\renewcommand{\thefigure}{\Roman{figure}}

%\section*{Executive Summary}

\begin{center}
\huge
{\bf Executive Summary}
\normalsize
\end{center}

\bigskip
\bigskip
\bigskip

In the Fall of 1999, the Fermilab Directorate chartered a study group 
to investigate the physics motivation for a \textit{neutrino factory} 
based on a muon storage ring that would operate in the era beyond the 
current set of neutrino-oscillation experiments.  We were charged to 
evaluate the prospective physics program as a function of the stored 
muon energy (up to $50\hbox{ GeV}$), the number of useful muon decays 
per year (in the range from $10^{19}$ to $10^{21}$ decays per year), 
and the distance from neutrino source to detector; and to assess the value 
of muon polarization within the storage ring.  A companion study 
evaluated the technical feasibility of a neutrino factory and 
identified an R\&D program that would lead to a detailed design.

The principal motivation for a neutrino factory is to provide the 
intense, controlled, high-energy beams that will make possible 
incisive experiments to pursue the mounting evidence for neutrino 
oscillations.  The composition and spectra of intense neutrino beams 
from a muon storage ring will be determined by the charge, momentum, 
and polarization of the stored muons, through the decays $\mu^{-} 
\rightarrow e^{-}\nu_{\mu}\bar{\nu}_{e}$ or $\mu^{+} \rightarrow 
e^{+}\bar{\nu}_{\mu}\nu_{e}$.  There is no other comparable source of 
electron neutrinos and antineutrinos.  The neutrino beam also offers 
unprecedented opportunities for precise measurements of nucleon 
structure and of electroweak parameters.  The intense muon source 
needed for the neutrino factory would make possible exquisitely 
sensitive searches for muon-electron conversion and other rare 
processes.

Experiments carried out at a neutrino factory within the next decade 
can add crucial new information to our understanding of neutrino 
oscillations. By studying the oscillations of $\nu_{\mu}$, $\nu_{e}$, 
$\bar{\nu}_{\mu}$, and $\bar{\nu}_{e}$, it will be possible to 
measure, or put stringent limits on, all of the appearance modes 
$\nu_e \rightarrow \nu_\tau$, $\nu_e \rightarrow \nu_\mu$, and 
$\nu_\mu \rightarrow \nu_\tau$. This will provide a basic test of 
our understanding of neutrino oscillations. In addition it will 
be possible to determine precisely (or place 
stringent limits on) all of the leading oscillation parameters; to 
infer the pattern of neutrino masses; and, under the right 
circumstances, to observe \textsf{CP} violation in the lepton sector.  
Baselines greater than about 2000~km will enable a quantitative study 
of matter effects and a determination of the mass hierarchy.  If the 
Mini\textsc{BooNE} experiment confirms the $\nu_{\mu} \leftrightarrow 
\nu_{e}$ effect reported by the LSND experiment, experiments with 
rather short baselines (a few tens of km) could be extremely 
rewarding, and enable, for example, the search for 
$\nu_e \rightarrow \nu_\tau$ oscillations. 

\begin{figure} 
%\epsfysize=2.5in
%\epsfxsize=3.0in
\epsfxsize=3.3in
\centerline{
\epsffile{summary_cp.eps}}
\caption{Predicted ratios of 
$\bar\nu_e \to \bar\nu_\mu$ to $\nu_e \to \nu_\mu$ 
rates at a 20~GeV neutrino factory. 
The upper (lower) band 
is for $\delta m^2_{32} < 0$ ($\delta m^2_{32} > 0$).
The range of possible CP violation determines 
the widths of the bands. 
The statistical error shown corresponds to
$10^{20}$ muon decays of each sign and a 50~kt detector. 
Results are from Ref.~\ref{bgrw00}.
}
\label{fig:summary_cp}
\end{figure}

\begin{figure} 
%\epsfysize=2.5in
%\epsfxsize=3.0in
\epsfxsize=3.3in
\centerline{
\epsffile{summary_all.eps}}
\caption{The required number of muon decays needed in a 
neutrino factory to observe $\nu_e \rightarrow \nu_\mu$ 
oscillations in a 50~kt detector and determine the sign of $\delta m^2$, 
and the number of decays needed to observe 
$\nu_e \rightarrow \nu_\tau$ oscillations in a few~kt detector, 
and ultimately 
put stringent limits on (or observe) CP violation in the 
lepton sector with a 50~kt detector. 
Results are from Ref.~\ref{bgrw00}.}
\label{fig:summary_all}
\end{figure}


If the atmospheric neutrino deficit 
is correctly described by three flavor oscillations with
$\delta m^2$ in the range favored by the SuperKamionkande 
data, and if the parameter $\sin^2 2\theta_{13}$ is not 
smaller than $\sim 0.01$, then exciting cutting--edge 
long baseline oscillation physics could begin with an 
$\sim50$~kt detector at a 
neutrino factory with muon energies as low as 20~GeV 
delivering as few as $10^{19}$ muon decays per year. 
This ``entry--level" facility would be able to measure 
$\nu_e \rightarrow \nu_\mu$ and 
$\overline{\nu}_e \rightarrow \overline{\nu}_\mu$ 
oscillations. For baselines of a few thousand km 
the ratio of rates 
$N(\overline{\nu}_e \rightarrow \overline{\nu}_\mu) / 
N(\nu_e \rightarrow \nu_\mu)$ is sensitive to the 
sign of $\delta m^2$, and hence to the pattern of 
neutrino masses (Fig.~\ref{fig:summary_cp}). With $10^{19}$ decays 
and a 50~kt detector a unique and statistically 
significant measurement of the neutrino mass spectrum 
could be made. In addition, the $\nu_e \rightarrow \nu_\mu$ 
event rate is approximately proportional to 
the parameter $\sin^2 2\theta_{13}$, which could therefore 
be measured.

\begin{figure} 
%\epsfysize=2.5in
%\epsfxsize=3.0in
\epsfxsize=3.5in
\centerline{
\epsffile{summary_t13.eps}}
\caption{Limits in oscillation parameter space that 
would result from the absense of a $\nu_e \rightarrow \nu_\mu$ 
signal in a 10~kt detector 7400~km downstream of a 
30~GeV neutrino factory in which there are $10^{20}$ and 
$10^{21} \mu^+$ decays, followed by the same number of $\mu^-$ decays.
The impact of including backgrounds in the analysis is shown. 
Results are from Ref.~\ref{camp00}.
}
\label{fig:summary_t13}
\end{figure}

\begin{figure} 
%\epsfysize=2.5in
%\epsfxsize=3.5in
\epsfxsize=5.0in
\centerline{
\epsffile{summary_t13meas.eps}}
\caption{Precision with which the oscillation parameters 
$\sin^2 2\theta_{23}$ and $\sin^2 2\theta_{13}$ can be 
measured in a 10~kt detector 7400~km downstream of a 
30~GeV neutrino factory in which there are $10^{19}$, $10^{20}$, and 
$10^{21} \mu^+$ decays.
Results are from Ref.~\ref{camp00}.
}
\label{fig:summary_precision}
\end{figure}


With higher beam intensities and/or higher beam energies the
physics potential of a neutrino factory is enhanced 
(Fig.~\ref{fig:summary_all}). 
In particular, as the intensity is increased to O($10^{20}$) 
decays/year $\nu_e \rightarrow \nu_\tau$ oscillations might 
be measured, and eventually CP violation in the lepton 
sector observed if the large mixing angle MSW solution is the
correct description of the solar neutrino deficit. 
Higher beam intensities would also allow smaller values of 
$\sin^2 2\theta_{13}$ to be probed (Figs. ~\ref{fig:summary_cp},~\ref{fig:summary_t13}), 
and higher precision 
measurements of the oscillation parameters to be made.
An example of the improvement of measurement precision with 
neutrino factory intensity is shown in
Fig.~\ref{fig:summary_precision} for the 
determinations of $\sin^2 2\theta_{23}$ and $\sin^2 2\theta_{13}$.

The physics program at detectors located close to the neutrino factory is
also very compelling.  The neutrino fluxes are four orders of magnitude
higher than those from existing beams. Such intense beams make experiments
with high precision detectors and low mass targets feasible for the first
time.Using these detectors and the unique ability of neutrinos to 
probe 
only particular flavors of quarks will allow a precise measurement of the
individual light quark contents of the nucleon in both an isolated and
nuclear environment. 
In addition,
neutrinos prove to be an elegant tool in probing the spin structure of
the nucleon and may finally enable resolution of the nucleon spin among
its partonic components.
The high statistics of a neutrino factory will 
also enable meticulous studies of electro-weak and strong interaction parameters as well as
searches for exotic phenomena other than oscillations.  
%In addition,
%neutrinos prove to be an elegant tool in probing the spin structure of
%the nucleon and may finally enable resolution of the nucleon spin among
%its partonic components.

\renewcommand{\thefigure}{\arabic{figure}}
\setcounter{figure}{0}