence, high
neutrino energies can readily be achieved.  
Time-dilation is also beneficial, allowing sufficient time to produce
a pure, collimated beam.
Charged-current interactions induced by ``golden channel'', 
$\nu_e \rightarrow \nu_\mu$, oscillations produce muons of charge
opposite to those produced by the $\bar{\nu}_\mu$ in the beam and thus
a magnetised detector is required.   
The additional capability to investigate the ``silver'' 
($\nu_e \rightarrow \nu_\tau$) and ``platinum'' 
($\nubarmu \rightarrow \bar \nu_e$) channels makes the Neutrino
Factory the ideal place to look for oscillation phenomena that are
outside the standard, three-neutrino-mixing paradigm.
It is thus the ideal facility to serve the precision era of neutrino
oscillation measurements. 
The performance of the Neutrino Factory is described in detail in
section \ref{Sect:PPEG}.

\subsection*{The IDS-NF baseline}

The optimisation of the Neutrino Factory baseline to maximise the
performance of the facility for the discovery of CP-invariance
violation, the mass hierarchy, and the determination of
$\theta_{13}$ is described in section \ref{Sect:PPEG}.
The optimum requires two distant detectors. 
One at the ``magic baseline'', $7\,000$--$8\,000$\,km from the
source, will have excellent sensitivity to the mass hierarchy and 
$\sin^2 2 \theta_{13}$.
The second source-detector distance in the range
$2\,500$--$5\,000$\,km will give the best sensitivity to CP-invariance
violation but requires a stored-muon energy in excess of 20~GeV. 
The sensitivity to non-standard interactions at the Neutrino Factory
improves as the stored-muon energy is increased, reaching a plateau at
around $\sim25$~GeV \cite{Kopp:2007mi}.   
A baseline stored muon energy of $25$~GeV has therefore been adopted.

The baseline accelerator facility described in section
\ref{Sect:AccWG} provides a total of $10^{21}$ muon decays per year
split between the two distant neutrino detectors.  
The process of creating the muon beam begins with the bombardment of a
pion-production target with a 4\,MW, pulsed proton beam.
The target must be sufficiently heavy to produce pions copiously, yet
not so large as to cause a significant rate of interaction of the
secondary pions within the target material. 
In addition, the target must withstand the substantial beam-induced
shock.
The IDS-NF baseline calls for a free-flowing, liquid-mercury jet
target operating in a solenoid-focusing, pion-capture channel.  
This is followed by a solenoidal transport channel in which the pions
decay to muons.
The emerging muon beam is then bunched and rotated in phase space to
produce a beam with small energy spread.
At this point, the muon beam occupies a large volume of
phase space which must be reduced, ``cooled'', before it can be injected
into the acceleration sections.  
As a consequence of the short muon lifetime, traditional cooling
techniques are inappropriate, so the required phase-space reduction is
achieved by means of ionisation cooling.
This involves passing the muon beam through a material in which
it loses energy through ionisation and then re-accelerating the beam
in the longitudinal direction to replace the lost energy.   
The IDS-NF baseline calls for lithium-hydride absorbers embedded in a
solenoidal transport channel with re-acceleration achieved using
201\,MHz cavities at a gradient of 16\,MV/m.  
Subsequent muon acceleration must be rapid, especially at low muon
energy. 
For the baseline, muons are accelerated to 0.9\,GeV in a
superconducting linac and then to 12.6\,GeV in a sequence of two
re-circulating linear accelerators (RLAs). 
The final stage of acceleration, from 12.6\,GeV to the stored-muon
energy of 25\,GeV, is provided by a fixed-field alternating-gradient
(FFAG) accelerator. 
 
The baseline neutrino detector described in \ref{Sect:DetWG} is a
revision of the Magnetised Iron Neutrino Detector (MIND) developed
within the ISS \cite{Abe:2007bi}.
MIND is a MINOS-like iron-scintillator sandwich calorimeter with a
sampling fraction optimised for the Neutrino Factory beam
\cite{Cervera:2010rz}.
The baseline calls for a fiducial mass of 100~kTon to be placed at
the intermediate baseline and a 50\,kTon detector at the magic
baseline. 
The performance of the IDS-NF baseline Neutrino Factory in terms of
the $3 \sigma$ discovery reach for CP violation, the mass hierarchy,
and $\theta_{13}$ is shown in figure \ref{Fig:Performance}.  
The discovery reach is presented in terms of the fraction of all
possible values of $\delta$ (the ``CP fraction'') and plotted as a
function of $\sin^2 2 \theta_{13}$.
As described in detail in section \ref{Sect:PPEG}, the discovery reach
of the Neutrino Factory is significantly better than the realistic
alternative facilities, particularly for small values of
$\theta_{13}$. 
Should $\theta_{13}$ be discovered to be large, i.e. close to the
present upper bound, a re-optimisation of the baseline Neutrino
Factory will still yield superior performance.
\begin{figure}
  \begin{center}
    \includegraphics[width=0.31\textwidth]{00d-Executive-summary/Figures/idr-exec-cpv}%
    \includegraphics[width=0.31\textwidth]{00d-Executive-summary/Figures/idr-exec-sgn}%
    \includegraphics[width=0.31\textwidth]{00d-Executive-summary/Figures/idr-exec-the}
  \end{center}
  \caption{
    The discovery potential at $3 \sigma$ for CP violation (left
    panel), the mass hierarchy (central panel), and 
    $\sin^2 2 \theta_{13}$ (right panel).
    The discovery reach is plotted in terms of the CP fraction as a
    function of $\sin^2 2 \theta_{13}$.  
    The performance of the IDS-NF baseline Neutrino Factory is shown
    as the black solid line. 
    The Neutrino Factory re-optimised for large $\sin^2 2 \theta_{13}$ 
    is shown as the blue solid line. 
  }
  \label{Fig:Performance} 
\end{figure}

\subsection*{The Neutrino Factory as part of the muon-physics
             programme}

The properties of the muon make it a unique tool for particle
physics. 
In addition to the decays that provide intense, high-energy $\nu_e$
and $\bar{\nu}_e$ beams, the great precision with which properties
such as $g-2$ can be calculated using the Standard Model makes it an
ideal tool in the search for new phenomena. 
Furthermore, the observation of charged lepton flavour violation (cLFV)
in muon decay, predicted in many models, would revolutionise current
theories, whilst the muon's comparatively large mass and point-like
nature make it an appealing candidate to provide multi-TeV
lepton-antilepton collisions at a Muon Collider. 

Neutrino oscillations involve processes in which lepton flavour is not
conserved.
Therefore, processes such as $\mu \rightarrow e \gamma$, 
$\mu \rightarrow eee$, and muon to electron conversion in the field of
the nucleus ($\mu N \rightarrow e N$) will occur.
Rates for such cLFV processes can be calculated in the Standard Model
extended to take into account neutrino oscillations but they are
minuscule (of the order of $10^{-54}$) and so the observation of such
processes would be a clear signal of new physics. 
To achieve the requisite sensitivities, intense muon beams are
required and the techniques proposed for the Neutrino Factory, such as
high power, pulsed proton beams with short ($\lesssim 10\,{\rm ns}$)
bunches, pion capture in solenoidal fields, the manipulation of muon
beams of large emittance, and FFAG acceleration are of great
relevance.

A Muon Collider \cite{Alsharoa:2002wu} offers crucial advantages over
an $e^+e^-$ collider of the same centre-of-mass energy and luminosity
because the muon mass is roughly 200 times that of the electron.
The large muon mass leads to a relatively low rate of synchrotron
radiation, making it possible to design a circular machine in which
100\% of multi-TeV $\mu^+ \mu^-$ collisions occur within $\sim 0.1$\%
of the nominal centre-of-mass energy of the collider.
In addition, should the Higgs boson be discovered and have the
expected coupling proportional to mass, the Muon Collider could be
used as a ``Higgs Factory'' at which detailed studies of its
properties may be carried out.

A conceptual design for the Muon Collider has been proposed
\cite{Palmer:2009zzb} in which the systems that make up the Neutrino
Factory form the ``front-end'' of the Muon Collider.
Indeed, should the techniques required to realise the Neutrino
Factory be demonstrated, the principal accelerator-system challenge
that would remain for the Muon Collider would be the development of an 
ionisation-cooling system that could reduce all six phase-space
dimensions of the muon beams such that a luminosity in excess of
$10^{34}$\,cm$^{-2}$ could be achieved.
Therefore, the implementation of the Neutrino Factory is desirable to
mitigate the technical risks presented by the Muon Collider. 

The Neutrino Factory is the facility of choice for the study of
neutrino oscillations: it has excellent discovery reach and offers the
best precision on the mixing parameters, particularly in the difficult
region of small $\theta_{13}$.
The ability to vary the stored-muon energy and perhaps the detector
technology can provide the flexibility to respond to developments in
our understanding and the discovery of new phenomena.
The R\&D programme required to make the Neutrino Factory a reality
will directly benefit the development of the Muon Collider and
experiments that seek to discover cLFV.
A comprehensive muon-physics programme is compelling indeed. 
