%% introduction.tex, Mike's new version, received Jan.9 \section{Introduction\label{intro}} Recent results from the SNO collaboration~\cite{snolatest} coupled with data from the SuperK collaboration~\cite{superk} have provided convincing evidence that neutrinos oscillate and that they very likely do so among the three known neutrino species. Experiments currently under way or planned in the near future will shed further light on the nature of these mixings among neutrino species and the magnitudes of the mass differences between them. Neutrino oscillations and the implied non-zero masses and mixings represent the first experimental evidence of effects beyond the Standard Model, and as such are worthy of vigorous scientific study. This document indicates our progress along a path toward establishing an ongoing program of research in accelerator and experimental physics based on muon beams, and neutrino beams derived therefrom, that can proceed in an incremental fashion. At each step, new physics vistas open, leading eventually to a Neutrino Factory and possibly a Muon Collider. This concept has aroused significant interest throughout the world scientific community. In the U.S., a formal collaboration of some 110 scientists, the Neutrino Factory and Muon Collider Collaboration, also known as the Muon Collaboration (MC)~\cite{EPP:collaboration}, has undertaken the study of designing a Neutrino Factory, along with R\&D activities in support of a Muon Collider design. The MC comprises three sponsoring national laboratories (BNL, FNAL, LBNL) along with groups from other U.S. national laboratories and universities and individual members from non-U.S. institutions. One of the first steps toward a Neutrino Factory is a proton driver that can be used to provide intense beams of conventional neutrinos in addition to providing the intense source of low energy muons (from pion decay) that must first be ``cooled'' before being accelerated and stored. Our vision is that while a proton driver is being constructed, R\&D on collecting and cooling muons would continue. A source of intense cold muons could be immediately used for physics measurements, such as determining the electric and magnetic dipole moments of the muon to higher precision, muonium-antimuonium oscillations, muon spin rotation experiments and rare muon decays. Once the capability of cooling and accelerating muons is fully developed, a storage ring for such muons would serve as the first Neutrino Factory. Its specific beam energy and its distance from the long-baseline experiment will be chosen using the knowledge of neutrino oscillation parameters gleaned from the present generation of solar and accelerator experiments (Homestake, Kamiokande, SuperKamiokande, SAGE, GALLEX, K2K, SNO), the next generation experiments (MiniBooNE, MINOS, CNGS, KamLAND, Borexino), and the high-intensity conventional beam experiments that would already have taken place. A Neutrino Factory provides both $\nu _{\mu }$ and $\anti\nu _{e}$ beams of equal intensity from a stored $\mu ^{-}$ beam, and their charge-conjugate beams for a stored $\mu ^{+}$ beam. Beams from a Neutrino Factory are intense compared with today's neutrino sources. In addition, they have smaller divergence than conventional neutrino beams of comparable energy. These properties permit the study of non-oscillation physics at near detectors, and the measurement of structure functions and associated parameters in non-oscillation physics, to unprecedented accuracy. Likewise, they permit long-baseline experiments that can determine oscillation parameters to unprecedented accuracy. Depending on the value of the parameter $\sin ^{2}2\theta _{13}$ in the three-neutrino oscillation formalism, the oscillation $\nu _{e}\rightarrow \nu _{\mu }$ is expected to be measurable. By comparing the rates for this channel with its charge-conjugate channel $\anti\nu _{e}\rightarrow \anti\nu _{\mu }$, the sign of the leading mass difference in neutrinos, $\delta m_{32}^{2}$, can be determined by observing the passage through matter of the neutrinos in a long-baseline experiment. Such experiments can also shed light on the CP-violating phase, $\delta $, in the lepton mixing matrix and enable the study of CP violation in the lepton sector. (It is known that CP violation in the quark sector is insufficient to explain the baryon asymmetry of the Universe; lepton sector CP violation possibly played a crucial role in creating this asymmetry during the initial phases of the Big Bang.) While the Neutrino Factory is being constructed, R\&D aimed at making the Muon Collider a reality would be performed. A Muon Collider, if realized, provides a tool to explore Higgs-like objects by direct $s$-channel fusion, much as LEP explored the $Z$. It also provides a potential means to reach higher energies (3--4~TeV in the center of mass) using relatively compact collider rings. \subsection{History} The concept of a Muon Collider was first proposed by Budker~\cite {PREFACE:budker} and by Skrinsky~\cite{PREFACE:skrinsky} in the 60s and early 70s. However, additional substance to the concept had to wait until the idea of ionization cooling was developed by Skrinsky and Parkhomchuk~\cite {INTRO:ref3}. The ionization cooling approach was expanded by Neuffer~\cite {INTRO:ref4} and then by Palmer~\cite{PREFACE:palmer}, whose work led to the formation of the Neutrino Factory and Muon Collider Collaboration (MC)~\cite {EPP:collaboration} in 1995\footnote{ A good summary of the Muon Collider concept can be found in the Status Report of 1999~\cite{INTRO:ref5}; an earlier document~\cite{INTRO:ref6}, prepared for Snowmass-1996, is also useful reading. MC Notes prepared by the Collaboration are available on the web~\cite{INTRO:ref11}}. The concept of a neutrino source based on a pion storage ring was originally considered by Koshkarev~\cite{INTRO:ref7}. However, the intensity of the muons created within the ring from pion decay was too low to provide a useful neutrino source. The Muon Collider concept provided a way to produce a very intense muon source. The physics potential of neutrino beams produced by high-intensity muon storage rings was briefly investigated in 1994 by King~\cite{king94}and in more detail by Geer in 1997 at a Fermilab workshop~\cite{rajageer,geer} where it became evident that the neutrino beams produced by muon storage rings needed for the Muon Collider were exciting in their own right. As a result, the MC realized that a Neutrino Factory could be an important first step toward a Muon Collider. With this in mind, the MC has shifted its primary emphasis toward the issues relevant to a Neutrino Factory. The Neutrino Factory concept quickly captured the imagination of the particle physics community, driven in large part by the exciting atmospheric neutrino deficit results from the SuperKamiokande experiment. The utility of non-oscillation neutrino physics from neutrinos produced by muon storage rings has been studied in detail from 1997 onwards~\cite{non-osc}. There is also considerable international activity on Neutrino Factories, with international conferences held at Lyon in 1999~\cite{INTRO:ref13}, Monterey in 2000~\cite{INTRO:ref14}, Tsukuba in 2001~\cite{nufact01}, London in 2002~\cite{nufact02} and another planned in New York in 2003~\cite{nufact03}. There are also efforts in Europe~\cite{europenf} and Japan~\cite{japannf} to study different approaches to realizing the neutrino factory. Recently a proposal has been submitted to perform an International Muon Ionization Cooling Experiment (MICE) to the Rutherford Appleton Laboratories~\cite{mice-prop}. \subsection{Feasibility Studies} Complementing the MC experimental and theoretical R\&D program, which includes work on targetry, cooling, rf hardware (both normal conducting and superconducting), high-field solenoids, liquid hydrogen absorber design, muon scattering experiments, theory, simulations, parameter studies, and emittance exchange~\cite{INTRO:ref12}, the Collaboration has participated in several paper studies of a complete Neutrino Factory design. In the fall of 1999, Fermilab, with help from the MC, undertook a Feasibility Study (``Study-I'') of an entry-level Neutrino Factory~\cite {INTRO:ref1}. Study-I showed that the evolution of the Fermilab accelerator complex into a Neutrino Factory was clearly possible. The performance reached in Study-I, characterized in terms of the number of 50-GeV muon decays aimed at a detector located 3000 km away from the muon storage ring, was $N$ = 2 $\times $ 10$^{19}$ decays per ``Snowmass year'' (10$^{7}$ s) per MW of protons on target. Simultaneously, Fermilab launched a study of the physics that might be addressed by such a facility~\cite{INTRO:ref9} and, more recently, initiated a study to compare the physics reach of a Neutrino Factory with that of conventional neutrino beams~\cite{superbeams} powered by a high-intensity proton driver (referred to as ``superbeams''). As will be described later in this paper, a steady and diverse physics program will result from following the evolutionary path from a superbeam to a full-fledged Neutrino Factory. Subsequently, BNL organized a follow-on study (``Study-II'')~\cite{EPP:studyii} on a high-performance Neutrino Factory, again in collaboration with the MC. Study-II demonstrated that BNL was likewise a suitable site for a Neutrino Factory. Based on the improvements in Study-II, the number of 20-GeV muon decays aimed at a detector located 3000 km away from the muon storage ring, was $N$ = 1.2 $\times $ 10$^{20}$ decays per Snowmass year per MW of protons on target. Thus, with an upgraded 4 MW proton driver, the muon decay intensity would increase to 4.8 $\times $ $10^{20}$ decays per Snowmass year. (R\&D to develop a target capable of handling this beam power would be needed.) Though these numbers of neutrinos are potentially available for experiments, in the current storage-ring design the angular divergence at both ends of the production straight section is higher than desirable for the physics program. In any case, we anticipate that storage-ring designs are feasible that would allow 30--40\% of the muon decays to provide useful neutrinos. Both Study-I and -II are site specific in that each has a few site-dependent aspects; otherwise, they are generic. In particular, Study-I assumed a new Fermilab booster to achieve its beam intensities and an underground storage ring. Study-II assumed BNL site-specific proton driver specifications corresponding to an upgrade of the 24-GeV AGS complex and a BNL-specific layout of the storage ring, which is housed in an above-ground berm to avoid penetrating the local water table. The primary substantive difference between the two studies is that Study-II aimed at a lower muon energy (20 GeV), but higher intensity (for physics reach) than Study-I. Taking the two Feasibility Studies together, we conclude that a high-performance Neutrino Factory could easily be sited at either BNL or Fermilab. Figure \ref {studycomp} shows a comparison of the performance of the Neutrino Factory designs in Study-I and Study-II~\cite{INTRO:ref9} with the physics requirements. \begin{figure}[tbh] \centerline{\includegraphics[width=4.0in]{studyIvsII.eps}} \caption[Muon decays in a straight section \textit{vs.} muon energy]{ Muon decays in a straight section per $10^{7}\,$s \textit{vs.} muon energy, with fluxes required for different physics searches assuming a 50~kT detector. Simulated performance of the two studies is indicated.} \label{studycomp} \end{figure} To put the above performance figures in context, it is important to note that a $\mu ^{+}$ storage ring with an average neutrino energy of 15~GeV and $2\times 10^{20}$ useful muon decays would yield (in the absence of oscillations) $\approx $30,000 charged-current events in the $\nu _{e}$ channel per kiloton-year in a detector located 732~km away. In comparison, a 1.6~MW superbeam~\cite{superbeams} from the Fermilab Main Injector with an average neutrino energy of 15~GeV would yield only $\approx $13,000 $\nu_\mu$ charged-current events per kiloton-year. In addition to having lower intensity than a Neutrino Factory beam, a superbeam would have significant $\nu_e$ contamination, which will be the major background in $\nu_\mu\rightarrow \nu_e$ appearance searches. That is, it will be much easier to detect the oscillation $\nu_e\rightarrow \nu_\mu$ from a muon storage ring neutrino beam than to detect the oscillation $\nu_\mu \rightarrow \nu_e$ from a conventional neutrino beam, because the electron final state from the conventional beam has significant background contribution from $\pi^{0}$'s produced in the events. \subsection{Neutrino Factory Description\label{NFsection}} The muons we use result from decays of pions produced when an intense proton beam bombards a high-power production target. The target and downstream transport channel are surrounded by superconducting solenoids to contain the pions and muons, which are produced with a larger spread of transverse and longitudinal momenta than can be conveniently transported through an acceleration system. To prepare a beam suitable for subsequent acceleration, we first perform a ``phase rotation,'' during which the initial large energy spread and small time spread are interchanged using induction linacs. Next, to reduce the transverse momentum spread, the resulting long bunch, with an average momentum of about 250 MeV/c, is bunched into a 201.25-MHz bunch train and sent through an ionization cooling channel consisting of LH$_{2}$ energy absorbers interspersed with rf cavities to replenish the energy lost in the absorbers. The resulting beam is then accelerated to its final energy using a superconducting linac to make the beam relativistic, followed by one or more recirculating linear accelerators (RLAs). Finally, the muons are stored in a racetrack-shaped ring with one long straight section aimed at a detector located at a distance of roughly 3000 km. A schematic layout is shown in Fig.~\ref{nufact-scheme-bnl}. \begin{figure}[tbh] \centerline{\includegraphics[width=4.0in,angle=-90]{nufact_scheme_bnl.ps}} \caption[Schematic of the Neutrino Factory Study-II version]{Schematic of the Neutrino Factory Study-II version.} \label{nufact-scheme-bnl} \end{figure} \subsection{Detector} Specifications for the long-baseline Neutrino Factory detector are rather typical for an accelerator-based neutrino experiment. However, because of the need to maintain a high neutrino rate at these long distances ($\approx $% 3000 km), the detectors considered here are 3--10 times more massive than those in current neutrino experiments. Several detector options could be considered for the far detector: \begin{itemize} \item A 50 kton steel--scintillator--proportional-drift-tube (PDT) detector \item A large water-Cherenkov detector, similar to SuperKamiokande but with either a magnetized water volume or toroids separating smaller water tanks~\cite{DET:uno}. \item A massive liquid-argon magnetized detector~\cite{landd}. \end{itemize} For the near detector, a compact liquid-argon TPC (similar to the ICARUS detector~\cite{ICARUS}) could be used. An experiment with a relatively thin Pb target (1~$L_{rad}$), followed by a standard fixed-target spectrometer could also be considered. \subsection{Staging Scenario} If desired by the particle physics community, a fast-track plan leading directly to a Neutrino Factory could be executed. On the other hand, the Neutrino Factory offers the distinct advantage that it can be built in stages. This could satisfy both programmatic and cost constraints by allowing an ongoing physics program while reducing the annual construction funding needs. Depending on the results of our technical studies and the results of ongoing searches for the Higgs boson, it is hoped that the Neutrino Factory is really the penultimate stage, to be followed later by a Muon Collider (e.g., a Higgs Factory). Such a collider offers the potential of bringing the energy frontier in particle physics within reach of a moderate-sized machine. Possible stages for the evolution of a muon beam facility are described in Section~\ref{StagingOps}. \subsection{R\&D Program\label{RDprog}} Successful construction of a muon storage ring to provide a copious source of neutrinos requires development of many novel approaches; construction of a high-luminosity Muon Collider requires even more. It was clear from the outset that the breadth of R\&D issues to be dealt with would be beyond the resources available at any single national laboratory or university. For this reason, in 1995, interested members of the high-energy physics and accelerator physics communities formed the MC to coordinate the required R\&D efforts nationally. The task of the MC is to define and carry out R\&D needed to assess the technical feasibility of constructing initially a muon storage ring that will provide intense neutrino beams aimed at detectors located many thousands of kilometers from the accelerator site, and ultimately a $\mu ^{+}\mu ^{-}$ collider that will carry out fundamental experiments at the energy frontier in high-energy physics. The MC also serves to coordinate muon-related R\&D activities of the NSF-sponsored University Consortium (UC) and the state-sponsored Illinois Consortium for Accelerator Research (ICAR), and is the focal point for defining the needs of muon-related R\&D to the managements of the sponsoring national laboratories and to the funding agencies (both DOE and NSF). As already noted, though the MC was formed initially to carry out R\&D that might lead eventually to the construction of a Muon Collider, more recently its focus has shifted mainly, but not exclusively, to a Neutrino Factory. The MC maintains close contact with parallel R\&D efforts under way in Europe (centered at CERN) and in Japan (centered at KEK). Through its international members, the MC also fosters coordination of the international muon-beam R\&D effort. Two major initiatives, a Targetry Experiment (E951) in operation at BNL and a Muon Cooling R\&D program (MUCOOL), have been launched by the MC. In addition, the Collaboration, working in conjunction with the UC and ICAR in some areas, coordinates substantial efforts in accelerator physics and component R\&D to define and assess parameters for feasible designs of muon-beam facilities. \subsection{Outline of Report} In what follows, we give the motivation and a scenario for a staged approach to constructing a Neutrino Factory and eventually a Muon Collider. Section~\ref{physics} discusses the physics opportunities, starting from conventional ``superbeams'' and going to cold muon beams, then a Neutrino Factory with its near and far detectors, and finally a Muon Collider. In Section~\ref{neufact}, we describe the components of a Neutrino Factory, based on the Study-II design, and indicate a scientifically productive staged path for reaching it. Section~\ref{higgsfact} covers our present concept of an entry-level Higgs Factory Muon Collider. In support of the construction of a Neutrino Factory, an R\&D program is already under way to address various technical issues. A description of the status and plans for this program is presented in Section~\ref{r_and_d}. Section~\ref{mice} describes current thinking about a cooling demonstration experiment that would be carried out as an international effort. Finally, in Section~\ref{Summary} we provide a brief summary of our work.