\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{tab:LEexpts}):
\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 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 drawn.
\begin{center}
{
\newsavebox{\rotbox}
\begin{table}[bthp]
\sbox{\rotbox}{
{
%
\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}.
\label{tab:LEexpts}
%
}
\end{minipage}}
\rotate[l]{\usebox{\rotbox}}
%
\end{table}
%
}
\end{center}
%
\begin{table} \centering
\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}.
\label{tab:LE_beams}
} {
%
\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 severe 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.