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\subsection*{\texorpdfstring{%
  \superb experimental reach}{%
  SuperB experimental reach}}

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

A first search for \CP violation in tau decay has been conducted by the CLEO
collaboration~\cite{Bonvicini:2001xz}, looking for a
tau-charge-dependent asymmetry of the angular distribution of the
hadronic system produced in $\tau \to K_S\pi\nu$.  In multi-Higgs
doublet New Physics, the \CP-violating asymmetry arises from the Higgs coupling
and the interference between $S$ wave scalar exchange and $P$ wave
vector exchange.  The Cabibbo-suppressed decay mode into $K_S\pi\nu$
has a larger mass-dependent Higgs coupling;  the events in the
sidebands of the $K_S$ mass distributions can thus be used to calibrate the
detector response.  With a data sample of 13.3\invfb ($12.2\EE{6}$ tau
pairs), the mean of the optimal asymmetry observable is $\left<\xi\right> =
(-2.0 \pm 1.8)\EE{-3}$.
As the above measurement relies on detector calibration with side-band
events, it is conceivable that \superb with 75\invab would not be
limited by systematics and would therefore reach an experimental
resolution $\Delta\left<\xi\right> \approx 2.4\EE{-5}$.

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\subsubsection*{Tau electric dipole moment}

The tau electric dipole moment (EDM) influences both the angular
distributions and the polarization of the tau produced in \epem
annihilation. With a polarized beam, it is possible to
construct observables from the angular distribution of the products of
a single tau decay that unambiguously discriminate between the
contribution due to the tau EDM and other
effects~\cite{GonzalezSprinberg:2007qj,Bernabeu:2006wf}. 
%The more recent of those two papers provides 
Recent work has provided
an estimate of the \superb
upper limit sensitivity for the real part of the tau EDM
$\left|\text{Re}\{d_\tau^\gamma\}\right| \le
7.2\EE{-20}\,e\,\text{cm}$ with
75\invab~\cite{GonzalezSprinberg:2007qj}. The result
assumes a $100\%$ polarized electron beam colliding with unpolarized
positrons at the \FourS peak, no uncertainty on the polarization, and
perfect reconstruction of the tau decays $\tau \to \pi\nu$. Studies
have been done assuming more realistic conditions:
\begin{itemize}
\item an electron beam with a linear polarization of $80\% \pm 1\%$;
\item $80\%$ geometric acceptance;
\item track reconstruction efficiency $97.5\%\pm 0.1\%$ (similarly to
  what has been achieved in LEP analyses~\cite{Schael:2005am} and
  \babar ISR analyses~\cite{Davier:2008:babarIsrEffSyst}.
\end{itemize}
The process $\epem \to \tautau$ is simulated with the KK
generator~\cite{Jadach:1999vf} and the Tauola package for tau
decay~\cite{Jadach:1999vf}; the simulation includes the
complete spin correlation density matrix of the initial-state beams
and  the final state tau leptons. Tau EDM effects are simulated by
weighting the tau decay product angular distributions.
The studies are not complete, and do not yet include
uncertainties in reconstructing the tau direction. The preliminary
indications are that the tau EDM experimental resolution is $\approx
10\EE{-20} e\,\text{cm}$, corresponding to an angular asymmetry of
$3\EE{-5}$; the uncertainties in track reconstruction give a $\approx
1\EE{-20}$ systematic contribution.  Asymmetries
proportional to the tau EDM depend on events that go into the same
detector regions but arise from tau leptons produced at different angles,
minimizing the impact of efficiency uncertainties. It must be added
that all the hadronic tau channels have at least theoretically the same
statistical power as the $\tau \to \pi\nu$ mode in measuring the tau
polarization~\cite{Kuhn:1995nn}, and can therefore be used to improve
the experimental resolution.

A search for the tau EDM with unpolarized beams has been completed at
Belle~\cite{Inami:2002ah}.  In this case, one
must measure correlations of the angular distributions of both tau
leptons in the same events, thereby losing in both reconstruction efficiency and
statistical precision.  The analysis shows the impact of inefficiency
and uncertainties in the tau direction reconstruction, and also
demonstrates that all tau decays, including leptonic decays with two
neutrinos, provide statistically useful information for measurement of the tau
EDM.  With $29.5\invfb$ of data, the experimental resolution on the
real and imaginary parts of the tau EDM is
$[0.9{-}1.7]\EE{-17}\,e\,\text{cm}$, including systematic effects.  An
optimistic extrapolation to \superb at $75\invab$, assuming systematic
effects can be reduced according to statistics, corresponds to an
experimental resolution of $[17{-}34]\EE{-20}$.

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

In a manner similar to an EDM, the tau anomalous moment ($g\! - \!\! 2$) influences both the angular
distribution and the polarization of the tau produced in \epem
annihilation.  Polarized beams allow the measurement of the real part of the
$g\! - \!\! 2$ form factor by statistically measuring the tau polarization with
the angular distributions of its decay
products. Bernab\'eu {\it et al.}~\cite{Bernabeu:2007rr} estimate that \superb
with 75\invab will measure the real and imaginary part of the $g\! - \!\! 2$
form factor at the \FourS with a resolution in the range
$[0.75-1.7]\EE{-6}$. Two measurements of the real part of
$g\! - \!\! 2$ are proposed, one fitting the polar angle distribution of the tau leptons,
and one based on the measurement of the tau transverse and
longitudinal polarization from the angular distribution of its decay
products.  All events with tau leptons decaying either in $\pi\nu$ or
$\rho\nu$ are considered, but no detector 
%statistical or systematic
effects are accounted for. For the tau polarization measurements,
electron beams with perfectly known 100\% polarization are assumed.
Studies simulating more realistic experimental conditions are ongoing.
While the polar angle distribution measurement will conceivably suffer
from uncertainties in the tau direction reconstruction, the
preliminary results on the tau EDM measurement, mentioned above,
indicate that asymmetries measuring the tau polarization are least
affected by reconstruction systematics. Transposing  the preliminary results obtained with
simulations for the tau EDM to the real part
of the $g\! - \!\! 2$ form factor, one can estimate that $a_\mu = (g-2)/2$
can be measured with a statistical error of $2.4\EE{-6}$, with
systematic effects from reconstruction uncertainties one order of
magnitude lower.
