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\subsection*{Predictions from New Physics models}


\subsubsection*{\CP violation and $T$-odd observables in tau decay}

\CP violation in the quark sector has been observed both
in the $K$ and in the $B$ systems; the experimental results are thus far
fully explained by the complex phase of the CKM matrix.
On the contrary, $\CP$ violation in the lepton sector has yet not been
observed. Within the Standard Model, $\CP$-violating effects in charged-lepton
decays are  predicted to be vanishingly small.
For instance, the $\CP$ asymmetry rate of $\tau^{\pm}\to K^{\pm}\pi^0\nu$
is estimated to be of order ${\cal O}(10^{-12})$~\cite{Delepine:2005tw}.
Evidence for \CP violation in tau decay would therefore be a clear signal of
New Physics.
In one instance, the $\tau^{\pm}\to K_S \pi^\pm \nu$
rate asymmetry, a small \CP\ asymmetry of $3.3 \times 10^{-3}$
is induced by the known \CP-violating phase of the $\KzKzb$
mixing amplitude~\cite{Bigi:2005ts}. This asymmetry is known to 2\% precision. Thus, this mode can serve as a calibration, and in addition, any deviation from the expected asymmetry would be a sign of New Physics.
%Due to this large Standard Model contribution,
%this asymmetry is not a particularly interesting observable for New Physics searches.

Most of the known New Physics models cannot generate observable
\CP-violating effects in $\tau$ decays (see {\it e.g.},~\cite{Raidal:2008jk}).
The only known exceptions are R parity-violating supersymmetry~\cite{Delepine:2007qg}
or specific non-supersymmetric multi-Higgs models.
In such a framework, the $\CP$ asymmetries of various $\tau$-decay channels
can be enhanced up to the $10^{-1}$ level, without conflicting with
other observables, and saturating the experimental limits
obtained by CLEO~\cite{Bonvicini:2001xz}.
Similar comments also apply to $T$-odd  \CP-violating asymmetries in
the angular distribution of $\tau$ decays.


\subsubsection*{Tau electric dipole moment}


In natural SUSY frameworks, lepton EDMs ($d_{\ell}$) scale linearly with the
lepton mass. As a result, the existing limits on the electron EDM generally
preclude any visible effect in the $\tau$ and $\mu$ cases.
In multi-Higgs models, however, EDMs scale with the cube of the lepton
masses~\cite{Barger:1996jc}, $d_{\tau}$ can thus be substantially enhanced.
However, in this case the electron and muon EDMs receive sizable
two-loop effects via Barr-Zee diagrams, which again scale linearly with the lepton masses.  As a result, one can derive an approximate bound
 $d_{\tau}\lsim 0.1\times (m_{\tau}/m_{\mu})^3 (m_{\mu}/m_e)d_{e}$
which is still very strong.  From the
present experimental upper bound on the electron EDM,
$d_{e}\lsim 10^{-27} e\,{\rm cm}$, it follows that $d_{\tau}\lsim 10^{-22} e\,{\rm cm}$.




\subsubsection*{Tau $g\! - \!\! 2$}

The Standard Model prediction for the muon anomalous magnetic
moment is not in perfect agreement with recent experimental results. In particular,
 $\Delta a_{\mu} = a_{\mu}^{\rm exp} - a_{\mu}^{\rm SM}
\approx(3 \pm 1)\times 10^{-9}$.
Within the MSSM, this discrepancy can naturally
be accommodated, provided $\tan\beta \gsim 10$ and $\mu >0$.

A measurement of the $\tau$ anomalous magnetic moment
could be very useful to confirm or disprove the
interpretation of $\Delta a_{\mu}$ as due to New Physics contributions.
The natural scaling of heavy-particle effects
on lepton magnetic dipole moments,
%with respect to the lepton masses,
implies $\Delta a_\tau/\Delta a_\mu \sim m^{2}_{\tau}/m^{2}_{\mu}$.
Thus, if we interpret the present muon discrepancy
$\Delta a_{\mu} = a_{\mu}^{\rm exp} - a_{\mu}^{\rm SM} \approx(3 \pm 1)\times 10^{-9}$
as a signal of New Physics, we should expect
$\Delta a_{\tau}\approx 10^{-6}$.

In the supersymmetric case, such an estimate holds for all
the SPS points (see Table~\ref{tab:SPS:gm2}) and, more generally,
in the limit of almost
degenerate slepton masses. If $m_{\tilde{\nu}_{\tau}}^2<<m_{\tilde{\nu}_{\mu}}^2$
(as happens, for instance, in the so-called effective-SUSY scenario),
$\Delta a_{\tau}$ could be enhanced up to the $10^{-5}$ level.

\begin{table}[!htb]
\caption{\label{tab:SPS:gm2}
Values of $\Delta a_{\mu}$ and $\Delta a_{\tau}$ for various SPS points.}
\begin{tabular}{ccccccc}
\hline\hline
SPS               &  1\,a   &  1\,b   &  2  &  3  &  4  &  5   \\ \hline
$\Delta a_{\mu}\times 10^{-9}$ &  3.1 & 3.2 & 1.6  & 1.4  & 4.8  & 1.1 \\
$\Delta a_{\tau}\times 10^{-6}$ &  0.9 & 0.9 & 0.5  & 0.4  & 1.4  & 0.3 \\ \hline\hline
\end{tabular}
\end{table}
