\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.