%\documentstyle[12pt,epsf,epsfig,rotating]{article} \documentstyle[12pt,epsf,epsfig]{article} %\documentstyle[aps,epsf,epsfig,preprint,tighten,rotating]{revtex} %\documentstyle[aps,preprint,epsf,tighten]{revtex} \special{header=Draft.ps} \parskip= 4pt plus 1pt \textwidth=5.65in \textheight=23.0cm \oddsidemargin=0.4in \evensidemargin=0.4in \headsep=0.1mm \topmargin=0.001in \input hep_macro %\input epsf \newcommand{\centii}{\hbox{\rm cm$^2$}} %%% Chris Quigg %\usepackage{hyperref} %\newcommand{\hepex}[1]{(hep-ex/#1)} \newcommand{\hepex}[1]{\mbox{\href{http://xxx.lanl.gov/abs/hep-ex/#1}{(hep-ex/ #1)}}} %\newcommand{\hepph}[1]{(hep-ph/#1)} \newcommand{\hepph}[1]{\mbox{\href{http://xxx.lanl.gov/abs/hep-ph/#1}{(hep-ph/ #1)}}} %\newcommand{\hepth}[1]{(hep-th/#1)} \newcommand{\hepth}[1]{\mbox{\href{http://xxx.lanl.gov/abs/hep-th/#1}{(hep-th/ #1)}}} %\newcommand{\heplat}[1]{(hep-lat/#1)} \newcommand{\heplat}[1]{\mbox{\href{http://xxx.lanl.gov/abs/hep-lat/#1}{(hep- lat/#1)}}} %\newcommand{\astro}[1]{(astro-ph/#1)} \newcommand{\astroph}[1]{\mbox{\href{http://xxx.lanl.gov/abs/astro-ph/ #1}{(astro-ph/#1)}}} \def\url#1{\mbox{\href{#1}{\sf #1}}} \def\urll#1#2{\mbox{\href{#1}{\sf #2}}} \def\urlp#1#2{\mbox{\href{#1}{#2}}} \def\ltap{\mathop{\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$<$}}} \def\gtap{\mathop{\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$>$}}} \newcommand{\CP}{\textsf{CP}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % \def\hepph#1{(hep-ph/#1)} % % \def\hepex#1{(hep-ex/#1)} % % \def\astroph#1{(astro-ph/#1)} % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\pr#1#2#3{\frenchspacing{\it Phys. 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Phys. }{\bf #1}, #2 (19#3)} %%%%%%%%%%%%%%%%%%String definitions%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\xw}{\ensuremath{\sin^2\theta_W}} \newcommand{\ev}{\ensuremath{\hbox{ eV}}} \newcommand{\evcc}{\ensuremath{\hbox{ eV}\!/\!c^2}} \newcommand{\mevcc}{\ensuremath{\hbox{ MeV}\!/\!c^2}} \newcommand{\mev}{\ensuremath{\hbox{ MeV}}} \newcommand{\gevcc}{\ensuremath{\hbox{ GeV}\!/\!c^2}} \newcommand{\gev}{\ensuremath{\hbox{ GeV}}} %\newcommand{\cm}{\ensuremath{\hbox{ cm}}} %\newcommand{\etal}{et al.} \def\ltap{\mathop{\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$<$}}} \def\gtap{\mathop{\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$>$}}} \newcommand{\km}{\hbox{ km}} \newcommand{\m}{\hbox{ m}} %%% Steve Parke \def\Bra#1{\left\langle #1\right|} \def\Ket#1{\left| #1\right\rangle} \def\bra#1{\langle #1|} \def\ket#1{| #1\rangle} \def\aprle{\buildrel < \over {_{\sim}}} \def\aprge{\buildrel > \over {_{\sim}}} \newcommand{\gtwid}{\mathrel{\raise.3ex\hbox{$>$\kern-.75em\lower1ex \hbox{$\sim$}}}} \newcommand{\ltwid}{\mathrel{\raise.3ex\hbox{$<$\kern-.75em\lower1ex \hbox{$\sim$}}}} \def\beq{\begin{equation}} \def\eeq{\end{equation}} \begin{document} \begin{flushright} {\bf FERMILAB-FN-692}\\ \today \end{flushright} \vspace{1.0cm} \begin{center} \huge {\bf Physics at a Neutrino Factory} \vspace{1.0cm} \large DRAFT 3 \vspace{1.0cm} \input authors \end{center} \normalsize \newpage \input report_0 \clearpage \section*{Executive Summary} 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 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 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 compelling new information to our understanding of neutrino oscillations, provided that the number of useful muon decays exceeds $10^{19}$ per year and the muon energy is at least $20\hbox{ GeV}$. 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 $\nu_\mu \rightarrow \nu_\tau$; 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. The physics program at detectors located close to the neutrino factory is also very interesting. 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. The spin and flavor structure of the weak interactions allow unique studies of nucleon structure and of the electro-weak couplings themselves. \subsection*{Recommendations} The physics program we have explored for a neutrino factory is highly promising. We recommend a sustained effort to study both the physics opportunities and the machine realities. \begin{description} \item{(i)} We encourage support for the R\&D needed to learn whether a neutrino factory can be a real option in the next decade. \item{(ii)} We propose continued studies of oscillation physics to better understand how to build very massive detectors for long--baseline neutrino oscillation physics at a neutrino factory. These studies should identify the detector R\&D that is required to realize detectors with masses of a few times 10~kt or more that are able to detect and measure wrong--sign muons, and detectors of a few kt or more able to observe tau--lepton appearance with high efficiency. It is also desirable to identify and measure the charge of electrons. Because of the size of such detectors both the detector technologies themselves and the civil engineering issues of building such massive detectors need to be addressed. \item{(iii)} We have not completed the optimization of physics performance in terms of baseline. More work is also needed to understand the benefits of polarization. These are appropriate topics for a continuing study. \item{(iv)} This study concentrated on the muon storage ring as a neutrino source and did not cover the additional physics programs which would use the proton driver and the high intensity muon beams. A further study directed at these other facets of physics at a muon storage ring facility would be very useful. \end{description} \clearpage \tableofcontents \clearpage \input report_1 \input report_2_v3 \input report_3a \input report_3b \input report_3c_v3 \input report_4_v3 \section{Summary and Recommendations} The main goal of the physics study presented in this report has been to answer the question: Is the physics program at a neutrino factory compelling ? The answer is a resounding yes, provided there are $10^{19}$ or more muon decays per year in the beam forming straight section and the muon beam energy is $\sim20$~GeV or greater. Based on our study, we believe that a neutrino factory in the next decade would be the right tool at the right time. \subsection*{The neutrino oscillation physics program} The recent impressive atmospheric neutrino results from the Super-Kamiokande experiment have gone a long way towards establishing the existence of neutrino oscillations. This is arguably the most dramatic recent development in particle physics. Up to the present era, neutrino oscillation experiments at accelerators were searches for a phenomenon that might or might not be within experimental reach. The situation now is quite different. The atmospheric neutrino deficit defines the $\delta m^2$ and oscillation amplitude to which future long baseline oscillation experiments must be sensitive to, namely $\delta m^2 = $~O($10^{-3}$)~eV$^2$ and $\sin^2 2\theta =$~O(1). Experiments that achieve these sensitivities are guaranteed an excellent physics program that addresses fundamental physics questions. Furthermore, should $all$ of the experimental indications for oscillations (LSND, atmospheric, and solar) be confirmed, we may be seeing evidence for the existence of sterile neutrinos. This would be a very exciting discovery which would raise many new questions requiring new experimental input. A neutrino factory would be a $unique$ $facility$ for oscillation physics, providing beams containing high energy electron neutrinos (antineutrinos) as well as muon antineutrinos (neutrinos). These beams could be exploited to provide answers to the questions that we are likely to be asking after the next generation of accelerator based experiments. The oscillation physics that could be pursued at a neutrino factory is compelling. Experiments at a neutrino factory would be able to simultaneously measure, or put stringent limits on, all of the appearance modes $\nu_e \rightarrow \nu_\tau$, $\nu_e \rightarrow \nu_\mu$, and $\nu_\mu \rightarrow \nu_\tau$. Comparing the sum of the appearance modes with the disappearance measurements would provide a unique basic check of candidate oscillation scenarios that cannot be made with a conventional neutrino beam. In addition, for all of the specific oscillation scenarios we have studied, the $\nu_e$ component in the beam can be exploited to enable crucial issues to be addressed. These include: \begin{description} \item{(i)} A precise determination of (or stringent limits on) all of the leading oscillation parameters, which in a three--flavor mixing scenario would be $\sin^22\theta_{13}$, $\sin^22\theta_{23}$, and $\delta m^2_{32}$. \item{(ii)} A determination of the pattern of neutrino masses. \item{(iii)} A quantitative test of the MSW effect. \item{(iv)} Stringent limits on, or the observation of, CP violation in the lepton sector. \end{description} To be more quantitative in assessing the beam energy, intensity, and baseline required to accomplish a given set of physics goals it is necessary to consider two very different experimental possibilities: (a) the LSND oscillation results are not confirmed, or (b) the LSND results are confirmed. \begin{description} \item{(a) LSND not confirmed.} A 20~GeV neutrino factory providing $10^{19}$ muon decays per year is a good candidate ``entry--level" facility which would enable either (i) the first observation of $\nu_e \rightarrow \nu_\mu$ oscillations, the first direct measurement of matter effects, and a determination of the sign of $\delta m^2_{32}$ and hence the pattern of neutrino masses, or (ii) a very stringent limit on $\sin^22\theta_{13}$ and a first comparison of the sum of all appearance modes with the disappearance measurements. The optimum baselines for this entry--level physics program appears to be of the order of 3000~km or greater, for which matter effects are substantial. Longer baselines also favor the precise determination of $\sin^22\theta_{13}$. A 20~GeV neutrino factory providing $10^{20}$ muon decays per year is a good candidate ``upgraded" neutrino factory (or alternatively a higher energy facility providing a few $\times 10^{19}$ decays per year). This would enable the first observation of, or meaningful limits on, $\nu_e \rightarrow \nu_\tau$ oscillations, and precision measurements of the leading oscillation parameters. In the more distant future, a candidate for a second (third ?) generation neutrino factory might be a facility that provides O($10^{21}$) decays per year and enables the measurement of, or stringent limits on, CP violation in the lepton sector. \item{(b) LSND confirmed.} Less extensive studies have been made for the class of scenarios that become of interest if the LSND oscillation results are confirmed. However, in the scenarios we have looked at we find that the $\nu_e \rightarrow \nu_\tau$ rate is sensitive to the oscillation parameters and can be substantial. With a large leading $\delta m^2$ scale medium baselines (for example a few $\times 10$~km) are of interest, and the neutrino factory intensity required to effectively exploit the $\nu_e$ beam component might be quite modest ($< 10^{19}$ decays per year). If sterile neutrinos play a role in neutrino oscillations, we will have an exciting window on physics beyond the SM, and we anticipate that a neutrino factory would enable crucial measurements to be made exploiting the electron neutrino beam component. \end{description} \subsection*{The non-oscillation physics program} A neutrino factory could provide beams that are a factor of $10^4-10^5$ more intense than conventional neutrino beams. This would have an enormous impact on the detector technology that could be used for non--oscillation neutrino experiments. For example, the use of silicon pixel targets and hydrogen or deuterium polarized targets would become feasible. Hence, a neutrino factory would offer experimental opportunities that do not exist with lower intensity conventional beams. We have looked at a few explicit examples of interesting experiments that might be pursued at a neutrino factory: \begin{itemize} \item Precise measurements of the detailed structure of the nucleon for each parton flavor, including the changes that occur in a nuclear environment. \item A first measurement of the nucleon spin structure with neutrinos. \item Charm physics with several million tagged particles. Note that charm production becomes significant for storage ring energies above 20 GeV. \item Precise measurements of standard model parameters - $\alpha_s$, the weak mixing angle, and the CKM matrix elements. \item Searches for exotic phenomena such as neutrino magnetic moments, anomolous couplings to the tau and additional neutral leptons. \end{itemize} The non-oscillation measurements benefit from higher beam energies since event rates and the kinematic reach scale with energy, and perturbative calculations become more reliable in the kinematic regions accessed by higher energies. % Charm production becomes %significant for storage ring energies above 20 GeV while bottom %production requires machine energies above 80-100 GeV. \subsection*{Recommendations} The physics program we have explored for a neutrino factory is highly promising. We recommend a sustained effort to study both the physics opportunities and the machine realities. \begin{description} \item{(i)} We encourage support for the R\&D needed to learn whether a neutrino factory can be a real option in the next decade. \item{(ii)} We propose continued studies of oscillation physics to better understand how to build very massive detectors for long--baseline neutrino oscillation physics at a neutrino factory. These studies should identify the detector R\&D that is required to realize detectors with masses of a few times 10~kt or more that are able to detect and measure wrong--sign muons, and detectors of a few kt or more able to observe tau--lepton appearance with high efficiency. It is also desirable to identify and measure the charge of electrons. Because of the size of such detectors both the detector technologies themselves and the civil engineering issues of building such massive detectors need to be addressed. \item{(iii)} We have not completed the optimization of physics performance in terms of baseline. More work is also needed to understand the benefits of polarization. These are appropriate topics for a continuing study. \item{(iv)} This study concentrated on the muon storage ring as a neutrino source and did not cover the additional physics programs which would use the proton driver and the high intensity muon beams. A further study directed at these other facets of physics at a muon storage ring facility would be very useful. \end{description} \subsection*{Acknowledgments} We would like to thank Mike Witherell, Mike Shaevitz, and Steve Holmes for initiating the two companion 6 month neutrino factory studies, and their continued support that enabled these studies to be productive. We thank Mike Shaevitz in particular for our charge. We would also like to thank the members of the Neutrino Source/Muon Collider Collaboration, whose enthusiastic efforts over the last few years have enabled us to seriously contemplate a facility that requires an intense source of muons. Finally we would like to thank the participants of neutrino factory and related physics studies initiated in Europe and Japan that have given us encouragement and shown interest in the present study. \clearpage %\begin{references} \begin{thebibliography}{99} \input ref_1 \input ref_2_v3 \input ref_3a \input ref_3b \input ref_3c \input ref_4_v3 \end{thebibliography} %\end{references} \end{document}