\subsection{Non-oscillation physics at a Neutrino Factory} The study of the utility of intense neutrino beams from a muon storage ring in determining the parameters governing non-oscillation physics was begun in 1997~\cite{rajageer}. More complete studies can be found in~\cite{INTRO:ref9} and recently a European group has brought out an extensive study on this topic~\cite{cern-nonosc}. A Neutrino Factory can measure individual parton distributions within the proton for all light quarks and anti-quarks. It could improve valence distributions by an order of magnitude in the kinematical range $x\gsim 0.1$ in the unpolarized case. The individual components of the sea ($\bar{u}$, $\bar{d}$, ${s}$ and $\bar{s}$), as well as the gluon, would be measured with relative accuracies in the range of 1--10\%, for $0.1\lsim x \lsim 0.6$. A full exploitation of the Neutrino Factory potential for polarized measurements of the shapes of individual partonic densities requires an {\it a priori} knowledge of the polarized gluon density. The forthcoming set of polarized deep inelastic scattering experiments at CERN, DESY and RHIC may provide this information. The situation is also very bright for measurements of $C$-even distributions. Here, the first moments of singlet, triplet and octet axial charges can be measured with accuracies that are up to one order of magnitude better than the current uncertainties. In particular, the improvement in the determination of the singlet axial charge would allow a definitive confirmation or refutation of the anomaly scenario compared to the `instanton' or `skyrmion' scenarios, at least if the theoretical uncertainty originating from the small-$x$ extrapolation can be kept under control. The measurement of the octet axial charge with a few percent uncertainty will allow a determination of the strange contribution to the proton spin better than 10\%, and allow stringent tests of models of $SU(3)$ violation when compared to the direct determination from hyperon decays. A measurement of $\as(M_Z)$ and $\sin^2\theta_W$ will involve different systematics from current measurements and will therefore provide an important consistency check of current data, although the accuracy of these values is not expected to be improved. The weak mixing angle can be measured in both the hadronic and leptonic modes with a precision of approximately $2\times 10^{-4}$, dominated by the statistics and the luminosity measurement. This determination would be sensitive to different classes of new-physics contributions. Neutrino interactions are a very good source of clean, sign-tagged charm particles. A Neutrino Factory can measure charm production with raw event rates up to 100 million charm events per year with $\simeq$ 2 million double-tagged events. (Note that charm production becomes significant for storage ring energies above 20~GeV). Such large samples are suitable for precise extractions of branching ratios and decay constants, the study of spin-transfer phenomena, and the study of nuclear effects in deep inelastic scattering. The ability to run with both hydrogen and heavier targets will provide rich data sets useful for quantitative studies of nuclear models. The study of $\Lambda$ polarization both in the target and in the fragmentation regions will help clarify the intriguing problem of spin transfer. Although the neutrino beam energies are well below any reasonable threshold for new physics, the large statistics makes it possible to search for physics beyond the Standard Model. The high intensity neutrino beam allows a search for the production and decay of neutral heavy leptons with mixing angle sensitivity two orders of magnitude better than present limits in the 30--80 MeV range. The exchange of new gauge bosons decoupled from the first generation of quarks and leptons can be seen via enhancements of the inclusive charm production rate, with a sensitivity well beyond the present limits. A novel neutrino magnetic moment search technique that uses oscillating magnetic fields at the neutrino beam source could discover large neutrino magnetic moments predicted by some theories. Rare lepton-flavor-violating decays of muons in the ring could be tagged in the deep inelastic scattering final states through the detection of wrong-sign electrons and muons, or of prompt taus. % % below modified K.J. 28.jul.2002 % \subsection{Physics that can be done with Intense Cold Muon Beams} Experimental studies of muons at low and medium energies have had a long and distinguished history, starting with the first search for muon decay to electron plus gamma-ray~\cite{Hincks-Pontecorvo}, and including along the way the 1957 discovery of the nonconservation of parity, in which the $g$ value and magnetic moment of the muon were first measured~\cite{Garwinetal}. The years since then have brought great progress: limits on the standard-model-forbidden decay $\mu\to e\gamma$ have dropped by nine orders of magnitude, and the muon anomalous magnetic moment $a_\mu=(g_\mu-2)/2$ has yielded one of the more precise tests ($\approx1$ ppm) of physical theory~\cite{BNLg-2}. The front end of a Neutrino Factory has the potential to provide $\sim10^{21}$ muons per year, five orders of magnitude beyond the most intense beam currently available\footnote{The $\pi$E5 beam at PSI, Villigen, providing a maximum rate of $10^9$ muons/s~\cite{Edgecock}.}. Such a facility could enable a rich variety of precision measurements. In the area of low energy muon physics a majority of experiments with a high physics potential is limited at present by statistics. The list of conceivable projects includes (see Table \ref{muon_experiments}): \begin{itemize} \item precise determinations of the properties characterizing the muon, which are the mass $\mu_{\mu}$, magnetic moment $\mu_{\mu}$, magnetic anomaly $a_{\mu}$, charge $q_{\mu}$ and lifetime $\tau_{\mu}$, \item measurements the muon decay parameters (Michel parameters), \item CPT tests from a comparison of $\mu^-$ and $\mu^+$ properties, \item measurements of fundamental constants of general importance (e.g. the electromagnetic fine structure constant $\alpha$ or the weak interaction Fermi constant $G_F$) \item sensitive searches for physics beyond the Standard Model either through measuring differences of muon parameters from Standard Model predictions or in dedicated searches for rare and forbidden processes, such as $\mu \rightarrow e \gamma$, $\mu \rightarrow eee$, $\mu^-N \rightarrow e^-N$ conversion and muonium-antimuonium (${\rm M}-\overline{\rm M}$) conversion or searches for a permanent electric dipole moment $d_{\mu}$ of the particle, \item searches for $P$ and $T$ violation in muonic atoms, \item precise determinations of nuclear properties in muonic (radioactive) atoms, and \item applications in condensed matter, thin films and at surfaces, \item applications in life sciences \item and muon catalyzed fusion($\mu$CF). \end{itemize} A detailed evaluation of the possibilities has recently been made by a CERN study group, where a a typical facility with a 4 MW proton driver was assumed \cite{Aysto_01}. Of the possibilities to search for forboidden decays, Marciano~\cite{Marciano97} has suggested that muon LFV (especially coherent muon-to-electron conversion in the field of a nucleus) is the ``best bet" for discovering signatures of new physics using low-energy muons. The MECO experiment \cite{MECO} presently proposed at BNL offers through a novel detector concept very high sensitivity and some 4 orders of magnitude improvement over the presently best results from PSI \cite{SINDRUM}. At a future high muon flux facility this could be further improved by 1-2 orders. The search for $\mu\to e \gamma$ is also of great interest. The MEGA experiment recently set an upper limit $B(\mu^+\to e^+\gamma)<1.2\times10^{-11}$~\cite{MEGA}. Ways to extend sensitivity to the $10^{-14}$ level have not only been discussed~\cite{Cooper97} but also lead to an active proposal at PSI \cite{Mori_99}. The experiment aims for three orders of magnitude improvement over MEGA which was systematics limited. The $\mu$-to-$e$-conversion approach has the additional virtue of sensitivity to possible new physics that does not couple to the photon. A measurement of $d_{\mu}$ could prove equally exciting; it uses a novel approach via exploiting the large motional electric fields of relativistic particles in a magnetic storage ring. It needs to be as well developed, being only at the Letter of Intent stage at present~\cite{EDMLOI}. As CP violation comes in in the quark sector starting with the second generation, the muon is a particularly valuble probe, despite the already low limits for electrons. Moreover, some models have stronger than linear scaling of a permanent lepton electric dipole moment \cite{Ellis_01}. It is the advantage of searches of rare decays and for $d_{\mu}$ that the standard model predictions are zero or orders of magnitude below the presently established limits. Any observation which can be shown to be not an artefact of the experimental method or due to background would therefore be a direct sign of new physics. There is at present high activity in three experiments to improve the muon lifetime $\tau_\mu$ \cite{tau_mu}. Note, $\tau_\mu$ is the source for a precision value of the Fermi coupling constant $G_F$. The efforts are therefore worthwhile whenever the state of the art allows substantial improvement. One should however be aware that a comparison with theory is presently dominated by theoretical uncertainties. In the case of precision measurements ($\tau_\mu$, $a_\mu$, etc.), new-physics effects can appear only as small corrections arising from the virtual exchange of new massive particles in loop diagrams. In contrast, LFV and EDMs are forbidden in the standard model, thus their observation at any level constitutes evidence for new physics. One should note, that the correctness of detailed precise calculations must be assured before conclusions can be drwan. \begin{center} { \newsavebox{\rotbox} \begin{table}[bthp] \sbox{\rotbox}{ \label{tab:LEexpts} % { % \begin{tabular}[b]{|c|c||c|c|c||c|} % \hline % %&&&&&\\ % Type of & Physics Issues & Possible & previously established &present activities &projected for \\ % Experiment& & Experiments&accuracy&(proposed accuracy)& SMS @ CERN \\ % \hline \hline % % ''Classical'' & Lepton Number Violation;&$\mu^-N \rightarrow e^-N$ &$6.1 \cdot 10^{-13}$ & PSI, proposed BNL ($5 \cdot 10^{-17}$) & $ < 10^{-18}$ \\ Rare \& & Searches for New Physics:&$\mu \rightarrow e \gamma$ &$1.2 \cdot 10^{-11}$ & proposed PSI ($1 \cdot 10^{-14}$) & $ < 10^{-15}$ \\ Forbidden & SUSY, L-R Symmetry,&$\mu \rightarrow eee$ & $1.0 \cdot 10^{-12}$ & completed 1985 PSI & $ < 10^{-16}$ \\ Decays & R-parity violation,.....&$\mu^+e^- \rightarrow \mu^-e^+$&$8.1 \cdot 10^{-11}$ & completed 1999 PSI & $ < 10^{-13}$ \\ % \hline % Muon & $G_F$; Searches for New Physics;&$\tau_{\mu}$ &$18 \cdot 10^{-6}$ & PSI (2x), RAL ($1 \cdot 10^{-6}$) & $ < 10^{-7}$ \\ Decays & Michel Parameters&$non (V-A)$ &$typ.\, few\, 10^{-3}$& PSI, TRIUMF ($1 \cdot 10^{-3}$) & $ < 10^{-4}$ \\ % \hline % &Standard Model Tests;&&&&\\ Muon & New Physics; CPT Tests &$g_{\mu}-2$ &$1.3 \cdot 10^{-6} $ & BNL ($3.5\cdot10^{-7}$) & $ < 10^{-7}$ \\ Moments &T- resp. CP-Violation &$edm_{\mu}$ &$3.4 \cdot 10^{-19} e\,cm$ & proposed BNL ($10^{-24} e\,cm$) & $ < 5 \cdot 10^{-26} e\,cm$ \\ &in 2nd lepton generation&&&&\\ % \hline % Muonium & Fundamental Constants, $\mu_{\mu}$,$m_{\mu}$,$\alpha$;&$M_{HFS}$ &$12 \cdot 10^{-9}$ & completed 1999 LAMPF & $ 5 \cdot 10^{-9}$ \\ Spectroscopy & Weak Interactions; Muon Charge &$M_{1s2s}$ &$1 \cdot 10^{-9}$ & completed 2000 RAL & $ < 10^{-11}$ \\ % \hline % Muonic Atoms & Nuclear Charge Radii;&$\mu^- atoms$ &$depends$ & PSI, possible CERN & $ new nuclear$\\ &Weak Interactions&&&($$to $10^{-3}$)& $structure$\\ % \hline % Condensed & surfaces, catalysis & surface $\mu$SR &$n/a$ & PSI, RAL ($ n/a $)& $high rate$ \\ Matter&bio sciences ... &&&&\\ % \hline % KJ 14 Nov 2000 \end{tabular} } } \sbox{\rotbox}{% \begin{minipage}{\wd\rotbox} \usebox{\rotbox} \caption[]{ Experiments which could beneficially take advantage of the intense future stopped muon source. The numbers were worked out for scenarios at a future Stopped Muon Source (SMS) of a neutrino factory at CERN \cite{Aysto_01}. They are based on a muon flux of $10^{21}$ particles per annum in which beam will be available for $10^7$ s. Typical beam requirements are given in Table \ref{tab:LE_beams}.} \end{minipage}} \rotate[l]{\usebox{\rotbox}} % \end{table} % } \end{center} % \begin{table} \centering \label{tab:LE_beams} % \caption[]{ Beam requirements for new muon experiments. Given are the necessary sign of charge $q_{\mu}$ and the minimum of the total muon number $\int I_{\mu}dt$ above which significant progress can be expected in the physical interpretation of the experiments. Measurements which require pulsed beams are sensitive to the muon suppression $I_0/I_{m}$ between pulses of length $\delta T$ and separation $\Delta T$. Most experiments require energies up to 4 MeV corresponding to 29 MeV/c momentum. Thin targets, respectively storage ring acceptances, demand rather small momentum bites $\Delta p_{\mu}/p_{\mu}$ \cite{Aysto_01}. } { % \begin{tabular}[hbt]{|c|c|c|c|c|c|c|c|} % \hline % &&&&&&&\\ % Experiment & $q_{\mu}$ &$\int I_{\mu}dt$&$I_0/I_{\mu}$&$\delta T$&$\Delta T$&$E_{\mu}$&$\Delta p_{\mu}/p_{\mu}$\\ & & & & [ns] & [ns] & [MeV] & [\%] \\ % \hline % $\mu^-N \rightarrow e^-N$ &-- &$10^{19}$&$<10^{-9}$&$\leq 100$&$\geq 1000$ &$<20$ &1...5 \\ $\mu \rightarrow e \gamma$ &+ &$10^{16}$& n/a &continuous &continuous &1...4 &1...5 \\ $\mu \rightarrow eee$ &+ &$10^{15}$& n/a &continuous &continuous &1...4 &1...5 \\ $\mu^+e^- \rightarrow \mu^-e^+$&+ &$10^{16}$&$<10^{-4}$&$<1000$s &$\geq 20000$ &1...4 &1...2 \\ % \hline % $\tau_{\mu}$ &+ &$10^{13}$&$<10^{-4}$&$<100 $ &$\geq 20000$ &4 &1...10 \\ $non (V-A)$ &$\pm$&$10^{13}$&$ n/a $ &continuous &continuous &4 &1...5 \\ % \hline % $g_{\mu}-2$ &$\pm$&$10^{15}$&$<10^{-7}$&$\leq 50 $ &$\geq 10^6$ &3100 &$10^{-4}$ \\ $edm_{\mu}$ &$\pm$&$10^{16}$&$<10^{-6}$&$\leq 50 $ &$\geq 10^6 $ &$\leq$1000&$\leq 10^{-5}$\\ % \hline % $M_{HFS}$ &+ &$10^{15}$&$<10^{-4}$&$\leq 1000$ &$\geq 20000$ &4 &1...3 \\ $M_{1s2s}$ &+ &$10^{14}$&$<10^{-3}$&$\leq 500 $ &$\geq 10^6$ &1...4 &1...2 \\ % \hline % $\mu^- atoms$ &-- &$10^{14}$&$<10^{-3}$&$\leq 500 $&$\geq 20000$ &1...4 &1...5 \\ % \hline % $condensed$ $matter$ &$\pm$&$10^{14}$&$<10^{-3}$&$< 50 $ &$\geq 20000$ &1...4 &1...5 \\ $(incl.$$bio$ $ sciences)$ &&&&&&&\\ % \hline % KJ 14 Nov 2000 \end{tabular} } \end{table} % The current status and prospects for advances in these areas are included in Table~\ref{tab:LEexpts}, which list present efforts in the field and prospected improvements at a neutrino factory or muon collider facility. The beam parameters necessary for the expected improvements are listed in Table~\ref{tab:LE_beams} It is worth recalling that LFV as a manifestation of neutrino mixing is suppressed as $(\delta m^2)^2/m_W^4$ and is thus entirely negligible. However, a variety of new-physics scenarios predict observable effects. Table~\ref{tab:newmuphys} lists some examples of limits on new physics that would be implied by nonobservation of $\mu$-to-$e$ conversion ($\mu^-N\to e^-N$) at the $10^{-16}$ level~\cite{Marciano97}. \begin{table} \caption[New physics probed by $\mu\rightarrow e$ experiments] {Some examples of new physics probed by the nonobservation of $\mu\rightarrow e$ conversion at the $10^{-16}$ level (from~\protect\cite{Marciano97}).\label{tab:newmuphys}} \begin{center} \begin{tabular}{|lc|} \hline New Physics & Limit \\ \hline Heavy neutrino mixing & $|V_{\mu N}^*V_{e N}|^2<10^{-12}$\\ Induced $Z\mu e$ coupling & $g_{Z_{\mu e}}<10^{-8}$\\ Induced $H\mu e$ coupling & $g_{H_{\mu e}}<4\times10^{-8}$\\ Compositeness & $\Lambda_c>3,000\,$TeV\\ \hline \end{tabular} \end{center} \end{table} the muon magnetic anomaly (muon g-2 value \cite{Farley_90}) has been measured recently at the Brookhaven National Laboratory (BNL) with 1.3 ppm accuracy \cite{Brown_01}. At present, no definite statement can be made whether this result agrees or disagrees with standard theory. The theory has come under sever scrutiny and in particlar an error has been found in the calculation of hadronic light by light scattering \cite{Knecht{02}. At present the theoretical situation is unclear and theory and experiment differ by about between 1.5 and 2.5 standard deviations. Higher accuracy will be required for theory and experiment. There is a good chance that this might eventually hint to new physics \cite{Czarnecki_01}. But also in case the experiment would finally agree with standard theory, there stringent limits could be extracted for various models beyond standard theory. The final goal of the experiment is 0.35 ppm. This value could be superseded by about an order of magnitude at an, provided 3.1 GeV muons would be made available. A central point would however remain the difficulty to obtain a reliable theoretical value, because some important contributions to the muon magnetic anomaly are hadronic vacuum polarization and hadronic light by light scattering, which both can only be determined with limited accuracy \cite{Marciano_2001}. In the framework of a rather general ansatz the past muon g-2 experiments at CERN have provided the best test of CPT invariance at a level of $2\cdot10^{-22}$ which is a more than 3 orders of magnitude tighter bound than the mostly quoted ${\rm K}^0-\overline{{\rm K}^0}$ mass difference \cite{Kostelecki_00}. From any new measurement of the magnetic anomaly for muons of both signs of charge one can expect a further improvement. Precision studies of atomic electrons have provided notable tests of QED ({ e.g,} the Lamb shift in hydrogen) and could in principle be used to search for new physics were it not for nuclear corrections. Studies of muonium ($\mu^+e^-$) are free of such corrections since it is a purely leptonic system. Muonic atoms also can yield new information complementary to that obtained from electronic atoms. A number of possibilities have been enumerated by Kawall {\it et al.}~\cite{Kawall97}, Jungmann \cite{Jungmann_01} and Molzon~\cite{Molzon97}. As an example we consider the muonium atom. Because the electromagnetic interactions of the muons can be calculated to the required accuracy in the framework of standard theory, particularly Quantum Electrodynamics (QED), most precise determinations of fundamental constants and sensitive searches for New Physics can be performed on this solid basis. The muonium ground state hyperfine structure has been measured to 12 ppb~\cite{Liu_99} and currently furnishes the most sensitive test of the relativistic two-body bound state in QED~\cite{Jungmann_01}. The precision could be further improved significantly with increased statistics. The theoretical error is 120~ppb. The uncertainty arising from the muon mass is five times larger than that from calculations. If one assumes the theory to be correct, the muon-electron mass ratio can be extracted to 27~ppb. A precise value for the electromagnetic fine structure constant $\alpha$ can be extracted. Its good agreement with the number extracted from the electron magnetic anomaly must be viewed as the best test of internal consistency of QED, as one case involves bound state QED and the other that of free particles. The Zeeman effect of the muonium hyperfine structure allows the best direct measurment of the muon magnetic moment, respectively its mass, to 120~ppb. improved by higher-precision measurements in muonium and muon spin resonance, also areas in which the Neutrino Factory front end could contribute. Laser spectroscopy of the muonium 1s-2s transition \cite{Meyer_00} has not only resulted in a precise value of the muon mass, moreover the muon-electron charge ratio was tested to about $2\cdot 10^{-9}$. This is by far the best test of charge equality in the first two particle generations. The search for muonium-antimuonium conversion has been proposed by Pontecorvo already three years before the atom was first produced by Hughes {\it et al.}~\cite{Hughes_60}. A variety of possible in new-physics models allow violation of lepton family number by two units. The current limit is $R_g \equiv G_C / G_F< 0.0030$~\cite{Willmann_99}, where $G_C$ is the new-physics coupling constant. % and $G_F$ is the Fermi coupling constant. This sets a lower limit of $2.6 \,$TeV$/c^2$ (90\% C.L.) on the mass of a grand-unified dileptonic gauge boson and also strongly disfavours among others models with heavy lepton seeded radiative mass generation~\cite{Willmann_99}. The search for muonium-antimuonium conversion has the by far strongest gain in sensitivity of all rare muon decay experiments \cite{Jungmann_01}. A high intensity proton machine would also allow in close proximity of the muon beams to set up a new generation ISOL facility which would have much higher rates compared to the present ISOLDE facility. Nuclids yet not addressed could be produced at quantities which allow precision investigations of their properties \cite{Aysto_01}. The exact measurements on muonic spectra can yield most precise values for the charge radii of nuclei as well as other ground state properties such as moments and even B(E2) transition strengths for even-even nuclei. An improved understanding of nuclear structure can be expected which may be of significant relevance for interpreting various neutrino experiments, rare decays involving nuclei and nuclear capture. A most urgent need exists for accurate charge and neutron radii of Francium and Radium isotopes which are of interest for atomic parity violation research and edm searches in atoms and nuclei. Muonic x-ray experiments generally promise higher accuracy for most of these quantities compared to electron scattering, particularly because the precision of electron scattering data depends on the location of the minimum of the cross section where rates are naturally low. In principle, for chains of isotopes charge radii can be inferred from isotope shift measurements with laser spectroscopy. However, this gives only relative information. For absolute values calibration is necessary and has been obtained in the past for stable nuclei from muonic spectra. In general, two not too distant nuclei are needed. % for a good calibration. The envisaged experimental discussed approaches include i) the technique pioneered by Nagamine and Strasser \cite{Strasser_01}, which involves cold films for keeping radioactive atoms and as a host material in which muon transfer takes place; ii) merging beams if radioactive ions and of muons; and iii) trapping of exotic isotopes in a Penning trap which is combined with a cyclotron trap. Large formation rates can be expected with from a setup containing a Penning trap \cite{Penning_trap} the magnetic field of which serves also for a cyclotron muon trap \cite{Simons}. For muon energies in the range of electron binding energies the muon capture cross sections grow to atomic values, efficient atom production can be expected of order 50 systems per second. CERN could be a unique place worldwide where such experiments become possible. It should be noted that antiprotonic atoms could be produced similarly \cite{Hayano_2001} and promise measurements of neutron distributions in nuclei.