\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}