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\begin{document}
\begin{flushright}
FERMILAB-Conf-00/016-t \\
17 January, 2000 \\
\end{flushright}
\vspace{0.5cm}
\title{NEUTRINO FACTORY PHYSICS STUDY~\cite{members}
STATUS AND AN ENTRY LEVEL SCENARIO}
\author{S. GEER}
\address{Fermi National Accelerator Laboratory,
P.O. Box 500, Batavia, IL 60510, USA}
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\maketitle\abstracts{The status of an ongoing neutrino
factory physics study at Fermilab is described, together with a personal view of
the parameters required for an ``entry--level" neutrino factory.
}
\section{Introduction: Why study neutrino factories now ?}
Recent measurements of atmospheric muon neutrino
($\nu_\mu$) fluxes from the Super--Kamiokande (SuperK) collaboration
have shown an azimuth--dependent ($\rightarrow$ baseline dependent)
depletion that strongly suggests neutrino oscillations of the
type $\nu_\mu \rightarrow \nu_x$. Since the atmospheric $\nu_e$
flux is not similarly depleted, $\nu_x$ cannot be $\nu_e$, and
must therefore be either $\nu_\tau$, or $\nu_s$ (a sterile neutrino).
These observations have inspired many theoretical papers, several
neutrino oscillation experiment proposals,
and much interest in the physics community.
This interest is well motivated. Understanding the neutrino-mass
hierarchy and the mixing matrix that drives flavor oscillations
may provide clues that lead to a deeper understanding of physics
at very high mass-scales and insights into the physics associated
with the existence of more than one lepton flavor.
Hence, there is a strong incentive to
find a way of measuring the neutrino flavor
mixing matrix, confirm the oscillation scheme (three--flavor mixing,
four--flavor, n-flavor ?), and determine which mass eigenstate is
the heaviest (and which is the lightest). This will require a further
generation of accelerator based experiments beyond those currently
proposed.
High energy neutrino beams are currently produced by creating
a beam of charged pions that decay in a long channel pointing
in the desired direction. This results in a beam of muon neutrinos
($\pi^+ \rightarrow \mu^+ + \nu_\mu$) or muon anti--neutrinos
($\pi^- \rightarrow \mu^- + \overline{\nu}_\mu$). In the future,
to adequately unravel the mixing matrix, we will need $\nu_e$
and $\overline{\nu}_e$ (as well as $\nu_\mu$ and $\overline{\nu}_\mu$)
beams. To illustrate this, consider neutrino oscillations
within the framework of three-flavor mixing, and
adopt the simplifying approximation that only the
leading oscillations contribute (those driven by the largest
$\delta m^2_{ij}$ defined as $\delta m^2_{32} \equiv m^2_3 - m^2_2$,
where $m_i$ is the mass associated
with mass eigenstate $i$). The probability that a neutrino
of energy $E$~(GeV) and flavor $\alpha$ oscillates into a neutrino of
flavor $\beta$ whilst traversing a distance $L$~(km) is given by:
%
\begin{equation}
P(\nu_e\to \nu_\mu) =
\sin^2\theta_{23} \; \sin^22\theta_{13} \; \sin^2 (1.267 \delta m_{32}^2 L/E)\,,
\nonumber
\end{equation}
\begin{equation}
P(\nu_e\to \nu_\tau) =
\cos^2\theta_{23} \; \sin^22\theta_{13} \; \sin^2 (1.267 \delta m_{32}^2 L/E)\,,
\label{eq:probs}
\end{equation}
\begin{equation}
P(\nu_\mu\to \nu_\tau) =
\cos^4\theta_{13} \; \sin^22\theta_{23} \; \sin^2 (1.267 \delta m_{32}^2 L/E)\,
\,. \nonumber
\end{equation}
%
Each of the oscillation probabilities depend on $\delta m^2_{32}$
and two mixing angles $\theta_{ij}$. To adequately
determine all the $\theta_{ij}$ and
sort out the various factors contributing to the
$P(\nu_\alpha \rightarrow \nu_\beta$) will require
$\nu_e$ as well as $\nu_\mu$ beams !
In addition, there is a bonus
in using $\nu_e$ beams since electron neutrinos
can elastically forward scatter off electrons in matter
by the charged current (CC) interaction. This introduces a term in the
mixing matrix corresponding to $\nu_e \rightarrow \nu_e$ transitions
that is not present for neutrinos of other flavors. Hence, if
electron--neutrinos
travel sufficiently far through the Earth, matter effects modify the
oscillation probabilities. This modification depends on the sign of
$\delta m^2_{32}$, and provides a unique way of measuring which mass
eigenstate is heaviest, which is lightest !
We conclude that if we can find
a way of producing $\nu_e$ beams {\it of sufficient intensity}, we are
highly motivated to do so.
The obvious way to attempt to produce high energy $\nu_e$ beams
is to exploit muon decays. Since muons live 100 times longer than
pions, we need to avoid using a linear decay channel, which would
be impractically long for high energy muons. The solution is to use a muon
storage ring with long straight sections, one of which points in the
desired direction. This yields a neutrino beam consisting of 50\% $\nu_e$ and
50\% $\overline{\nu}_\mu$ if $\mu^+$ are stored, or 50\% $\nu_\mu$ and
50\% $\overline{\nu}_e$ in $\mu^-$ are stored.
Using a storage ring to produce secondary beams of $\mu^\pm, e^\pm,
\overline{p}$, and $\nu$ was proposed by Koshkarev~\cite{koshkarev} in
1974. The idea (also ascribed to Wojcicki~\cite{wojcicki} and
Collins~\cite{collins}) therefore dates back to the early days of the
ISR at CERN.
The key questions that need to be addressed in order to produce a viable
proposal for the production of secondary beams by this method are:
(i) How can enough particles be stored ? and
(ii) How can their phase-space be
compressed to produce sufficiently intense beams for physics ?
The calculated beam fluxes using the Koshkarev scheme were too low to
motivate the construction of a secondary beam storage ring.
A viable solution to the key question
(how to make sufficiently intense beams) was implemented at the beginning
of the 1980's for
antiproton production, leading directly to the CERN proton--antiproton
collider and the discovery of the weak Intermediate Vector Bosons. The
solution to the intensity question involved using lithium lenses to collect
as many negative particles as possible, and stochastic
cooling to reduce the phase-space of the $\overline{p}$ beam before
acceleration. In 1980 it was suggested~\cite{cline} that the negative
particle collection ring (the Debuncher) at the proposed Fermilab
antiproton source could be used to provide a neutrino beam downstream
of one of its long straight sections. The Debuncher collects negative
pions (as well as antiprotons) which decay to produce a
flux of captured negative muons. The muon flux in the Debuncher was
subsequently measured and found to be modest. The short baseline
neutrino oscillation experiment proposal (P860~\cite{p860})
that was developed
following these ideas was not approved ... the problem of intensity
had not been solved !
To make progress we need a method of cooling muon beams and a way of
producing more muons. Stochastic cooling cannot be used
since the cooling time much longer than the muon lifetime.
Ionization cooling was proposed as a possible solution
(see~\cite{kolomensky}).
A way of collecting more pions (that subsequently decay into muons)
using a very high-field solenoid was proposed by Djilkibaev and
Lobashev~\cite{melc} in 1989. Thus by the end of the 1980's the conceptual
ingredients required for very intense muon sources were in place, but
the technical details had not been developed. Fortunately in the 1990's
the desire to
exploit an intense muon source to produce muon beams for
a high energy muon collider
motivated the formation of an R\&D collaboration
({\it The Muon Collider Collaboration}). This has resulted in
a more complete technical understanding of the design of an
intense muon source~\cite{status_report}.
In 1997 it was proposed (Geer~\cite{geer})
to use a muon collider type muon source,
together with a dedicated muon storage ring with long straight sections,
to produce a very intense neutrino source. It was shown that this
``neutrino factory" was sufficiently intense
to produce thousands of events per year in a reasonably sized detector on the
other side of the Earth ! The intensity problem had been solved !
In addition, it was shown that the ring could be tilted at large
angles to provide beams for very long (trans--Earth) neutrino oscillation
experiments, and that muon polarization could in principle be exploited
to turn on/off the initial $\nu_e$ flux~\cite{geer}.
This proposal came at a time of increasing interest in neutrino oscillation
experiments due to the SuperK results, and also at a time when the
particle physics community was/is considering possible facilities
needed at its laboratories in the future~\cite{cern}. Thus, the
neutrino factory concept quickly caught the imagination of the physics
community, and the interest of its laboratory directors. This interest
led to the first NUFACT workshop at Lyon in 1999,
and a request from the Fermilab
directorate for a 6 month technical study~\cite{tech} to explore an explicit
neutrino factory design and identify the associated R\&D issues,
together with a parallel 6 month physics study~\cite{physics}
to explore the physics
potential of a neutrino factory as a function of its energy, intensity,
and the baseline for oscillation experiments.
\section{Physics study: status and results}
We are, at the time of writing, half way through the Fermilab 6 months
neutrino factory physics study~\cite{members}.
The charge for the study is given below.
Fortunately there have been many recent
papers~\cite{geer,cern,many_papers,paper2} that address the
physics potential of neutrino factories and provide valuable insight
that the study can draw on. However,
it is too early to give comprehensive results from the ongoing study,
or draw firm conclusions.
Instead, I will use results from calculations done in collaboration
with my colleagues~\cite{paper2} to anticipate some of the results that
may come from the full study, and give a personal view on the parameters
of what might be considered an ``entry--level" neutrino factory.
\subsection{Charge}
The charge for the physics study is to deliver a concise report by March 31,
2000 that will explicitly include:
\begin{description}
\item{1.} The physics motivation for a neutrino source based
on a muon storage ring, operating in the era
beyond the current set of neutrino oscillation
experiments.
\item{2.} The physics program that could be accomplished at a
neutrino factory as a function of:
(a) The stored muon energy, with the maximum energy
taken to be 50~GeV.,
(b) The number of muon decays per year in the beam-forming
straight section, taken to be in the range from $10^{19}$
to $10^{21}$ decays per year.,
(c) The presence or absence of muon polarization within the
storage ring, and for oscillation experiments,
(d) The baseline length including
investigations evaluating matter effects.
\end{description}
\subsection{Neutrino oscillations: points in parameter space}
To fulfill the charge, we are proceeding by defining~\cite{theory_group}
a handful
of representative points in oscillation parameter space, and
studying, for each of these points, the physics reach as a function
of the neutrino factory parameters. So far three points (1A, 1B, 1C)
have been defined within the framework of three--flavor mixing, and
one point (2A) has been defined within the framework of four--flavor
mixing (one sterile neutrino flavor):
\begin{description}
\item{Point 1A:} Three-flavor oscillations, with $\delta m^2_{ATM}$ and
$\sin^2 2\theta_{ATM}$ corresponding to the central value favored
by the current SuperK data, $\delta m^2_{SUN}$ and
$\sin^2 2\theta_{SUN}$ corresponding to the LMA MSW solution.
Explicitly,
$\delta m_{32}^2 = 3.5 \times 10^{-3}$~eV$^2$/c$^4$,
$\delta m_{21}^2 = 5.0 \times 10^{-5}$~eV$^2$/c$^4$,
$\sin^2 2\theta_{12} = 0.8$,
$\sin^2 2\theta_{23} = 1.0$,
$\sin^2 2\theta_{31} = 0.04$,
$\delta = 0$.
\item{Point 1B:}
Three-flavor oscillations, with $\delta m^2_{ATM}$ and
$\sin^2 2\theta_{ATM}$ corresponding to the central value favored
by the current SuperK data, $\delta m^2_{SUN}$ and
$\sin^2 2\theta_{SUN}$ corresponding to the SMA MSW solution.
Explicitly,
$\delta m_{32}^2 = 3.5 \times 10^{-3}$~eV$^2$/c$^4$,
$\delta m_{21}^2 = 6.0 \times 10^{-6}$~eV$^2$/c$^4$,
$\sin^2 2\theta_{12} = 0.006$,
$\sin^2 2\theta_{23} = 1.0$,
$\sin^2 2\theta_{31} = 0.04$,
$\delta = 0$.
\item{Point 1C:}
Three-flavor oscillations, with $\delta m^2_{ATM}$ and
$\sin^2 2\theta_{ATM}$ corresponding to the central value favored
by the current SuperK data, $\delta m^2_{SUN}$ and
$\sin^2 2\theta_{SUN}$ corresponding to the low mass
MSW solution.
Explicitly,
$\delta m_{32}^2 = 3.5 \times 10^{-3}$~eV$^2$/c$^4$,
$\delta m_{21}^2 = 1.0 \times 10^{-7}$~eV$^2$/c$^4$,
$\sin^2 2\theta_{12} = 0.9$,
$\sin^2 2\theta_{23} = 1.0$,
$\sin^2 2\theta_{31} = 0.04$,
$\delta = 0$.
\item{Point 2A:} Four-flavor oscillations with one sterile neutrino flavor.
Explicitly:
$\delta m_{34}^2 = 3.5 \times 10^{-3}$~eV$^2$/c$^4$,
$\delta m_{12}^2 = 5.0 \times 10^{-5}$~eV$^2$/c$^4$,
$\delta m_{13}^2 = 0.3$~eV$^2$/c$^4$,
$\sin^2 2\theta_{34} = 1.0$,
$\sin^2 2\theta_{12} = 0.8$,
$\sin^2 2\theta_{14} = \sin^2 2\theta_{13} = \sin^2 2\theta_{24} =
\sin^2 2\theta_{23} = 0.03$,
$\delta_1 = \delta_2 = \delta_3 = 0$.
\end{description}
\begin{figure}
\epsfxsize3.0in
\vspace{-2.0cm}
\centerline{\epsffile{fig1.ps}}
%\bigskip
\caption[]{The value of $\sin^2 2\theta_{13}$ that yields, in a 10~kt detector
(a) 10 events per $2 \times 10^{20} \mu^+$ decays (boxes), and
(b) a three standard deviation determination of the sign of $\delta m^2_{32}$
when the wrong-sign muon event rates for $2 \times 10^{20} \mu^+$ decays are
compared with the corresponding rates for $2 \times 10^{20} \mu^-$decays
(circles). The $\sin^2 2\theta_{13}$ sensitivity is shown versus $E_\mu$ and
$L$ (as labeled). The calculations assume values for $\delta m^2_{32}$,
$\delta m^2_{12}, s_{23}, s_{12}$, $\delta$ corresponding to parameter
point 1A (see text).
The shaded region is excluded by the existing data.}
\label{fig1}
\end{figure}
\begin{figure}
\epsfxsize3.0in
\vspace{-1.0cm}
\centerline{\epsffile{fig2.ps}}
%\bigskip
\caption[]{As figure 1, but for parameter
point 1C (see text).}
\label{fig2}
\end{figure}
\begin{figure}
\epsfxsize3.0in
\vspace{-1.0cm}
\centerline{\epsffile{fig3.ps}}
%\bigskip
\caption[]{As figure 1, but for parameter
point 1C (see text).}
\label{fig3}
\end{figure}
\subsection{Neutrino oscillations: wrong-sign muons}
The most important oscillation channels to be explored
at a neutrino factory seem to be $\nu_e \rightarrow \nu_\mu$
and $\overline{\nu}_e \rightarrow \overline{\nu}_\mu$. In
addition to providing a first observation of these transitions
and a measurement of the mixing angle $\theta_{13}$,
a comparison of the two oscillation modes would also enable
a measurement of matter effects, a determination of
whether $m_3 > m_2$ or $m_3 < m_2$, and provide knowledge of (limits on)
the CP--phase $\delta$. Armed with this information the consistency
of the oscillation scenario (three--flavor, four--flavor, ...)
could be checked.
The transitions $\nu_e \rightarrow \nu_\mu$
and $\overline{\nu}_e \rightarrow \overline{\nu}_\mu$ result
in CC interactions producing ``wrong--sign" muons. If positive (negative)
muons are stored in the neutrino factory, oscillated neutrinos undergoing
CC interactions produce negative (positive) muons in the detector at the
far site.
In the leading oscillation approximation, the oscillation probability
$P(\nu_e \rightarrow \nu_\mu)$ is proportional to $\sin^2 2\theta_{13}$
(see Eq.~1). The experimental sensitivity of the $\nu_e \rightarrow \nu_\mu$
measurements therefore decreases with decreasing $\sin^2 2\theta_{13}$.
For a given oscillation and neutrino factory scenario we can ask
(i) What value of $\sin^2 2\theta_{13}$ would yield 10 wrong--sign muon
events per year ?
(ii) What value of $\sin^2 2\theta_{13}$ would enable the sign of
$\delta m^2_{32}$ to be determined with a statistical precision of
3 standard deviations ?
The answers to these questions have recently been explored by
Barger et al.~\cite{paper2} for parameters that correspond to
the LMA MSW solar solution (parameter point 1A)
as a function of the energy of the stored muons
($E_\mu$), and for three baselines ($L = 732, 2800,$ and 7332~km).
The results from this study are shown in
Fig.~\ref{fig1}. The 10~event level ``reach" in $\sin^2 2\theta_{13}$--space
improves with increasing
$E_\mu$ and decreasing $L$. However, 732~km is too short to obtain significant
matter effects. Hence, to obtain reasonable sensitivity to the sign of
$\delta m^2_{32}$ longer baselines (for example $L = 2800$~km) are preferred.
As an example, choosing $E_\mu = 30$~GeV and $L = 2800$~km we find that
with $2 \times 10^{20}$ muon decays we would expect to observe $> 10$ wrong--sign
muon events in a 10~kt detector provided $\sin^2 2\theta_{13} > 0.0007$, and
make a $3\sigma$ determination of the sign of $\delta m^2_{32}$ provided
$\sin^2 2\theta_{13} > 0.005$. Extending the study to points 1B and 1C
in oscillation parameter space (Figs.~\ref{fig2} and \ref{fig3}), we
obtain similar sensitivities. These results are encouraging, but do not
yet take account of experimental backgrounds
or systematic effects. These possible experimental limitations are
under study~\cite{detector_group}. Finally, it has been noted~\cite{paper2}
that the measured $\nu_e \rightarrow \nu_\mu$
and $\overline{\nu}_e \rightarrow \overline{\nu}_\mu$
CC interaction energy distributions, as well as the rates,
are sensitive to the magnitude and sign of $\delta m^2_{32}$. Thus,
a fit to these distributions would be expected to enhance the sensitivity
to the oscillation parameters. This deserves further study.
\begin{figure}
\epsfxsize3.0in
\vspace{-1.0cm}
\centerline{\epsffile{fig4.ps}}
\vspace{-0.2cm}
\caption[]{Values of $\sin^2 2\theta_{13}$ that yield, as a function
of $|\delta m^2_{32}|$, 10 wrong--sign
muon events in a 50~kt detector with
$1 \times 10^{19} \mu^+$ decays in the beam forming section of a 20~GeV
neutrino factory with $L = 732$~km.
The calculations assume
$\delta m^2_{12}$, $\sin^2 2\theta_{23}$, and $\sin^2 2\theta_{13}$ as
listed. The four curves correspond to four thresholds for muon
detection (as labeled).
The shaded region is excluded by the existing data.}
\label{fig4}
\end{figure}
\begin{figure}
\epsfxsize3.0in
%\vspace{-1.0cm}
\centerline{\epsffile{fig5.ps}}
\vspace{-0.1cm}
\caption[]{As figure 4, but for baseline $L = 7332$~km.}
\label{fig5}
\end{figure}
\subsection{Other measurements}
The interest in neutrino factories is primarily motivated
by the need for high energy $\nu_e$ and $\overline{\nu}_e$ beams
to enable measurements of
$\nu_e \rightarrow \nu_\mu$,
$\overline{\nu}_e \rightarrow \overline{\nu}_\mu$ , and possibly
$\nu_e \rightarrow \nu_\tau$, and
$\overline{\nu}_e \rightarrow \overline{\nu}_\tau$ oscillations.
In addition to these fundamentally important measurements there
are a variety of other interesting physics topics that could be pursued
at a neutrino factory. These
``bread and butter" physics measurements include precision
oscillation measurements that exploit the
$\nu_\mu$ and $\overline{\nu}_\mu$ neutrino--beam components.
It has been shown~\cite{paper2} that
at a neutrino factory it may be possible to improve the statistical
precision of the measured values of $\delta m^2_{32}$ and $\sin^2 2\theta_{23}$
by an order of magnitude beyond the precision that will be
achieved by the next generation of long--baseline
experiments. Finally, the non--oscillation physics topics include
unique measurements of structure functions (including spin structure
functions), charm production, $D - \overline{D}$ mixing, B physics,
a more precise measurement of the weak mixing angle, and searches for exotic
processes (multiplicative lepton number violation, radiative neutrino decays,
...). The scope of this physics program is under study~\cite{non_osc}.
\section{An entry--level Neutrino Factory: a tentative proposal}
What is the minimum neutrino factory energy
and beam intensity required to provide a cutting--edge
oscillation physics program ?
To try to address this question, consider first a 20~GeV neutrino
factory pointing at a 50~kt detector with a baseline of 732~km.
We will assume that our goal is to make the first
observation of $\nu_e \rightarrow \nu_\mu$
oscillations and
the first (low precision) measurements of $\sin^2 2\theta_{13}$.
The signal event rate will depend on $\delta m^2_{32}$, which we must
allow to vary over the favored SuperK range.
Fig.~\ref{fig4} shows as a function of $\delta m^2_{32}$
the value of $\sin^2 2\theta_{13}$ that would yield 10 wrong--sign
muon events if $10^{19}$ muons decay in the beam--forming section
of the neutrino factory. The expected event rates depend upon the
threshold energy for detecting the wrong--sign muon, and the figure
therefore shows the variation of the $\sin^2 2\theta_{13}$ ``reach"
with the threshold energy $E_{min}$. We note that if the value of
$\delta m^2_{32}$ is in the upper half of the favored SuperK parameter
space, then a 20~GeV neutrino factory delivering $10^{19}$ muons decays
per year would enable us to achieve out goals provided
$\sin^2 2\theta_{13}$ was not less than about an order of magnitude below
the currently excluded region. We expect to know soon from the K2K
measurements whether the upper half of the $\delta m^2_{32}$ region is
favored. If this is the case, then a 20~GeV factory with $10^{19}$ decays
per year and $L = 732$~km would seem a candidate entry--level scenario.
Let us now consider other candidate entry--level scenarios.
Can we reduce the neutrino factory energy further ?
Note that the sensitivities shown in Fig~\ref{fig4} vary with $E_{min}$
by about a factor of 2 over the range of $E_{min}$ considered.
It will be important to try to minimize $E_{min}$
to obtain good sensitivity and minimize the bias a high threshold
introduces into measured energy distributions. At present $E_{min}$ values
of 3--4~GeV are being considered as plausible. If $E_{min}$ cannot be
further reduced in a realistic very massive detector then it would seem
unwise to reduce the neutrino factory energy significantly below
20~GeV. Hence we adopt 20~GeV for our entry--level scenario.
Next consider changing the baseline. The signal event rate increases
with decreasing $L$. However, at $L = 732$~km our entry--level scenario
yields a total CC rate of O($10^5$) events per year in our 50~kt detector.
Hence we require the backgrounds to be at or below the 1 event per
$10^5$ CC events level. It is believed that backgrounds are likely to be
close to this level (or perhaps a little higher). Hence we would not want
to decrease $L$, and may in fact want to go to a larger $L$ to further
reduce the background rate. How about a longer baseline ?
Figure~\ref{fig5} shows as a function of $\delta m^2_{32}$
the value of $\sin^2 2\theta_{13}$ that would yield 10 wrong--sign
muon events if $L = 7332$~km. The $\sin^2 2\theta_{13}$ reach has
been reduced by only a factor of 2 -- 3. On the other hand the total
event rate (and hence backgrounds) are reduced by a factor of O(100) !
In addition, should a first observation of wrong--sign muon events
be made, higher statistics measurements (an intensity upgrade) would
then enable matter effects to be measured and the sign of
$\delta m^2_{32}$ determined. Hence the very--long baseline entry--level
scenario has some advantages.
Let us assume there are no sterile neutrinos.
We are now ready to propose a candidate entry--level scenario, which
we take to be a 20~GeV storage ring with the product of the
number of muon decays per year and the detector mass being
$5 \times 10^{20}$~kt. A fairly long baseline is desirable ($L \geq 2000$~km)
to minimize background rates and enable the eventual measurement of matter effects.
It should be noted that if the MiniBooNE experiment confirms the LSND oscillation
results and we will need to rethink our entry--level scenario to address the exciting
prospect of a relatively large leading $\delta m^2$ and the possibility of one or more
sterile neutrino--types participating in the oscillations.
\section{Summary}
Given the recent SuperK results, neutrino factories have understandably
caught the attention of the high energy physics community, and its
laboratory directors. A Fermilab directorate initiated study of the
physics potential of neutrino factories is in progress. This study is expected
to deepen our understanding of the desired neutrino factory parameters.
I believe that the real question to be addressed now is not
so much ``What physics can be done with
a {\it Cadillac} neutrino factory ?" but rather ``What is the
entry--level neutrino factory scenario that would enable this new type of
physics facility to be developed and built in principle on a relatively
short time-scale ?"
What do we need to get the show on the road and start climbing the
learning curve ?
%\begin{table}[t]
%\caption{Experimental Data bearing on
%$\Gamma(K \rightarrow \pi \pi \gamma)$
%for the $K^0_S$, $K^0_L$ and $K^-$ mesons.\label{tab:exp}}
%\vspace{0.2cm}
%\begin{center}
%\footnotesize
%\begin{tabular}{|c|c|c|l|}
%\hline
%{} &\raisebox{0pt}[13pt][7pt]{$\Gamma(\pi^- \pi^0)\; s^{-1}$} &
%\raisebox{0pt}[13pt][7pt]{$\Gamma(\pi^-\pi^0\gamma)\; s^{-1}$} &{}\\
%\hline
%\multicolumn{2}{|c|}{\raisebox{0pt}[12pt][6pt]{Process
%for Decay}} & &\\
%\cline{1-2}
%$K^-$ &$1.711 \times 10^7$
%&\begin{minipage}{1in}
%\begin{center}
%$2.22 \times 10^4$ \\ (DE $ 1.46 \times 10^3)$
%\end{center}
%\end{minipage}
%&\begin{minipage}{1.5in}
%\phantom{xxx}
%No (IB)-E1 interference seen but data shows excess events
%relative to IB over
%$E^{\ast}_{\gamma} = 80$ to $100$~MeV
%\end{minipage} \\[22pt]
%\hline
%\end{tabular}
%\end{center}
%\end{table}
%{\em $\backslash$section$\ast$\{Acknowledgments\}}.
\section*{References}
\begin{thebibliography}{99}
\bibitem{members}
People actively participating in the working groups, at the
time of writing, are:
C. Albright,
G. Anderson,
V. Barger,
R. Bernstein,
R. Cahn,
M. Campanelli,
C. Crisan,
P. Cushman,
F. DeJongh,
J. Formaggio,
G. Garvey,
S. Geer (organizer),
D. Harris,
E. Hawker,
J. Krane,
Z. Ligeti,
J. Lykken,
K. McFarland,
G. Mills,
I. Mocioiu,
J. Morfin,
H. Murayama,
D. Naples,
S. Parke,
R. Plunkett,
E. Prebys,
R. Raja,
A. Rubbia,
H. Schellman (organizer),
P. Spentzouris,
M. Shaevitz,
R. Shrock,
R. Stefanski,
C. Quigg,
M. Velasco,
G. Unel,
K. Whisnant,
J. Yu.
\bibitem{koshkarev}
D.G.~Koshkarev, Preprint ITEP-33, 1974 and
``Proposal for a decay ring to produce
intense secondary particle beams st the SPS", CERN/ISR-DI/74-62.
\bibitem{wojcicki}
S. Wojcicki, unpublished (1974).
\bibitem{collins}
T. Collins, unpublished (1975).
\bibitem{cline}
D. Cline and D. Neuffer,
AIP Conf. Proc.. 68, 846 (1980).
\bibitem{p860}
W. Lee (spokesperson) et al., FNAL Proposal P860, ``A Search for
neutrino oscillations using the Fermilab Debuncher", 1992.
\bibitem{kolomensky}
A.A. Kolomensky, Sov. Atomic
Energy Vol. 19, 1511 (1965).
\bibitem{melc}
R.M. Djilkibaev and V.M. Lobashev,
Sov. J. Nucl. Phys. {\bf 49(2)}, 384 (1989).
\bibitem{status_report}
C. Ankenbrandt et al. (Muon Collider Collaboration),
Phys. Rev. ST Accel. Beams 2, 081001 (1999).
\bibitem{geer}
S. Geer, ``Neutrino beams from muon storage rings: characteristics
and physics potential", FERMILAB-PUB-97-389, 1997; Presented in
the Workshop on Physics at the First Muon Collider and Front-End
of a Muon Collider (Editors: S.~Geer and R.~Raja),
November, 1997, and Published in
S.~Geer, Phys.Rev.D57:6989-6997,1998.
\bibitem{cern}
J. Ellis, E. Keil, G. Rolandi,
``Options for future colliders at CERN",
CERN--SL/98-004 (1998).,
B. Autin, A. Blondel, J. Ellis (editors),
``Prospective study of muon storage rings at CERN",
CERN 99-02, April (1999).,
D. Finley, S. Geer, J. Sims,
``Muon Colliders: A vision for the future of Fermilab",
FERMILAB-TM-2072, Jun 1999.,
S.-C.~Ahn et al.,
``Muon Colliders: A Scenario for the evolution of the Fermilab",
FERMILAB-FN-677, Aug 1999.
\bibitem{tech}
Neutrino factory technical study co--ordinator: N.~Holtkamp.
See
http://www.fnal.gov/projects/muon$_-$collider/nu-factory/nu-factory.html
\bibitem{physics}
Neutrino factory physics study co--ordinators: S.~Geer and H.~Schellman.
See
http://www.fnal.gov/projects/muon$_-$collider/nu/study/study.html
\bibitem{many_papers}
A. De Rujula, M.B. Gavela, and P. Hernandez, Nucl. Phys. {\bf B547}, 21 (1999).,
M. Tanimoto, Phys.Lett. B462, 115 (1999).,
C. Giunti, Phys.Lett. B467, 83 (1999).,
A. Kalliomaki, J. Maalampi, M. Tanimoto, Phys.Lett. B469, 179 (1999).,
A. Bueno, M. Campanelli, A. Rubbia, hep-ph/9809252, hep-ph/9808485.,
M. Campanelli, A. Bueno, and A. Rubbia, hep-ph/9905240.,
S. Dutta, R. Gandhi, B. Mukhopadhyaya, hep-ph/9905475.,
V. Barger, S. Geer, and K. Whisnant, hep-ph/9906487.,
D. Dooling et al., hep-ph/9908513.,
A. Romanino, hep-ph/9909425.,
O. Yasuda, hep-ph/9909469.,
J. Sato, hep-ph/9910442.,
A. Donini, M.B. Gavela, P. Hernandez, S. Rigolin, hep-ph/9910516.,
I. Mocioiu, R. Shrock, hep-ph/9910554.,
M. Freund, M. Lindner, S.T. Petcov, hep-ph/9912457.
\bibitem{theory_group}
Members of the sub--group defining the points in oscillation parameter
space are:
S. Parke (convener), C. Albright,
G. Anderson,
V. Barger,
R. Cahn,
Z. Ligeti,
J. Lykken,
I. Mocioiu,
H. Murayama,
C. Quigg,
R. Shrock,
K. Whisnant.
\bibitem{paper2}
V. Barger, S. Geer, R. Raja, K. Whisnant,
``Long--baseline study of the leading neutrino oscillation
at a neutrino factory", hep-ph/9911524, November 1999.
\bibitem{detector_group}
Members of the sub--group studying oscillation
measurements and detector effects are:
D. Harris (convener),
R. Bernstein (convener),
C. Albright,
M. Campanelli,
S. Geer,
K. McFarland,
G. Mills,
D. Naples,
S. Parke,
R. Plunkett,
E. Prebys,
R. Raja,
A. Rubbia,
P. Spentzouris,
R. Stefanski,
M. Velasco,
G. Unel.
\bibitem{non_osc}
Members of the sub--group studying non--oscillation
measurements:
E. Hawker (convener),
P. Cushman,
F. DeJongh,
J. Formaggio,
D. Harris,
G. Garvey,
J. Krane,
K. McFarland,
J. Morfin,
S. Parke,
H. Schellman,
R. Shrock,
R. Stefanski,
M. Velasco,
G. Unel,
J. Yu.
\end{thebibliography}
\end{document}
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