
{\centerline{\rule[0in]{0.9\columnwidth}{2pt}}
\vspace {-0.7cm}
\part*{\centerline{Charm Physics}}
\vskip -8pt
{\centerline{\rule[ 0.15in]{0.9\columnwidth}{2pt}}


%\part*{\centerline{Charm Physics}}

%\section*{Introduction}

\bigskip
\smallskip

New Physics, in general, generates flavor-changing neutral currents (FCNC). Those could be much less suppressed in the up-type than
the down-type quark sectors. Among the up-type quarks, only charm  allows the {\em full} range of probes for FCNC, and thus
New Physics, in oscillation phenomena, in particular those involving $\CP$ violation. The Standard Model makes nontrivial predictions for $\CP$ violation
in charm transitions: {\em direct} $\CP$ violation should occur
only  in Cabibbo-suppressed
modes at an observable level $\sim$ ${\cal O}(10^{-3})$.

The recent evidence for $\DzDzb$ oscillations -- with $x_D$, $y_D$ $\simeq$
0.005--0.01 --  does not prove the presence of New Physics. However it greatly
widens the stage on which $\CP$ violation can appear as a manifestation of New
Physics. Within the Standard Model, time dependent $\CP$ asymmetries could
reach the $10^{-5}$ [$10^{-4}$] level in Cabibbo-allowed and
once [doubly]-suppressed modes, whereas New Physics could enhance these asymmetries by almost three orders of magnitude. A search for New Physics
should then aim at sensitivity levels
of ${\cal O}(10^{-3})$ or better and ${\cal O}(10^{-2})$ or better
in Cabibbo-allowed or once-suppressed nonleptonic channels and in doubly Cabibbo-suppressed or
wrong-sign semileptonic modes, respectively. Signals for New Physics might actually be clearer in
$D$ than in $B$ decays: for while {\em conventional} New Physics scenarios tend to create larger effects in the latter than the former,
those signals must also contend with a much larger Standard Model ``background'' in the latter than the former.

These searches can be done at the $\FourS$ using $D^*$ tagging and tracking of the $D$ production
and decay vertices. Relatively short runs in the charm threshold region can provide unique and important information on strong phases needed
for a proper interpretation of results obtained in $\FourS$ runs.
They might reveal significantly enhanced effects that can be seen only in $e^+e^- \to \DzDzb$
exclusive production.
%They might also reveal significantly enhanced effects that can be seen only there.
%\end{abstract}
%\maketitle must follow title, authors, abstract
%\maketitle

%\thispagestyle{fancy}

% body of paper here - Use proper section commands
% References should be done using the \cite, \ref, and \label commands
% Put \label in argument of \section for cross-referencing
%\section*{\label{}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Beginning of Ikaros Part 1
\section{New Physics in charm decays: mainly \CP violation}%%%%%%
\label{sec:charm-intro}

\subsection*{The landscape}

New Physics in general generates flavor changing neutral currents (FCNC). The Standard Model had to be crafted carefully to suppress them in the
strangeness sector down to the observed level. Those FCNC could actually be much less suppressed in the up-type than the down-type quark
sectors. Among the up-type quarks, only charm allows the {\em full} range of probes for FCNC, and thus, New Physics in oscillation
phenomena, in particular those involving $\CP$ violation: (i) Top quarks decay before they can hadronize;
without top hadrons $T^0$ oscillations cannot occur. Furthermore the sheer size of phase space in top decays greatly reduces
the coherence between different amplitudes needed to make
direct $\CP$ violation observable. (ii) Hadrons built with $u$ and $\bar u$ quarks, like the $\pi^0$ and
$\eta$, are their own antiparticle; thus there can be no $\pi^0 - \pi^0$ etc. oscillations as a matter
of principle. They also decay very rapidly. In addition, they possess so few decay channels that
$C\!P T$ invariance largely rules out $\CP$ asymmetries in their decays.

%{\bf UPDATE to be consistent with hfag-charm}

Strong evidence for $\DzDzb$ oscillations has been recently found~\cite{ref:hfag}. The most recent averages for the mixing parameters are
\begin{eqnarray}
%x_D &\equiv& \frac{\Delta M_D}{\bar \Gamma_D} = 0.0081 \pm 0.0033~, \\
%y_D &\equiv& \frac{\Delta \Gamma_D}{2\bar \Gamma_D} = 0.0031 \pm 0.0028~.
x_D &\equiv& \frac{\Delta M_D}{\bar \Gamma_D} = 0.0097^{+0.0027}_{-0.0029}~, \\
y_D &\equiv& \frac{\Delta \Gamma_D}{2\bar \Gamma_D} = 0.0078^{+0.0018}_{-0.0019}~.
\end{eqnarray}
According to our present understanding -- or lack thereof -- these quantities could be produced by Standard Model dynamics, yet $x_D$ could still
harbour substantial contributions from New Physics. It will require a
theoretical breakthrough to resolve this ambiguity in the interpretation of the data.

We will be on much firmer ground in interpreting $\CP$ asymmetries. For on one hand, $\DzDzb$
oscillations greatly widen the stage on which $\CP$ violation can appear as a manifestation of New Physics; on the
other hand, the Standard Model makes nontrivial predictions for $\CP$ violation in charm transitions. In CKM dynamics there is a weak
phase in $\Delta C =1$ transitions
entering (in the Wolfenstein representation) through $V_{cs}$, yet it is highly diluted:
\beq
V_{cs} \simeq 1 - \frac{1}{2} \lambda ^2 - i \eta A^2 \lambda ^4 \simeq 0.97 - 6\cdot 10^{-4} i~.
\eeq
Furthermore two different, yet coherent, amplitudes must contribute to the same channel to produce a direct $\CP$ asymmetry.
Within the Standard Model this can happen at an observable level only in
Cabibbo-suppressed modes -- even in these channels, $\CP$ asymmetries can be no more than ${\cal O}(10^{-3})$. This means that any
observation of direct $\CP$ violation in Cabibbo-allowed or doubly-suppressed channel establishes the
intervention of New Physics. The only exception to this general rule is provided by modes like
$D^{\pm} \to K_S\pi^{\pm}$, where one becomes sensitive to (i) the interference between
$D^+ \to \bar K^0 \pi^+$ and $D^+ \to K^0 \pi^+$ and (ii) the slight $\CP$ impurity in the $K_S$ state. The latter effect dominates,
inducing a $\CP$ asymmetry of $3.3 \cdot 10^{-3}$.

With $x_D$, $y_D \sim$ 0.005 -- 0.01 the possibilities for $\CP$ asymmetries proliferate. In addition
to the aforementioned direct $\CP$ violation one can encounter {\em time dependent} $\CP$ asymmetries.
The latter can be induced by $\CP$ violation in $\Delta C=2$ dynamics, or even by $\CP$-conserving
contributions to the latter that can make the weak phase in a $\Delta C=1$ amplitude observable.
In both cases an educated Standard Model guess points to time-dependent $\CP$ asymmetries of order
$10^{-3} \sim x_D \sim 10^{-5}$.

%%%%%%%%%%%%%
\subsection*{The menu}
%%%%%%%%%%%%

There are three classes of $\CP$ asymmetries:
\begin{enumerate}
\item
Direct $\CP$ violation can lead to a difference in the rates for $D \to f$ and $\bar D \to \bar f$:
\beq
|A_f| \equiv |A(D \to f)| \neq |\bar A_{\bar f}| \equiv |A(\bar D \to \bar f)|~.
\label{ANEQBARA}
\eeq
Strong phase shifts due to final state
interactions, are required to produce such asymmetries in partial widths. Since charm decays proceed in an environment populated by many resonances,
this requirement will not, in general, represent a limiting factor; it might make, however, the interpretation of signals a more complex task.
\item
Indirect $\CP$ violation -- {\it i.e.}, that which occurs only in $\Delta C=2$ transitions. One measure for it
is provided by
\beq
|q/p| \sim 1 + \frac{\Delta \Gamma_D}{\Delta M_D}{\rm sin}\phi_{\rm weak}  \neq 1 ~.
\label{QOVERP}
\eeq
The  same educated Standard Model guess mentioned above points to $|1 - |q/p|| \sim {\rm several}\times 10^{-4}$.
One should note here that the factor $\Delta \Gamma_D/\Delta M_D$ apparently is close to unity and thus provides no suppression
to this observable, unlike the case of $B^0$ mesons. Thus one has practically undiluted access to a weak phase due to the
intervention of New Physics in $\DzDzb$
oscillations. As discussed below,
such an asymmetry can be searched for cleanly in semileptonic decays of neutral $D$ mesons. While we already know the ratio of
wrong-sign leptons is small, their $\CP$ asymmetry could conceivably be as large as several percent!  While the rate of wrong-sign
leptons oscillates with time, the $\CP$ asymmetry does not.

\item
\CP violation in the interference between mixing and decay: In qualitative analogy to $B_d \to \jpsi \KS$, a time-dependent $\CP$ asymmetry can arise due to an interference between an oscillation
and decay amplitude:
\beq
{\phi_f} = {\rm arg}     \left(     \frac{q}{p}  \frac{ {\bar A}_{\bar f} }{A_f}        \right)      \ne 0 \; .
\label{INTER}
\eeq
A $\CP$ asymmetry generated by $\phi_f \neq 0$ is also proportional to sin$\Delta M_D t
\simeq x_D (t/\tau _D)$ and thus effectively bounded by $x_D$; {\ie}, the present lack of a signal for a
time-dependent $\CP$ asymmetry in $D^0 \to K^+K^-$ on about the 1\% level is not telling at all, in view
of $x_D \leq 1\%$. Yet any improvement in experimental sensitivity could reveal a genuine signal.
\end{enumerate}

Searching for $\CP$ violation in charm decays is not a ``wild goose chase''. We know that baryogenesis requires the presence of
$\CP$-violating New Physics. Signals for such New Physics might actually be clearer in
$D$ than in $B$ decays: for while {\em conventional} New Physics scenarios tend to create larger effects in the latter than the former,
those signals would also have to contend with a much larger Standard Model ``background'' in the latter than the former; \ie, the
theoretical ``signal-to-noise'' ratio could be better in charm decays.

The required searches can be undertaken very profitably in runs at the $\FourS$
by tagging the \Dz flavor at production time using $D^{*+} \to D^0 \pi^+$ decays
and reconstructing the proper decay time and its error.  This is done by tracking the $D$ production and decay vertices with
constraints provided by the position and size of the tight $e^+ e^-$ interaction region.
Relatively short runs in the charm threshold region, \eg, \psiprpr, can provide unique and important information on strong phases needed
for a proper interpretation of results obtained in $\FourS$ runs. In the latter \Dz flavor tagging exploits the
quantum correlations at \psiprpr; the poor proper time resolution (about the \Dz lifetime)
will make time-dependent measurements challenging.

{In summary}: Comprehensive and precise studies of $\CP$ invariance in charm decays provide sensitive probes for the presence of New Physics.
\begin{itemize}
\item
`Comprehensive' means that one analyses nonleptonic as well as semileptonic channels on all
Cabibbo levels in as many modes as possible; \ie, including final states containing neutrals.
\item
`Precise' means that one achieves sensitivity levels of $10^{-3}$ or better.

\end{itemize}

Charm decays provide another highly promising avenue towards finding $\CP$ violation, namely in final state distributions, rather
than in partial widths considered so far. This issue will be addressed separately
below.


\subsection*{Side remarks on rare decays}

The obvious motivation for measuring the branching fractions for \hbox{$D^+/D^+_s \to \mu^+ \nu$, $\tau^+\nu$} decays is to extract the decay
constants $f_D$ and $f_{D_s}$ in order to compare them with lattice QCD calculations and, hopefully, to validate
these calculations with high accuracy. A more ambitious goal is to probe for contributions from a charged Higgs field, as an indication of New Physics.

The mode $D^0 \to \mu^+\mu^-$ arises within the Standard Model mainly through a two photon intermediate
state -- $D^0 \to \gamma^* \gamma^* \to \mu^+\mu^-$ -- and can reach the $10^{-12}$ level. With the present
experimental upper bound of $1.3 \times 10^{-6}$ there is a search window for New Physics of six orders
of magnitude. Multi-Higgs models or SUSY models with $R$ parity breaking could conceivably induce a signal in
a range as ``large'' as few$\times 10^{-8}$ and $10^{-6}$, respectively.

Channels such as $D\to \gamma h$, $l^+l^-h$, $l^+l^-h_1h_2$, with $h$ denoting a hadron, receive
relatively sizable contributions within the Standard Model from long distance dynamics. Thus a search for New Physics contributions are
not very promising there, unless one can measure
precisely the lepton spectra in the final states.

One can probe a rather exotic variant of New Physics by searching for two-body modes
$D^+ \to K^+/\pi^+ f$; the charge neutral $f$ denotes a `familon', which could arise as the Nambu-Goldstone boson resulting
from the spontaneous breakdown of a global family symmetry. It has been searched for in $K^+$ and $B^+$ decays,
but apparently not yet in $D^+$ decays.

% end of Ikaros, part 1


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section*{\DzDzb mixing at \FourS and \psiprpr energies}
\section{\DzDzb mixing at \FourS and \psiprpr energies}
\label{sec:charm-mixing}


The parameters describing charm mixing can be measured in time-dependent
studies of $D$ mesons or with time-integrated observables of $D$ mesons
produced coherently near charm threshold.

The time-dependent $\DzDzb$ mixing formalism and a summary of recent
experimental results can be found in Ref.~\cite{pdg2008}.
Many different charm decay modes can be used to search for charm mixing.
\begin{itemize}
\item The appearance of ``wrong-sign'' kaons in semileptonic decays would provide
direct evidence for $\DzDzb$ oscillations (or another process of beyond Standard
Model origin).
\item The most precise limits are obtained by exploiting the time-dependence of
$D$ decays produced in $e^+e^-$ collision near 10~GeV.
\begin{itemize}
\item The wrong-sign hadronic decay $\DZ\to K^+\pi^-$ is sensitive to linear combinations of the mass and lifetime differences, denoted $x^{\prime 2}$ and $y^{\prime}$.
The relation of these parameters to $x_D$ and $y_D$ is controlled by a strong
phase difference $\delta_{K\pi}$.
\item Direct measurements of $x_D$ and $y_D$ independent of unknown
strong interaction phases can also be made using time-dependent studies of
amplitudes present in multi-body decays of the $\DZ$, for example,
$\DZ \to K^0_S\pi^+\pi^-$.
\item Direct evidence of $y_D$ can also appear through
lifetime differences between decays to $\CP$ eigenstates.
The measured quantity in
this case $\yCP$, is equivalent to $y_D$ in the absence of $\CP$ violation.
\end{itemize}
\item Another approach is to study quantum correlations near charm threshold
\cite{Asner:2005wf} in
$e^+e^- \to \DzDzb(\pi^0)$ and $e^+e^- \to \DzDzb\gamma(\pi^0)$ decays, which yield
$C$-odd and $C$-even $\DZ\DZB$ pairs, respectively. Taken together, the
time-integrated decay rate to semileptonic, $K\pi$, and $\CP$ eigenstates provide
sensitivity to $x_D$, $y_D$, and $\cos\delta_{K\pi}$.
\end{itemize}

Several recent results provide evidence that charm mixing is at the upper
end of the range of Standard Model predictions.

\babar~\cite{Aubert:2007wf} and CDF~\cite{Aaltonen:2007uc}
find evidence for oscillations in $\DZ \to K^+\pi^-$, with
3.9$\sigma$ $(\Delta {\rm Log} {\cal L})$ and 3.8$\sigma$ (Bayesian), respectively.
The most precise measurement is from Belle which
excludes $x^{\prime 2}=y^\prime=0$ at 2.1$\sigma$~\cite{Zhang:2006dp}
(Feldman-Cousins).

Belle~\cite{Staric:2007dt} and \babar~\cite{Aubert:2007en}
see 3.2$\sigma$ and 3$\sigma$ effects, respectively,
for $\yCP$ in $\DZ\to K^+K^-$.
The most precise measurement of $y_D$ is in $\DZ \to K^0_S\pi^+\pi^-$
from Belle~\cite{Abe:2007rd} and is only
1.2$\sigma$ significant. From the same analysis, Belle also reports a
2.4$\sigma$ significant result for $x_D$.
%The current situation is far from clear.
The current situation would greatly benefit from more precise
knowledge of the strong phase difference $\delta$; this would allow
one to unfold $x_D$ and $y_D$ from the $D^0 \to K^+\pi^-$ measurements of
$x^{\prime2}$ and $y^\prime$,
and directly compare them to the $D^0 \to K^0_S \pi^+\pi^-$ results.

All mixing measurements can be combined to obtain
world average (WA) values for $x$ and $y$. The Heavy Flavor
Averaging Group (HFAG) has done such a combination~\cite{Schwartz:2007fw,Schwartz:2008}.
%: {\it (a)}\
%adding together log-likelihood functions for $x$, $y$, and $\delta$ as
%obtained from measurements of relevant observables;
%%analyses of
%%resonance~\cite{hfag-charm}.
%{(b)}\ doing a global fit to the measured observables for $x$, $y$, $\delta$,
%$\delta^{}_2$, and $R_D$, being careful to account for the correlations among
%observables by using the corresponding error matrices as provided by the
%experimental collaborations. For both methods the observables used are obtained
%from measurements of $D^0\rightarrow K^+\ell\nu$, $D^0\rightarrow K^+K^-, \pi^+\pi^-$, $D^0\rightarrow K^+\pi^-$,
%$D^0\rightarrow K^+\pi^-\pi^0$, $D^0\rightarrow K^+\pi^-\pi^+\pi^-$, and
%$D^0\rightarrow K^0_S\pi^+\pi^-$ decays, as well as CLEO-c results for
%double-tagged
%branching fractions measured at the $\psi(3770)$ resonance (for details see
%previous sections of this review).
%The first method has the advantage that non-Gaussian errors are accounted for,
%whereas the second method has the advantage that it is readily expanded to
%allow for $CP$ violation. In that case three additional parameters are included
%in the fit:
%$A^{}_D\equiv (R^+_D-R^-_D)/(R^+_D+R^-_D)$, $|q/p|$, and
%${\rm Arg}(q/p)\equiv\phi$. When both methods are applied
%to the same set of observables, almost identical results
%are obtained.
%
%%The likelihood function is condensed to one dimension by
%%letting, for any value of a single fit parameter (column 1 of \Table{tab:HFAG}),
%%the other fit parameters take the preferred values. The resulting likelihoods
%%give central values, 68.3\% C.L. intervals and 95\% C.L. intervals are reported in
%%\Table{tab:HFAG}.
%%%The results of the CLEO-c extended fit\cite{cleoc-tqca} are
%%%compared with the HFAG $CP$ conserving fit are also shown in \Table{tab:HFAG}.
%%%The CLEO-c and HFAG results are comparable.
%%The HFAG likelihood function is condensed to two dimensions in
%%a similar manner. \Figure{fig:hfag_mixing_contour} and \Figure{fig:hfag_cpv_contour} show the two-dimensional $1\sigma$-$5\sigma$ contours for $(x,y)$ and
%%$(|q/p|=1+A_M,Arg(q/p)=\phi)$. The HFAG fit excluded the no mixing scenario
%%($x=y=0$) at $5.7\sigma$ - somewhat more restrictive than the CLEO-c WA.
%%The CLEO-c determination of mixing averages
%%%employs a different methodology and
%%does not yet incorporate the most recent results from BABAR\cite{Aubert:2007en} and
%%CDF\cite{Aaltonen:2007uc}.
%%The HFAG average\cite{hfag-charm} includes the
%%results of a fit to the CLEO-c data without external input.
%
%For the global fit, confidence contours in the two dimensions $(x,y)$
%and $(|q/p|,\phi)$ are obtained by letting, for any point in the
%two-dimensional plane, all other fit parameters take their
%preferred values.
The resulting $1\sigma$-$5\sigma$ contours
are shown in Fig.~\ref{fig:hfag_mixing_contour} and Fig.~\ref{fig:hfag_cpv_contour}.
The fits exclude the no-mixing
point ($x\!=\!y\!=\!0$) at $6.7\sigma$ for both the no $\CP$ violation scenario
and the case allowing for $\CP$ violation. One-dimensional
likelihood functions for parameters are obtained by allowing, for
any value of the parameter, all other fit parameters to take their
preferred values. The resulting likelihood functions give central
values, 68.3\% C.L. intervals, and 95\% C.L. intervals as listed
in Table~\ref{tab:HFAG}.

From the results of the HFAG averaging, we can conclude  the following:
\begin{itemize}
\item
The experimental data consistently indicates
that $D^0$ mesons undergo mixing. The effect is presumably dominated
by long-distance processes, and unless $|x|\gg |y|$, it may
be difficult to identify New Physics from mixing alone.
\item
Since $\yCP$ is positive, the $\CP$-even state is shorter-lived,
as in the $K^0$-$\overline K{^0}$ system. However, since $x$ appears to be
positive, the $\CP$-even state is heavier,
unlike in the $K^0$-$\overline K{^0}$ system.
\item
There is no evidence yet for $\CP$ violation in the $D^0$-$\overline D{^0}$
system.
\end{itemize}
%BEGIN TABLE 4
\begin{table}[!htb]
\caption{\label{tab:HFAG}
HFAG Charm Mixing Averages.}
%\vglue -18pt
\begin{tabular}{clcc} \hline\hline
Fit & Parameter & HFAG Average & 95\% C.L. Interval\\
%\hline
%No & $x(\%)$ & $0.98^{+0.26}_{-0.27}$  & \\
%CPV & $y(\%)$ & $0.75\pm 0.18$  & \\
%  & $R_D(\%)$ & $0.335\pm 0.009$  & \\
%  & $\delta_{K\pi}(^\circ)$ & $21.6^{+11.6}_{-12.6}$  & \\
% & $\delta_{K\pi\pi^0}(^\circ)$ & $30.8^{+25.8}_{-25.0}$  & \\
%%\tableheaddoublerule
%Fit & Parameter & HFAG Average & 95\% C.L. Interval \\
\hline
$C\!PV$ & $x(\%)$ & $0.97^{+0.27}_{-0.29}$ & (0.39:1.48) \\
 & $y(\%)$ & $0.78^{+0.18}_{-0.19}$ & (0.41:1.13) \\
 & $R_D(\%)$ &  $0.335\pm 0.009$ & (0.316:0.353) \\
  & $\delta_{K\pi}(^\circ)$ & $21.9^{+11.5}_{-12.5}$ & (-6.3:44.6) \\
 & $\delta_{K\pi\pi^0}(^\circ)$ &  $32.4^{+25.1}_{-25.8}$ & (-20.3:82.7) \\
 & $A_D(\%)$ &  $-2.2\pm 2.5$ & (-7.10:2.67) \\
 & $|q/p|$ & $0.86^{+0.18}_{-0.15}$ & (0.59:1.23) \\
 & $\phi(^\circ)$ & $-9.6^{+8.3}_{-9.5}$ & (-30.3:6.5) \\ \hline\hline
\end{tabular}
\end{table}


%\midfigure{fig:hfag_ycp}
%\FigureInsert{hfag_ycp.eps,width=3.25in}{center}
%\Caption
%World average value for $y_{CP}$, from HFAG~\cite{hfag-charm}.
%\endCaption
%\endfigure

\begin{figure}[!htb]
%\FigureInsert{hfag_contour_mixingcpv.eps,width=3.25in}{center}
\includegraphics[width=0.9\linewidth]{Charm/hfag_contour_mixingcpv.eps}
\caption{\label{fig:hfag_mixing_contour}
Two-dimensional $1\sigma$-$5\sigma$ contours
for $(x,y)$, obtained from a global fit to the measured observables
for $x$, $y$, $|q/p|$, ${\rm Arg}(q/p)$,
$\delta_{K\pi}$, $\delta_{K\pi\pi^0}$, and $R_D$
from
measurements of $D^0\rightarrow K^+\ell\nu$, $D^0\rightarrow h^+h^-$,
$D^0\rightarrow K^+\pi^-$, $D^0\rightarrow K^+\pi^-\pi^0$,
\hbox{$D^0\rightarrow K^+\pi^-\pi^+\pi^-$,} and $D^0\rightarrow K^0_S\pi^+\pi^-$ decays,
and double-tagged branching fractions measured
at the $\psi(3770)$ resonance (from HFAG~\cite{hfag-charm}).}
\end{figure}


\begin{figure}[!htb]
%\FigureInsert{hfag_contour_cpv.eps,width=3.25in}{center}
\includegraphics[width=0.9\linewidth]{Charm/hfag_contour_cpv.eps}
\caption{
Two-dimensional $1\sigma$-$5\sigma$ contours
for $(|q/p|$, ${\rm Arg}(q/p))$, obtained from a global fit to the measured observables
for $x$, $y$, $|q/p|$, ${\rm Arg}(q/p)$,
$\delta_{K\pi}$, $\delta_{K\pi\pi^0}$, and $R_D$
from
measurements of $D^0\rightarrow K^+\ell\nu$, $D^0\rightarrow h^+h^-$,
$D^0\rightarrow K^+\pi^-$, $D^0\rightarrow K^+\pi^-\pi^0$,
$D^0\rightarrow K^+\pi^-\pi^+\pi^-$, and $D^0\rightarrow K^0_S\pi^+\pi^-$ decays,
and double-tagged branching fractions measured
at the $\psi(3770)$ resonance (from HFAG~\cite{hfag-charm}).}
\label{fig:hfag_cpv_contour}
\end{figure}

{ The interpretation of the new results in terms of New Physics is inconclusive.
It is not yet clear whether the effect is caused by $x_D \neq 0$ or $y_D \neq 0$ or both, although the latter is favored,
as shown in Table~\ref{tab:HFAG}. Furthermore, there is no single 5$\sigma$
observation of charm mixing nor is one anticipated from the current $B$ Factories.
This situation will be remedied by results anticipated from \superb.
Table~\ref{tab:mixtab2} shows the sensitivity to mixing in $\DZ\to K^+\pi^-$, $K^+K^-$, and $K^0_S\pi^+\pi^-$ channels from the $\FourS$ data
is in excess of 5$\sigma$ if the lifetime and
mass differences in the $\DZ$ system lie at the upper end of the
range of Standard Model predictions.

Table~\ref{tab:mixtab2} also shows the sensitivity to mixing from two months of running at charm threshold. The sensitivity to the mixing parameters is comparable to
five years at $\FourS$, with different sources of systematic uncertainties.
The $\psiprpr$ data provides unique sensitivity to $\cos\delta_{K\pi}$.
Although
$\cos\delta_{K\pi}$
can be determined from a global fit to $\FourS$ results, the
direct measurement from $\psiprpr$ data allow $y^\prime$ and $x^{\prime 2}$
determined from $\DZ\to K^+\pi^-$ to contribute to the precision determination
of $x$ and $y$.

Although the $D$ mesons from $\psiprpr$ decay are produced nearly at rest in
the center-of-mass frame, the asymmetric $e^+e^-$ collisions make
time-dependent mixing analyses possible.
However, since the production rate of
charm during threshold running and $\FourS$ running is comparable, the
statistical power of the time-dependent analyses near threshold is small.



\begin{table}[!htb]
  \caption{
    Approximate expected precision ($\sigma$) on the measured
    quantities using methods described in the text for the integrated
    luminosity of 75~ab$^{-1}$ at \superb\ at 10~GeV and 300~fb$^{-1}$
    ($\sim$ two months) running at charm threshold.
  }
  \label{tab:mixtab2}
%% GW: add below plus numbers
%The upgraded LHCb numbers are merely the results from Table~\ref{mixtab1} scaled to the
%new integrated luminosity.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{tabular}{cccc}
%\noalign{\vspace{-8pt}}
\\ \hline\hline
Mode & Observable & $\FourS$  & $\psi(3770)$ \\
     &            & (75~ab$^{-1}$) &  (300~fb$^{-1}$)  \\ \hline
$\DZ\!\to\! K^+\pi^-$ & $x^{\prime 2}$  & $3\times 10^{-5}$ & \\
                  & $y^{\prime}$   & $7\times 10^{-4}$ & \\
$\DZ\!\to\! K^+K^-$ & $\yCP$ & $5\times 10^{-4}$ & \\
$\DZ\!\to\! K^0_S\pi^+\pi^-$ & $x$ & $4.9\times 10^{-4}$ & \\
                        & $y$  &  $3.5\times 10^{-4}$ & \\
                        & $|q/p|$  &  $3\times 10^{-2}$ & \\
                        & $\phi$  &  $2^\circ$ & \\
$\psi(3770) \!\to\! \DZ\DZB$ & $x^2$  & &  $(1\!-\!2)\times 10^{-5}$ \\
                         & $y$ & & $(1\!-\!2)\times 10^{-3}$ \\
                & $\cos\delta$ & & $(0.01\!-\!0.02)$ \\
\hline\hline
\end{tabular}
\end{table}

A serious limitation in the interpretation of charm oscillations in terms of New Physics is the theoretical uncertainty on the Standard Model prediction.
However, the recent evidence for oscillations opens the window to
searches for $\CP$ asymmetries that do provide unequivocal New Physics
signals. The sensitivity to these New Physics signals is shown in
Fig.~\ref{fig:hfag_cpv_projection}.
%\superb\ will probe $\CP$ violation in charm mixing at the ${\cal O}(10^{-3})$ level.


\begin{figure}[!htb]
%\FigureInsert{hfag_contour_cpv_75.eps,width=3.25in}{center}
\includegraphics[width=0.9\linewidth]{Charm/hfag_contour_cpv_75.eps}
%\vskip 0.7\linewidth
\caption{\label{fig:hfag_cpv_projection}
Projected two-dimensional $1\sigma$-$5\sigma$ contours with 75 ab$^{-1}$
for $(|q/p|$, ${\rm Arg}(q/p))$, obtained from a global fit to the observables
for $x$, $y$, $|q/p|$, ${\rm Arg}(q/p)$,
$\delta_{K\pi}$, $\delta_{K\pi\pi^0}$, and $R_D$
from the sensitivity estimates in Table~\ref{tab:mixtab2}.
A ``true value'' of $|q/p|=0.90$, ${\rm Arg}(q/p)=0$ is assumed.}
%measurements of $D^0\rightarrow K^+\ell\nu$,
%of $D^0\rightarrow h^+h^-$,
%$D^0\rightarrow K^+\pi^-$,
%$D^0\rightarrow K^+\pi^-\pi^0$, $D^0\rightarrow K^+\pi^-\pi^+\pi^-$,
%and $D^0\rightarrow K^0_S\pi^+\pi^-$ decays,
%and double-tagged branching fractions measured
%at the $\psi(3770)$ resonance.}
\end{figure}



%(In progress)

% David

%\begin{itemize}
%\item
%  Recap of sensitivities which can be reached at SuperB and comparison with other charm physics experiments
%  (CLEO-c, BESIII, SuperKEK, LHCb, Novosibirsk tau-charm). Emphasize that mixing
%  will mainly be used for validation, even if better precisions will be reached than any other experiment before.
%\item
%  Discussion of interplay between running at \FourS and at \psiprpr. Emphasis on model independent way to determine \Dz\Dzb relative
%  strong phase. Results against months of running at \psiprpr.
%\item
%  Brief discussion on our estimates showing that at \psiprpr time dependent CPV measurement could also be done since $\sigma (t) ~ \tau_D$).
%However, this is not the case for running at \psiprpr.
%\end{itemize}

%(David)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section*{$\CP$ violation}
\section{\CP violation}
\label{sec:charm-CPV}

%$\CP$ violation can only be implemented trough a complex phase in some effective couplings.
%To become $\CP$ violation observable, two different and coherent amplitudes have to contribute to an observable.
%This requirement can be implemented through two scenarios: two different $\Delta C=1$ amplitudes of fixed ratio
%leading to the same final state (direct $\CP$ violation),
%\begin{equation}
%\left|\frac{\overline{A}_f}{A_f}\right| \ne 1~,
%\end{equation}
%and $\Dz-\Dzb$ oscillations driven by $\Delta C=2$ dynamics providing the second amplitude, the weight of which varies with time.
%In processes involving oscillations there are two gateways through which $\CP$ violation can enter. The first,
%through
%\begin{equation}
%|q/p| \ne 1~,
%\end{equation}
%which unequivocally constitutes $\CP$ violation in $\Delta C=2$ dynamics (direct $\CP$ violation). $p$ and $q$ are the usual
%complex parameters obtained from diagonalizing the $\Dz - \Dzb$ mass matrix with $|p|^2 + |q|^2 = 1$.
%The second, via
%\begin{equation}
%\phi_f = {\rm arg} \left( \frac{q}{p}\frac{\overline{A}_f}{A_f} \right) \ne 0~,
%\end{equation}
%which reflects the interference of $\CP$ violation in $\Delta C = 1,2$ dynamics ($\CP$ violation in interference between mixing and decay).

%$\CP$ violation can also be searched for in transitions forbidden by $\CP$ invariance, where both the initial and final
%states can be prepared as CP-eigenstates. An example is the transition
%$\psiprpr \to \Dz\Dzb \to f_1 f_2$, where $f_1$ and $f_2$ are different final CP-eigenstates of the same parity.
%However, since the process involve CP-violating decay rates, the observables are of second order in the CP-violating
%parameters, making this strategy probably out of the required sensitivity reach.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection*{Direct $\CP$ violation}
\label{sec:charm-directCPV}

Searches for $\CP$ violation in $\Delta C=1$ transitions can be performed by measuring asymmetries in the partial widths or in final state distributions.

Golden modes
%-or the former
are the Cabibbo-suppressed decays $D^0 \to h^+ h^-$, $h=K,\pi$,
and the doubly Cabibbo-suppressed decay $D^0 \to K^+ \pi^-$.
These studies can be performed either time-integrated or by analyzing the time dependence
of the \Dz and \Dzb decay rates, although in both cases time-integrated asymmetries are measured.
Data at the \FourS provides the largest data sample
with excellent purities (as large as $\sim 99\%$). The contamination from \BB decays can be virtually eliminated by
imposing a $2.5$~\gevc cut on the $D$ momentum in the center-of-mass frame, which preserves more than 85$\%$ of signal events.

The most precise analysis to date~\cite{ref:babarDtoKKandDtoPiPi} compares time-integrated
$\Dz \to h^+ h^-$ and $\Dzb \to h^+ h^-$ rates,
$a_{\CP}^{hh} = [N_{\Dz} - N_{\Dzb}]/[N_{\Dz} + N_{\Dzb}]$, where $N_{\Dz}$ ($N_{\Dzb}$) is the
number of \Dz (\Dzb) mesons decaying into $h^+ h^-$ final state.
In this construction, all $\CP$ violation contributions, direct and
indirect are present. Direct $\CP$ violation in one or both modes would be signaled by a non-vanishing
difference between the asymmetries for $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$, $a_{\CP}^{KK} \neq a_{\CP}^{\pi\pi}$ .
%CP-violating asymmetries in these modes are predicted to be $\sim$ ${\cal O}(10^{-5}) - {\cal O}(10^{-4})$.
There are two main experimental challenges in these measurements.
Firstly, the experimental asymmetry in  \Dz flavor tagging.
This asymmetry is measured by determining the relative detection efficiency for soft pions in data, using
the Cabibbo-allowed decay $D^0 \to K^- \pi^-$ with (tagged) and without (non-tagged) soft-pion flavor tagging,
as a function of the pion-momentum  and the polar angle in the lab frame. For the azimuthal dependence, an
integrated scale factor is sufficient, since charm production is uniform in azimuth.
Since the reconstructed modes are $\CP$-even, this is the only detector asymmetry.
Secondly, the forward-backward (FB) asymmetry in $c\bar{c}$ production at \FourS,
a consequence of the $\gamma/Z^0$ interference and higher order QED corrections
(both at the percent level at this energy), coupled with the asymmetric acceptance of the detector,
which produces a difference in the number of reconstructed $D^0$ and $\bar{D}^0$ events.
This effect is directly measured by determining the number of \Dz and \Dzb events
(after soft pion asymmetry correction) as a function of $\cos\theta_D^{CM}$ and decomposing
these events  into even (representing the $\CP$ asymmetry and independent of $|\cos\theta_D^{CM}|$) and odd
(representing the FB production asymmetry) parts. The associated systematic uncertainties are therefore
not a limiting factor, and are mostly statistical in nature. Other potential
sources of uncertainty are highly suppressed because the
final states are reconstructed identically for $D^0$ and $\bar{D}^0$.
With a \superb\ data sample of 75 ab$^{-1}$, sensitivities at $3\times10^{-4}$ and $4\times10^{-4}$ level,
for $a_{\CP}^{KK}$ and $a_{\CP}^{\pi\pi}$ respectively, are foreseen.

A time-dependent $D$-mixing analysis of DCS (wrong sign) $\Dz \to K^+ \pi^-$ and $\Dzb \to K^- \pi^+$ decays can be
used to separate the contributions of DCS decays from $\DzDzb$ mixing, separately for \Dz and \Dzb.
A direct $\CP$ asymmetry can then be constructed from the difference of DCS \Dz and \Dzb decays,
$A_D = (R_{\Dz} - R_{\Dzb})/(R_{\Dz} + R_{\Dzb})$, where $R_{\Dz}(R_{\Dzb})$  is the \Dz(\Dzb) DCS rate.
%The main advantage of this strategy is that it provides a distinction between direct and indirect $\CP$ violation.
The main experimental difficulties in this analysis are accurate proper time reconstruction and calibration,
together with asymmetry in the \Dz flavor tagging and the modeling of the differences between $K^+$ and $K^-$
absorption in the detector. At \superb, the much smaller luminous region and the
significantly enhanced vertexing capabilities provide proper time significances at the $10\sigma$ level
(3-4 times better than in \babar~\cite{ref:babarDtoKPi}, with decay length resolution of about 80~$\mu$m, $\sim 3\sigma$),
%In the BaBar analysis~\cite{ref:babarDtoKPi}, the most probable value of the proper time resolution is 0.16 ps
%(decay length resolution of about 80~$\mu$m), providing a $3\sigma$ separation.
%At SuperB, with a much smaller luminous region and the significantly enhanced vertexing capabilities,
%the proper time significance will significantly increase (about a factor 3 or 4),
significantly reducing the systematic uncertainties associated with the modeling of the
long decay time component and possible biases.
%from other D decays in the signal region (outliers of the resolution function model) and possible biases.
Systematic uncertainties related to the asymmetry in the soft-pion tagging can be keep under
control using a similar procedure to that outlined above. Corrections %and systematic uncertainties
due to the FB production asymmetry and kaon hadronic interactions can be performed
relying mainly on data, through untagged $\Dz \to K^- \pi^+$ and $\Dzb \to K^+ \pi^-$
decays measured as a function of $\cos\theta_D^{CM}$.
Scaling the statistical uncertainty from the \babar\ analysis to 75 ab$^{-1}$ we obtain a
sensitivity on $A_D$ of $4\times10^{-3}$. To reach or improve this sensitivity level, systematic uncertainties,
currently $15\times 10^{-3}$, will have to be reduced by a factor of five or better, which is feasible since the uncertainty of the systematic corrections scale with the size of the data sample.

For asymmetries in final state distributions, the simplest way is to compare $\CP$ conjugate Dalitz plots for 3-body decays.
Different regions of the Dalitz plot may exhibit $\CP$ asymmetries of varying signs that largely cancel out when one
integrates over the entire phase space, therefore subdomains of the Dalitz plot could contain significantly larger
$\CP$ asymmetries than the whole phase space. Since understanding the dynamics is not an easy goal to achieve,
one could try up to four strategies, three of which are model-independent. First, quantify differences
between the \Dz and \Dzb Dalitz plots in two dimensions. Secondly, look for differences in the angular moments
of \Dz and \Dzb intensity distributions. Thirdly, in a model-dependent approach, look for $\CP$ asymmetries
in the amplitudes describing intermediate states in the \Dz and \Dzb decays. Finally, look for the phase-space
integrated asymmetry. Asymmetries in the \Dz flavor assignment and FB production asymmetries only affect the last
method, and can be kept under control, as discussed above. From the pioneering \babar\ analysis using
$\Dz \to \pi^- \pi^+ \pi^0$ and $\Dz \to K^- K^+ \pi^0$~\cite{ref:babarDtoKKpi0andDtoPiPiPi0},
sensitivities at $3\times10^{-4}$ and $9\times10^{-4}$ level, respectively, are anticipated.


For more complex final states other probes have to be employed.
A golden example is discussed below.
%% TJG labelling is not working correctly
% a golden example discussed in Sec.~\ref{sec:Todd}.


%  Double Cabibbo suppressed decays, $\Dp \to \KS \pip$.
%
% Fernando. Contact Brian Meadows; Jonathon Coleman.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection*{Indirect $\CP$ violation at the  \FourS and \psiprpr}
\label{sec:charm-indirectCPV}
% Arantza

$\CP$ violation in mixing can be investigated from the data taken at the \FourS and at the \psiprpr resonances
in semi-leptonic transitions.
%following different analysis strategies.
In both cases one measures an asymmetry from events in which the $D^0$ or $\bar D^0$, previously flavor tagged,
has oscillated (signaled as a wrong sign decay),%~\cite{ref:charm_cicerone},
\begin{equation}
a_{SL} = \frac{N^{--}(t)-N^{++}(t)}{N^{--}(t)+N^{++}(t)} = \frac{|q|^4 - |p|^4}{|q|^4 + |p|^4}~,
\end{equation}
where $N^{--}$ ($N^{--}$) represents the number of
$\Dz \to \ell^- \nu X$ ($\Dzb \to \ell^+ \nu X$) decays when the other $D$ meson was tagged as \Dz (\Dzb) at production time.
Data at the \psiprpr benefit from a very clean environment with almost no background. Several decay
channels can be exclusively reconstructed
%and combined
to increase the asymmetry sensitivity. Considering
the $D^0$ and $\bar D^0$ both decaying into $K^-\pi^+$, $K^-\pi^+\pi^0$, $K^-\pi^+\pi^+\pi^-$, $K^-e^+\nu$,
$K^-\mu^+\nu$, $K^{*-}e^+\nu$, $K^{*-}\mu^+\nu$, $K^{*-}e^+\nu$,  $\pi^- e^+\nu$, $\pi^-\mu^+\nu$, $K^-K^+$ and $\pi^-\pi^+$,
and using recent results for the $\DzDzb$ mixing parameters $x$ and $y$ \cite{ref:hfag}, a sensitivity to $\CP$
violation of 2.5$\%$ in one month of running at threshold is expected. The quantum correlation ensures that the
same-sign combinations
can only be due to mixing; thus hadronic modes can be treated like the semileptonic decays (no DCS contribution).
Control of systematic uncertainties is expected at the percent
level, dominated by channels with $\pi^0$ and $\nu$ particles~\cite{ref:cleoc_hbr,ref:cleoc_slbr}. Missing mass techniques with full reconstruction of
\psiprpr $\to D \bar D$ events, omitting one of the product particles, can be used to evaluate the accuracy in the reconstruction.
Large control samples of decay channels with unequivocal particle content like $D^0\to K^0_s\pi^+\pi^-$ and $D^+\to K^-\pi^+\pi^+$ will reduce
the uncertainty on PID efficiencies. Other sources of systematic uncertainties will also benefit from the precise measurement of the beam energy
and improved detector performance.
% {\bf (1m = 150/fb)}.

At the \FourS, the soft pion coming from $D^*$ decays ($D^{*+} \to D^0 \pi^+$)
can be used to tag the flavor of the $D^0$. The measurement of wrong sign leptons in
semileptonic decays then provides a clear signature of a mixed event. Data are taken from the continuum.
%Background events from $B$ decays can be reduced imposing a 2.5~\gevc cut on the $D$
%momentum in center-of-mass frame which keeps more than 85$\%$ of signal events and suppress almost all of the $B \bar B$
%events. %{\bf (other bkg?) }.
Background events from $B$ decays can be reduced by imposing a 2.5~\gevc cut on the $D$ momentum. %{\bf (other bkg?) }.
With this method, the statistical sensitivity in the decay asymmetries would reach the $1\%$ level in one
year of data taking. Systematic uncertainties are foreseen to arise from the control of backgrounds and PID management
(mainly lepton identification), which will benefit from the vertex capabilities to suppress the background
and large control samples to study the PID.
%{\bf (1y = 15/ab)}.
%The main issue here is to be able to control systematic uncertainty to this extend.
%{\bf (develop, try to improve and evaluate, ask K. Flood)}

  %Semileptonic and hadronic decays, running at \FourS and at \psiprpr. Quote reach at \psiprpr per month of running.
  %Fernando, Arantza.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection*{$\CP$V in the interference of mixing and decay}
\label{sec:charm-interferenceCPV}

% Gabriele

%Several experiments have now shown evidence for mixing in D mesons at
%the level of $1\%$~\cite{Aubert:2007wf,Staric:2007dt,Abe:2007rd,dmixcp}
%which is consistent with Standard Model predictions~\cite{foundations}.

%Unless there is new physics, $\CP$ violation in D decays is expected to be
%unobservably small and an observation it would be a clear sign of NP.

%Such $\CP$ violation effects can be
%searched in D decays into $\CP$ eigenstates, e.g.  $D \to \Kp\Km$, $D \to
%\pip\pim$, $D \to \KS\rho$, $D \to \KS\phi$.

$\CP$ violation in the interplay of $\Delta C = 1,2$ dynamics can be searched for through time-dependent analyses
of $\Dz \to K^+ K^-$ and $\Dz \to \pi^+ \pi^-$ decays. $\CP$ violation and $\DzDzb$ mixing alter the decay time
distribution of $\Dz$ and $\Dzb$ mesons that decay into final states of specific $\CP$, and a time-dependent
analysis of the tagged \Dz and \Dzb intensities allows a measurement of the $\phi_f$.
To a good approximation, these decay time distributions can be treated as exponential, with effective
lifetimes \tauhhp and \tauhhm.
%
%%, given by
%% \begin{equation}
%% \begin{array}{rcl}
%% \tauhhp   &=&
%% \tauKpi\left[ 1 + r_m \left( y\cos\varphi_f -
%%                                  x\sin\varphi_f \right) \right]^{-1} \\
%% \tauhhm &=&
%% \tauKpi\left[ 1 + r_m^{-1} \left( y\cos\varphi_f +
%%                                       x\sin\varphi_f \right) \right]^{-1} \;,
%% \end{array}
%% \end{equation}
%% where $\tauKpi$ is the lifetime for the Cabibbo-favored decays
%% $D^0 \to K^-\pi^+$ and $\Dzb \to K^+\pi^-$, and $\tauhhp$ ($\tauhhm$)
%% is the lifetime for the Cabibbo-suppressed decays
%% of the $D^0$ ($\Dzb$) into \CP-even final states (such as $K^-K^+$
%% and $\pi^-\pi^+$).

The effective lifetimes can be combined into the quantities $\yCP$ and $\Delta Y$:
\begin{displaymath}
\begin{array}{rcl}
\displaystyle y_{\CP}%L
= \frac{\tauKpi}{\langle\tauhh\rangle} - 1\;,%%\\[0.5cm]
&&
\displaystyle\Delta Y = \frac{\tauKpi}{\langle\tauhh\rangle} A_\tau \;,
\label{eq:yCPcalc}
\end{array}
\end{displaymath}
where $\langle \tauhh \rangle = (\tauhhp+\tauhhm)/2$ and
$A_\tau = (\tauhhp-\tauhhm)/(\tauhhp+\tauhhm)$.
%% Both $\yCP$ and $\deltaY$
%% are zero if there is no $D^0$-$\Dzb$ mixing.
%% In the limit of \$\CP$ conservation, $\y$\CP$ = y$ and $\deltaY = 0$,
%% with the convention that $\cos\varphi_f > 0$.
%
The golden mode is $\Dz \to \Kp\Km$, since the combinatorial background
is $\sim 10\times$ smaller than in the $\pi^+\pi^-$ channel, and the
selected sample is $\sim 2\times$ larger.  $\Dz \to \KS\phi$ instead has a
large ($\sim10\%$) contribution from $S$ wave, so it is better analyzed
using the Dalitz plot technique (see Sec.~\ref{sec:charm-3body}).

The \superb\ sensitivity to $\yCP$ and $\deltaY$ in the $KK$
and $\pi\pi$ modes can be extrapolated from the current \babar\
analysis~\cite{ref:babarDtoKKandDtoPiPi}, assuming that the systematic errors can be kept
under control. Provided that $\CP$ violation in mixing is small,
the sensitivity to the $\CP$-violating phase is dominated by
the first term in the expression for $\yCP$ and $\deltaY$.
\begin{eqnarray*}
2 y_{\CP}    = (|q/p|+|p/q|) y \cos\phi - (|q/p|-|p/q|) x \sin\phi, \\
2 \deltaY = (|q/p|-|p/q|) y \cos\phi - (|q/p|+|p/q|) x \sin\phi,
\end{eqnarray*}
therefore we can estimate the sensitivity as
$\delta(\cos \phi)\simeq \delta (y_{\CP}) /y \simeq  3\times 10^{-4} / y$,
$\delta(\sin \phi)\simeq \delta (\deltaY) / x \simeq  3\times 10^{-4} / x$.
%The results are summarized in Table~\ref{tab:kkpipi}.

%\begin{table}[htb]
%\centering{
%\begin{tabular}{ccccc}
%decay channel& $y_{cp}$         & $\Delta Y$      & $\cos \phi$ & $\sin \phi$\\
%\hline
%$K^+K^-$     & $3\times 10^{-4}$ & $3\times 10^{-4}$ & $3\times 10^{-4}/y $ & $3\times 10^{-4}/x $ \\
%%$\pi^+\pi^-$   &  xxx              &   xxx  \\
%\hline
%\end{tabular}
%}
%\caption{Sensitivity to $\CP$ violation parameters with 75 $ab^{-1}$
%  using $D^0\to f_{CP}$ decays.}
%\label{tab:kkpipi}
%\end{table}

Most of the systematic errors affecting the signal cancel in the
lifetime ratio. The errors associated with the background are
unrelated between \Dz and \Dzb and do not cancel; however they do improve
with statistics. In addition, the superior resolution of
the vertex detector will further reduce the systematic errors
associated with the position measurement. We therefore expect that the
systematic errors can be kept under control.
%% In the Babar systematic studies the main
%% remaining one is the cut on the error on the proper time which is
%% related to the fraction of outliers for which $\sim 2/3$ is statistical
%% and $\sim 1/3$ is systematic.%\footnote{from private communication}.

One underlying assumption in the recent \babar\
analysis~\cite{ref:babarDtoKKandDtoPiPi} is that the resolution bias
is the same for all the channels ($K\pi$, $KK$, $\pi\pi$) and does
not depend on the polar angle $\theta$. This could introduce a bias in
the measurements, because of the different polar angle acceptance in
the various channels. With a higher statistics sample, however, this
systematic effect can be overcome by splitting the sample into polar angle
(or other variable) intervals.  The production asymmetry is not
important with \babar\ statistics, but could become significant
at sensitivities of the order of few $\times 10^{-4}$. However this
can be handled using control samples, such as the untagged \Dz, which
have about 5 times more events (assuming \Dz and \Dstar have the same
asymmetry), as discussed in Sec.~\ref{sec:charm-directCPV}.

%% The total systematic error on the BaBar analysis is presently
%% $17\times 10^{-4}$. We estimate the total error with the SuperB sample
%% by adding in quadrature the statistical and systematic errors
%% (rescaled appropriately for the luminosity) with an estimate for the
%% irreducible part of the systematic error. The sensitivity as a
%% function of the luminosity is shown in Fig~\ref{fig:kkerr}.
%
%% \vskip0.5cm
%% \begin{figure}[htb] \begin{center}
%% \includegraphics[width=0.6\linewidth]{ycperr.eps}
%% \includegraphics[width=0.6\linewidth]{dyerr.eps}
%% \caption{Total and statistical error on $y_{cp}$ (top) and $\Delta Y$
%%   (left) extracted from $\Dz \to K^+K^-$ as a function of the integrated luminosity.}
%% \label{fig:kkerr}
%% \end{center} \end{figure}

  %Use decays into $\CP$ eigenstate, e.g. $D \to \Kp\Km$, $D \to \pip\pim$, $D \to \KS\rho$, $D \to \KS\phi$.
  %$D \to \Kp\Km$ is the golden mode. $D \to \KS\phi$ has large ($\sim10\%$ contribution from S-wave, so better if analyzed
  %using Dalitz plot technique). Measurement exclusively to be done at \FourS.

  %Contact BaBar authors: Chavez, Carlos A.; Coleman, Jonathon; Cowan, Ray; Flood, Kevin; Lockman, William; Petersen, Brian).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection*{$T$ odd correlations}
\label{sec:Todd}

% beginning of Ikaros, part 2

All $\CP$ asymmetries observed so far have surfaced in partial widths -- with one notable exception:
the forward-backward asymmetry $\langle A \rangle$ in the $\pi^+\pi^-$ and $e^+e^-$ planes in
$K_L \to \pi^+\pi^-e^+e^-$. $\langle A \rangle \simeq 14\%$ had been
predicted -- and confirmed by experiment -- as being driven by the indirect $\CP$ impurity $|\eta_{+-}| \simeq 0.23 \%$.
The reason for this magnification by two orders of magnitude is well understood:
$\langle A \rangle$ is induced by the interference between a $\CP$-violating and a $\CP$-conserving amplitude,
both of which are suppressed, albeit for different reasons. This explains why the enhancement of the $\CP$ asymmetry
comes at the expense of the branching ratio, which is about
$3\cdot 10^{-7}$; \ie, one has traded branching fraction for the size of the asymmetry.

It is possible that a similar effect and enhancement occurs in the analogous mode
$D_L \to K^+K^-\mu^+\mu^-$, where $D_L$ denotes the ``long-lived'' neutral $D$ meson. This mode
can be studied uniquely at \superb operating at the $\psi (3770)$ by
$\CP$-tagging the other neutral $D$ meson produced as a ``short-lived'' $D_S$:
\beq
e^+e^- \to \gamma^* \to \DzDzb \to [K^+K^-]_D D_L
\eeq

There is a more general lesson from the $\KL \to \pi^+\pi^-e^+e^-$ example, namely that
$\CP$ violation could surface in an enhanced  fashion in multi-body final states. This could turn
an apparent vice in charm decays -- the preponderance of multi-body final states -- into a virtue.
This issue will be addressed in detail in Sec.~\ref{sec:charm-3body}.
%The one drawback is the initial `overhead' needed for setting up the analysis. Yet such an investment is likely to bring great
%dividend in the long run: not only can one hope for numerically larger asymmetries, but also for better control
%over systematics due to nontrivial constraints and cross checks inherent in a Dalitz plot analysis.

These considerations also apply to four-body modes, although less experience with such studies has been accumulated so far.
Some intriguing pilot studies have been performed on a comparison of
$D^0 \to f$ and $\Dzb \to f$, $f=K ^+K^- \pi^+\pi^-$ channels. Denoting by $\phi$ the angle between
the $\pi^+\pi^-$ and $K^+K^-$ planes, one has

\beq
\frac{d\Gamma}{d\phi}(D^0 \to f) =
\Gamma_1 {\rm cos}^2 \phi + \Gamma_2 {\rm sin}^2 \phi + \Gamma_3 {\rm cos} \phi {\rm sin}\phi~,
\eeq
%
\beq
\frac{d\Gamma}{d\phi}(\overline D^0 \to f) =
\overline \Gamma_1 {\rm cos}^2 \phi + \overline \Gamma_2 {\rm sin}^2 \phi - \overline \Gamma_3 {\rm cos} \phi {\rm sin}\phi~.
\eeq
%
%$$
%\frac{d\Gamma}{d\phi}(D^0 \to K^+K^- \pi^+ \pi^-) =
%$$
%\beq \Gamma_1 {\rm cos}^2 \phi +
%\Gamma_2 {\rm sin}^2 \phi + \Gamma_3 {\rm cos} \phi {\rm sin}\phi
%\eeq
%$$
%\frac{d\Gamma}{d\phi}(\overline D^0 \to K^+K^- \pi^+ \pi^-) =
%$$
%\beq
%\overline \Gamma_1 {\rm cos}^2 \phi +
%\overline \Gamma_2 {\rm sin}^2 \phi - \overline \Gamma_3 {\rm cos} \phi {\rm sin}\phi
%\eeq
Upon integrating over $\phi$, the $\Gamma_3$ and $\overline \Gamma_3$ terms cancel;
$(\Gamma_1, \Gamma_2) \neq (\overline \Gamma_1, \overline \Gamma_2)$ thus represents a
$\CP$ asymmetry in the partial widths. The $\Gamma_3$ and $\overline \Gamma_3$ terms can be projected out by integrating over two quadrants:
\begin{eqnarray}
\langle A \rangle = \frac{\int _0^{\pi/2}d\phi \frac{d\Gamma}{d\phi} - \int _{\pi/2}^{\pi}d\phi \frac{d\Gamma}{d\phi}}
{\int _0^{\pi}d\phi \frac{d\Gamma}{d\phi}}= \frac{2\Gamma_3}{\pi (\Gamma_1 + \Gamma_2)}~,\\
\langle \overline A \rangle =
\frac{\int _0^{\pi/2}d\phi \frac{d\overline \Gamma}{d\phi} -
\int _{\pi/2}^{\pi}d\phi \frac{d\overline \Gamma}{d\phi}}
{\int _0^{\pi}d\phi \frac{d\overline \Gamma}{d\phi}}=
\frac{2\overline \Gamma_3}{\pi (\overline \Gamma_1 + \overline \Gamma_2)}~.
\end{eqnarray}
While $\Gamma_3$ and $\overline \Gamma_3$ represent $T$-odd moments, they do not necessarily
signal $T$ violation, since they could be induced by strong final state interactions. Yet
\beq
\Gamma_3 \neq \overline \Gamma_3 \; \; \Longrightarrow \; \; { \CP \; {\rm violation}}.
\eeq
Such an analysis is theoretically clean, since the dependence on the angle $\phi$ is specifically predicted, which in
turn allows cross checks to control experimental systematics.

Alternatively, one can define another $T$-odd correlation among the pion and kaon momenta, namely
$C_T \equiv \vec p_{K^+} \cdot (\vec p_{\pi^+} \times \vec p_{\pi^-})$ for $D^0$  and
$\overline C_T \equiv \vec p_{K^-} \cdot (\vec p_{\pi^-} \times \vec p_{\pi^+})$ for $\Dzb$.
Similar to the previous case one has: $C_T \neq - \overline C_T \; \; \Longrightarrow$  \CP violation.
One can then construct $T$-odd moments
\begin{eqnarray}
A_T &=& \frac{\Gamma(C_T > 0 ) - \Gamma(C_T < 0 )}{\Gamma(C_T > 0 ) + \Gamma(C_T < 0 )}~, \\
\overline A_T &=& \frac{\Gamma(\overline C_T > 0 ) -
\Gamma(\overline C_T < 0 )}{\Gamma(\overline C_T > 0 ) + \Gamma(\overline C_T < 0 )} \;~,
\end{eqnarray}
and therefore
\beq
A_{\not T} = \frac{1}{2} (A_T - \overline A_T) \neq 0 \; \; \Longrightarrow \; \;
{\CP \; {\rm violation}}.
\eeq
A preliminary study based on 380 fb$^{-1}$ of \babar\ data suggests a sensitivity of $5.3 \times 10^{-3}$
in $A_{\not T}$ that
%would extrapolate to $1\cdot 10^{-3}$ for 10 $ab^{-1}$ and presumably significantly less for 75 $ab^{-1}$.
%With a sample of 10 $ab^{-1}$ one can analyze even time slices of $A_{\not T}$.
would extrapolate to $4 \times 10^{-4}$ for 75 ab$^{-1}$. With such a sample one can analyze even time slices of $A_{\not T}$.
These are very promising sensitivities.

Similar $\CP$ studies can be performed for other four-body modes, and one can also compare
$Y^0_L$ moments and even full amplitude analyses.


\subsection*{Charm baryon decays}

Charm baryons decays are sensitive only to direct $\CP$ violation.
Longitudinally polarized beams -- motivated mainly by $\CP$ studies in $\tau$ production and decays --
provide an intriguing handle for $\CP$ studies in charm baryon decays, since charm baryons would be produced with a net
longitudinal polarization that would allow the formation of novel $\CP$-odd correlations with the momenta of the particles in
the final state. The control of the sign of longitudinal polarization provides an excellent handle on systematics.

%% end of Ikaros, part 2.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section*{Mixing and $\CP$V in 3-body decays}
\section{Mixing and $\CP$V in 3-body decays}
\label{sec:charm-3body}

A Dalitz plot analysis of
 $\Dz \to \KS \pip \pim$ events provides a golden method for studying mixing and $\CP$ violation in mixing/decay/interference. If Dalitz plot model systematics can be kept under control, direct $\CP$-violation
 can also be investigated.
Present \babar\ data~\cite{Aubert:2005iz} show that at the \FourS, signal events from the decay chain $\Dstarp \to \Dz \pip$ with
 $\Dz \to \KS \pip \pim$ can be selected at a rate close to 1000/\invfb with a purity of 97.0\%, and a mistag probability
 of 0.1\%. \KS are reconstructed in the $\pip\pim$ final state; a requirement that the \KS proper time be $\le 8 \tau_S$
allows us to reduce \KL contamination to a level of $10^{-5}$.
Reconstructing the $\Dz \to \KS \pip\pim$ decay vertex, the \Dz proper time ($\tau_D$) can be measured with
  an average error of $\pm 0.2\ps$ in \babar\ and $\pm0.1\ps$ at \superb, to be compared with the \Dz
 lifetime of 0.4\ps.
\par
We use the invariant mass of $K\pi$ pairs: $m_+^2=m^2(\KS,\pip)$ and $m_-^2=m^2(\KS,\pim)$, and we define
the following Dalitz plot amplitudes ($f_D$) and probabilities ($p_D$), which
also depend on $t$:
%
%
%
\begin{eqnarray}
p_D(m_+^2, m_{-}^2,t) &\equiv& | f_D(m_+^2,m_{-}^2,t) |^2  \quad \Dz \textrm{tag}\\
\overline{p}_D(m_+^2, m_{-}^2,t) &\equiv& | \overline{f}_D(m_+^2,m_{-}^2,t) |^2 \quad \Dzb \textrm{tag}
\end{eqnarray}
%
%
%
The signatures for interesting processes are the following ones:
\begin{itemize}

\item  Mixing without \CP violation
\begin{eqnarray}
 p_D(m_+^2, m_{-}^2,t) & = & \overline{p}_D(m_-^2, m_{+}^2,t) \quad  \forall\ t \quad  \textrm{but}\\
 p_D(m_+^2, m_{-}^2,0) & \neq & p_D(m_+^2, m_{-}^2,t)
\end{eqnarray}
\item \CP violation in mixing
\begin{eqnarray}
 p_D(m_+^2, m_{-}^2,0) & = & \overline{p}_D(m_-^2, m_{+}^2,0)  \quad  \textrm{and}\\
 p_D(m_+^2, m_{-}^2,t) & \neq & \overline{p}_D(m_-^2, m_{+}^2,t)
\end{eqnarray}
\item Direct \CP violation
\begin{equation}
 p_D(m_+^2, m_{-}^2,0)  \neq  \overline{p}_D(m_-^2, m_{+}^2,0)
\end{equation}
\end{itemize}
%
%
%
and the quantities, to be measured, that enter in the previous Dalitz plot distribution functions, are:
$x$, $y$ (mixing parameters), $|q/p|$ or $\epsilon=\frac{1-|q/p|}{1+|q/p|}$ and $\phi=\arg(\frac{q \bar A_f}{p A_f})$
(\CP-violation parameters).
\par
$x$, $y$, $\epsilon$ and $\phi$ can be extracted in a Dalitz model-dependent
analysis with the isobar or K-matrix approach, using global fits. Examples are
described in references~\cite{Asner:2005sz,Aubert:2005iz}.
For the model-dependent approach,
 we conservatively estimate the \superb\ sensitivity at 75 \invab by extrapolating from the current analyses.
 Statistical errors can be scaled with the square root of luminosity. The result exceeds
 the desired goal of $10^{-3}$, a level not reachable by BES-III.
The second source is from systematic errors due to the experiment. They are mainly due to background parametrization,
 efficiency variation over the Dalitz plot, experimental resolution biases on Dalitz plot variables, decay time
 parametrization, and mistag fractions. Background parametrization is checked with sidebands (according to the
 Monte Carlo, the background does not peak in the \Dz mass signal region), and scales with statistics.
 Efficiency variation studied with Monte Carlo events scales with the Monte Carlo statistics.
Biases on Dalitz plot variable mass resolution are negligible. Decay time parametrization improves with the size of the data sample and due to the
 time resolution at \superb. Mistag fractions can be checked with other final $D$ states;
 their contribution is negligible. It is thus plausible that the errors arising from experimental sources can be
scale with statistics as well, but we prefer to be conservative, and evaluate these systematic errors using an additional safety factor of two.
These errors are shown in Table~VI;   %%%%%%Table~\ref{tab:dalitz_belle};
we can see that they are smaller than the statistical errors.
%
%
%
{
\begin{table}[!htb]
\caption{\label{tab:dalitz_belle}
Current Belle errors with 0.54 \invab on relevant \newline
mixing and \CP violation parameters.}
\begin{tabular}{lcccc}
\hline\hline
Par. & Stat.         &  Exp. Syst.      &  Model Syst. &  Total \\    \hline
$x$ ($10^{-4}$)        & 30.0 & 8.0  & 12.0 & 33.3 \\
$y$ ($10^{-4}$)        & 24.0 & 10.0 &  7.0 & 26.9 \\
$\epsilon$ ($10^{-4}$) & 15.0 & 2.5  &  4.0 & 15.7 \\
$\phi$ (deg)           & 17.0 & 4.0  &  3.0 & 17.7  \\ \hline\hline
\end{tabular}
\end{table}
}
%
%
{\begin{table}[!htb]
\caption{\label{tab:dalitz_sens}
\superb\ errors with 75 \invab on relevant \newline
mixing and \CP violation parameters.}
\begin{tabular}{lcccc}
\hline\hline
Par. & Stat.         &  Exp. Syst.      &  Model Syst. &  Total  \\ \hline
$x$ ($10^{-4}$)        & 2.5  & 1.4   & 4.0 & 4.9  \\
$y$ ($10^{-4}$)        & 2.0 & 1.7  &  2.3 &  3.5  \\
$\epsilon$ ($10^{-4}$) & 1.3 & 0.4   &  1.3 & 1.9  \\
$\phi$ (deg)           & 1.4 & 0.7   &  1.0 & 1.9 \\  \hline\hline
\end{tabular}
\end{table}
}

The last, but not the least important, source of systematic errors, is the
model used, typically isobar or \hbox{K-matrix} models or a partial-wave
analysis. Uncertainties arise from radius parameters, masses and widths of the
resonances, and the choice of resonances included in the fit.
Recent results from CLEO and Belle~\cite{Asner:2005sz,Abe:2007rd} have, however, demonstrated that the mixing and \CP violation parameters
 are not very sensitive to Dalitz model variations.
The sensitivity to models will be checked using two model independent approaches:
\begin{itemize}
\item With a very large data sample, a partial-wave analysis is capable to determine the amplitude and phase
 variation over the phase space directly from data.
\item Data collected at charm threshold will make the \DzDzb relative phase accessible~\cite{White:2007br}.
\end{itemize}
%
%
%
Even if it is extremely difficult to make predictions on the Dalitz model systematics at \superb, it is
 reasonable to assume that these will be substantially reduced with respect to the present errors from Belle~\cite{Abe:2007rd}.   By comparing the CLEO analysis based on 9.0~\invfb with the Belle analysis based on
 540~\invfb, we realize an improvement of the Dalitz model systematic error of more than a factor of four on
 average. This improvement is mainly due to the fact that the larger statistics data sample allows
 a better determination of the Dalitz model parameters.
Contemplating a factor of three improvement for the model error
 at \superb\ seems conservative, since it does not take into account the benefits of partial-wave analysis,
 and the use of data collected at charm threshold.
 Sensitivity predictions for mixing and \CP violation parameters at \superb\ are shown in Table~VII.
 %Table~\ref{tab:dalitz_sens}.



%Golden method for mixing and $\CP$ violation from interference between mixing and decay (and may be also direct $\CP$ violation
%if Dalitz model systematics can be kept under control.
%Also, systematic errors in this analysis are different from other analysis (like lifetime ratio from $D \to \Kp\Km$).
%Must evaluate how the \psiprpr data (per month of running) impact the Dalitz systematics from the time-dependent analysis
%using \FourS data. Could take the current BaBar Dalitz model (not yet published, to be done very soon), generate toy MC event,
%count number of events in the various bins, then estimate the sensitivity on strong phase.

%David, Nicola, Giovanni.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{thebibliography}{99}

\vbox{
\bibitem{ref:hfag} Heavy Flavor Averaging Group (E.~Barberio {\em et al.}), [arXiv:hep-ex/0603003].
Updates and plots:\\
{\small http://www.slac.stanford.edu/xorg/hfag}.
}
%: Charm mixing parameters, \\
%{\scriptsize http://www.slac.stanford.edu/xorg/hfag/charm/index.html}.\\
%Values used in the document are Charm'07 averages, $x=0.0081\pm0.0033$, $y=0.0031\pm0.0028$.

%\bibitem{ref:charm_cicerone} S.~Bianco, F.~L.~Fabbri, D.~Benson and I.~Bigi, Il Nuovo Cimento, 26N.7, 1-200 (2003).

%

\bibitem{pdg2008} D.~M.~Asner, %``Review of $\DzDzb$ Mixing'' -
 to appear in the Review of Particle Physics.

\bibitem{Asner:2005wf}
  D.~M.~Asner and W.~M.~Sun,
  %``Time-Independent Measurements of D0-D0bar Mixing and Relative Strong Phases
  %Using Quantum Correlations,''
  Phys.\ Rev.\  D {\bf 73}, 034024 (2006)
  [arXiv:hep-ph/0507238].

\bibitem{Aubert:2007wf}
  B.~Aubert {\it et al.}  [\babar\ Collaboration],
  %``Evidence for D0 - anti-D0 mixing,''
  Phys.\ Rev.\ Lett.\  {\bf 98}, 211802 (2007)
  [arXiv:hep-ex/0703020].

\bibitem{Aaltonen:2007uc}
T.~Aaltonen {\it et al.}  [CDF Collaboration],
  %``Evidence for D0-D0bar mixing using the CDF II Detector,''
  Phys.\ Rev.\ Lett.\  {\bf 100}, 121802 (2008)
  [arXiv:0712.1567 [hep-ex]].

\bibitem{Zhang:2006dp}
  L.~M.~Zhang {\it et al.}  [Belle Collaboration],
  %``Improved constraints on D0 - anti-D0 mixing in D0 --> K+ pi- decays at
  %Belle,''
  Phys.\ Rev.\ Lett.\  {\bf 96}, 151801 (2006)
  [arXiv:hep-ex/0601029].

\bibitem{Staric:2007dt}
  M.~Staric {\it et al.}  [Belle Collaboration],
  %``Evidence for $D^0 - \bar{D}^0$ Mixing,''
  Phys.\ Rev.\ Lett.\  {\bf 98}, 211803 (2007)
  [arXiv:hep-ex/0703036].

\bibitem{Aubert:2007en}
  B.~Aubert {\it et al.}  [\babar\ Collaboration],
  %``Measurement of D0-anti-D0 Mixing using the Ratio of Lifetimes for the
  %Decays D0 --> K-pi+, K-K+, and pi-pi+,''
  arXiv:0712.2249 [hep-ex] - submitted to Phys. Rev. D.

\bibitem{Abe:2007rd}
  K.~Abe {\it et al.}  [Belle Collaboration],
  %``Measurement of D0-D0bar mixing in D0->Ks pi+ pi- decays,''
  Phys.\ Rev.\ Lett.\  {\bf 99}, 131803 (2007)
  [arXiv:0704.1000 [hep-ex]].

\bibitem{Schwartz:2007fw}
A.~J.~Schwartz,
%``Searches for Mixing and $\CP$ Violation in the D0-D0bar System,''
{\it Proceedings of 5th Flavor Physics and $\CP$ Violation Conference (FP$\CP$ 2007), Bled, Slovenia, 12-16 May 2007, pp 024}
  [arXiv:0708.4225 [hep-ex]].


\bibitem{Schwartz:2008}
A.~J.~Schwartz,
%``Searches for Mixing and $\CP$ Violation in the D0-D0bar System,''
{\it Proceedings of the BES-Belle-CLEO-\babar\ Workshop on Charm Physics,
IHEP, Beijing, 26-27 November 2007.}
[arXiv:0803.0082 [hep-ex]].

\bibitem{hfag-charm}
{Heavy Flavor Averaging Group (HFAG)-charm subgroup\hfil} \\
{\small http://www.slac.stanford.edu/xorg/hfag/charm/}.

%

\bibitem{ref:babarDtoKKandDtoPiPi} B.~Aubert {\it et al.}  [\babar\ Collaboration],
  %``Search for CP Violation in the Decays D0 --> K- K+ and D0 --> pi- pi+,''
  Phys.\ Rev.\ Lett.\  {\bf 100}, 061803 (2008)
  [arXiv:0709.2715 [hep-ex]].

\bibitem{ref:babarDtoKPi} B.~Aubert {\it et al.}  [\babar\ Collaboration], Phys.\ Rev.\ Lett. {\bf 98}, 211802 (2007) [arXiv:hep-ex/0703020].

\bibitem{ref:babarDtoKKpi0andDtoPiPiPi0} B.~Aubert {\it et al.}  [\babar\ Collaboration], submitted to Phys.\ Rev.\ Lett. [arXiv:0802.4035].

\bibitem{ref:cleoc_hbr}
Q. He {\it et al.} [CLEO Collaboration], Phys.\ Rev.\ Lett. {\bf 95}, 121801 (2005), Erratum-ibid. {\bf 96}, 199903 (2006) [arXiv:hep-ex/0504003].

\bibitem{ref:cleoc_slbr}
T. E. Coan {\it et al.} (CLEO Collaboration) Phys.\ Rev.\ Lett. {\bf 95}, 181802 (2005) [arXiv:hep-ex/0506052].

\bibitem{Aubert:2005iz}
  B.~Aubert {\it et al.}  [\babar\ Collaboration],
  %``Measurement of $\gamma$ in $B^\mp \to D^{(*)} K^\mp$ decays with a Dalitz
  %analysis of $D \to K^0_S \pi^- \pi^+$,''
  Phys.\ Rev.\ Lett.\  {\bf 95}, 121802 (2005)
  [arXiv:hep-ex/0504039].
  %%CITATION = PRLTA,95,121802;%%


\bibitem{Asner:2005sz}
  D.~M.~Asner {\it et al.}  [CLEO Collaboration],
  %``Search for D^0 - barD^0 Mixing in the Dalitz Plot Analysis of D^0 -->
  %K_S^0 pi^+ pi^-,''
  Phys.\ Rev.\  D {\bf 72}, 012001 (2005)
  [arXiv:hep-ex/0503045].
  %%CITATION = PHRVA,D72,012001;%%


%\bibitem{Abe:2007rd}
%  K.~Abe {\it et al.}  [Belle Collaboration],
%  %``Measurement of D0-D0bar mixing in D0->Ks pi+ pi- decays,''
%  Phys.\ Rev.\ Lett.\  {\bf 99}, 131803 (2007)
%  [arXiv:0704.1000 [hep-ex]].
%  %%CITATION = PRLTA,99,131803;%%


\bibitem{White:2007br}
  E.~White and Q.~He  [CLEO Collaboration],
  %``Impact on $\gamma\phi_3$ from CLEO-c Using CP-tagged $D\toK_{S,L}\pi\pi$
  %Decays,''
  arXiv:0711.2285 [hep-ex].
  %%CITATION = ARXIV:0711.2285;%%


\end{thebibliography}


\onecolumngrid\twocolumngrid\hbox{}


