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\title{Charm Theory Review (Non-lattice)}

\author{E. Golowich\address[MCSD]{Physics Department, 
        University of Massachusetts, \\
	Amherst, MA 01003 USA
        }%
        \thanks{Research supported in part by the U.S. National 
	  Science Foundation under Grant PHY--0244801.} }
               
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\begin{document}

\begin{abstract}

In this talk, I review aspects of $D^0$-${\bar D}^0$ mixing, 
rare decays of $D$ mesons and CP violations in $D$ meson decays, 
in a manner which emphasizes the interplay between experiment and 
theory.
\vspace{1pc}
\end{abstract}

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\maketitle

\section{INTRODUCTION}
The organizers of this conference recommended three subjects 
to choose amongst -- $D^0$ mixing, rare decays and CP-violations.  
Since there is currently activity in all three areas, 
this report will touch on each of them.

\section{MIXING}
The most newsworthy topic in the area of meson-antimeson oscillations 
is the recent detection of  $B_s$-${\bar B}_s$ mixing at Fermilab.  
This leaves $D^0$-${\bar D}^0$ as the only undetected candidate for 
mixing.  As such it will (I suspect) become an area of heightened 
experimental and theoretical scrutiny.  

On a quantitative level, the current PDG data collection lists \cite{pdg}
\begin{eqnarray*}
& & x_{\rm D} = {\Delta M_{\rm D} \over \Gamma_{\rm D}} < 0.029 \ \ 
(95\%~ {\rm C.L.}) \nonumber \\
& & y_{\rm D} \simeq {\Delta \Gamma_{\rm D} \over 2\Gamma_{\rm D}} < 0.008
\pm 0.005 \ \ . 
\end{eqnarray*}
$D^0$-${\bar D}^0$ mixing is indeed small and we know why -- 
there is Cabibbo angle suppression [$\sin^2\theta_{\rm C}$] and 
quark mass suppression [$(m_s^2 /m_c^2)^n$].  We cannot, however, 
yet precisely predict the size of mixing.  
This frustration is partly a reflection of the quark mass, too 
large to justify chiral methods and too small to yield a 
rapidly convergent heavy quark expansion.  

\subsection{Mixing in the Standard Model}
Our discussion will emphasize $\Delta\Gamma_{\rm D}$, 
\begin{eqnarray}
\Delta\Gamma_{\rm D} = - {{\cal I}m  ~
\langle {\bar D}^0 | i \int d^4 x T\left( H_{\rm w}(x) H_{\rm w}(0) 
\right) | D^0 \rangle \over M_{\rm D}} ~.
\nonumber 
\end{eqnarray}
To utilize this relation, we insert intermediate states between the 
$|\Delta C| = 1$ weak hamiltonians $H_{\rm w}$.  This can be done 
using either quark or hadron degrees of freedom.  
Let us consider each of these 
possibilities in turn.  


\subsubsection{Quark-level Analysis}
Using the heavy quark methodology to expand the 
mixing in terms of operator dimension, we find 
two four-fermion operators of dimension six, 
fifteen six-fermion operators of dimension nine, {\it etc}. \cite{hg,ohl,bu} 
Consider the familiar $D=6$ (box diagram) case.  If the $b$-quark 
contribution is ignored, there are $s{\overline s}$, $s{\overline s}$ and 
$s{\overline d} + d{\overline s}$ intermediate states.  Taking 
$m_d = 0$, the mixing functions will depend on $z \equiv m_s^2/m_c^2 
\simeq 0.006$.  Table~\ref{table:qkmix} uses one of the 
mixing functions for $\Delta\Gamma_{\rm D}$ to show what happens 
when an expansion in powers of $z$ is carried out.
The individual intermediate states are {\it not} intrinsically 
small -- they begin to contribute at ${\cal O}(z^0)$.  However, flavor 
cancellations remove all contributions through ${\cal O}(z^2)$, 
so the net result is ${\cal O}(z^3)$, which is 
tiny.  The corresponding result for $\Delta M_{\rm D}$ turns out to be 
${\cal O}(z^2)$ (the extra factor of $z$ for $\Delta\Gamma_{\rm D}$ 
is due to 'helicity suppression', the same mechanism that occurs in 
pion leptonic decay). 

%\vspace{-1pc}

\begin{table}[htb]
\caption{Flavor Cancellations in $\Delta\Gamma$.}
\label{table:qkmix}
%\newcommand{\m}{\hphantom{$-$}}
%\newcommand{\cc}[1]{\multicolumn{1}{c}{#1}}
%\renewcommand{\tabcolsep}{2pc} % enlarge column spacing
%\renewcommand{\arraystretch}{1.2} % enlarge line spacing
%\begin{tabular}{@{}llll}
\begin{tabular}{cccc}
\hline\hline
Int. State & ${\cal O}(z^0)$ & ${\cal O}(z^1)$ & ${\cal O}(z^2)$\\
\hline
$s{\overline s}$ & $1/2$ & $-3z$ & $3z^2$ \\
$d{\overline d}$ & $1/2$ & $0$ & $0$ \\
$s{\overline d}+d{\overline s}$ & $-1$ & $3z$ & $-3z^2$ \\
\hline
Total & $0$ & $0$ & $0$ \\ \hline
\end{tabular}\\[2pt]
\end{table}

%\vspace{-2pc}

For any given operator dimension, one must expand in powers of 
${\cal O}(\alpha_s)$.  Thus the work just described gives the 
leading-order (LO) term in an expansion in QCD, with
$x_{\rm D}^{\rm (LO)} \gg y_{\rm D}^{\rm (LO)}$.  
The NLO calculation has recently been done in Ref.~\cite{gp2005}, and 
the effects of QCD are found to be significant.  Summing 
the LO and NLO terms, the net result is 
$x_{\rm D} \simeq y_{\rm D} \sim 10^{-6}$.  No higher order QCD 
contributions have yet been computed.  

Higher dimensional sectors in the 
OPE are expected to be important, in part because the flavor 
cancellations will not universally be so severe. \cite{ohl,bu}  
For example, it is known that in the $D=9$ sector the contributions 
are ${\cal O}(z^{3/2})$.  A thorough study of $z$ dependence 
is underway.  \cite{ggp}

To summarize, a proper analysis of $D^0$ mixing at the quark level 
involves a {\it triple} expansion -- in dimension $D$, in powers 
of $\alpha_s$ and in powers of $m_s^2/m_c^2$.  
It is possible that as-yet uncalculated terms can lift 
$x_{\rm D}$ and $y_{\rm D}$ well above the LO + NLO 
${\cal O}(10^{-6})$ scale for dimension six cited above.

\subsubsection{Hadron-level Analysis}
Using hadronic intermediate states in the formula for 
$\Delta\Gamma_{\rm D}$ has been a well-studied approach to the 
problem.  

One possibility is to construct a theoretical model of $|\Delta C| = 1$ 
decays and to fit any undetermined model parameters via experiment.  
In 1995, a rather extensive model/fit 
of $D^0$ decays was applied to the determination of 
$\Delta\Gamma_{\rm D}$ and the result 
$y_{\rm D} \simeq 10^{-3}$ was found. \cite{blmps}  This is almost 
an order of magnitude smaller than the current experimental bound 
that I cited earlier.  

Even earlier (in 1985), a more phenomenological method had been
proposed in which one divides out phase space from experimental 
branching fractions and takes the square 
root to reconstruct the magnitudes of individual decay amplitudes.  
This can be used to then determine $y_{\rm D}$. \cite{dghp}  
The two-body sector of charged pseudoscalar branching fractions 
was explored as a trial horse,  
\begin{eqnarray*}
& & y_{\rm D}^{(P^+P^-)} = {\cal B}_{[D^0 \to K^+K^-]} 
+ {\cal B}_{[D^0 \to \pi^+\pi^-]} \nonumber \\
& & - 2 \cos\delta \left[ {\cal B}_{[D^0 \to K^-\pi^+]}\cdot 
{\cal B}_{[D^0 \to K^+\pi^-]} 
\right]^{1/2} \nonumber
\end{eqnarray*}
where $\delta$ is the relative phase between the $K^-\pi^+$ and 
$K^+\pi^-$ modes.  This contribution vanishes in the limit of 
exact SU(3) flavor symmetry, and the same must be true for all 
other decay sectors.  However, since the real world exhibits large
SU(3) symmetry breaking it was conjectured that 
this constraint might be invalidated.
Unfortunately, little was known in 1985 about the 
$D^0 \to K^+ \pi^-$ mode, and Ref.~\cite{dghp} could only reach 
the qualitative conclusion that SU(3) breaking might induce an 
unexpectedly large value for $y_{\rm D}$.  A more recent 
and much more complete analysis indicates that each decay sector 
experiences only muted SU(3) breaking. \cite{falk} If substantiated over time, 
this presumably reflects the fact that in $D^0$-${\bar D}^0$ mixing 
SU(3) breaking is of second order. \cite{su3}
There must be exceptions, however, since certain multi-particle final 
states ({\it e.g.} four-kaon modes) 
are disallowed due to phase space restrictions.  
It has been stated that such multi-particle sectors might lead 
to a value as large as $y_{\rm D} \sim 0.01$.  
As one of the originators of the `phenomenological' method, 
I would very much like for it to give the best prediction 
for $y_{\rm D}$.  Unfortunately, sector-by-sector it is the least 
precisely known branching fraction that controls the predictive power 
of the analysis.  Let us hope that this approach is not doomed to 
supply only 'fuzzy' estimates.

Finally, there is the possibility of exploiting the presence of 
resonances nearby the $D^0$ in mass, for which an enhancement of 
the mixing amplitude occurs.  \cite{nearby}  This promising approach 
is currently hindered by an inadequate database regarding such 
nearby resonances.  

\subsection{Mixing Beyond the Standard Model}
It has long been appreciated that meson-antimeson oscillations 
may be sensitive to heavy degrees of freedom which propagate 
in the mixing loop-amplitudes.  Detection of 
mixing in $K^0$ and $B_d$ systems led to predictions about charm and 
top quarks before these particles were actually discovered.
In like manner, by comparing observed mixing with predictions of the Standard 
Model we constrain models of New Physics, impressively 
so for $B_s$-${\bar B}_s$ mixing.  

Admittedly, this has not yet led to the discovery of New Physics 
and we are all becoming increasingly frustrated.  But it is important 
not to give up, so we keep trying.  $D^0$ mixing has the intriguing 
property that the SM signal is very small and vanishes in 
the not-so-distant world of exact SU(3) symmetry.  A group of us is 
currently involved in providing an up-to-date summary of New Physics 
in $D^0$ mixing. \cite{ghpp06}  Among other things, any such work 
should include a complete menu of NP possibilities ({\it e.g.} 
extra gauge bosons, {\it etc}), a proper treatment of NP amplitudes 
at the charm scale (basis operators and their QCD corrections) and 
an up-to-date knowledge of allowed NP parameter space.  

A somewhat related topic involves the realization that NP {\it can} 
affect $\Delta \Gamma_{\rm D}$.  There is often confusion about 
this point.  Although it is true that only light quarks and gluons 
are allowed as intermediate states in the mixing amplitude for 
$\Delta\Gamma_{\rm D}$, it is likewise true that one 
of the interaction verticies can be NP.  This line of reasoning 
would lead to a relation between NP contributions to 
$\Delta \Gamma_{\rm D}$ and to $|\Delta C| = 1$ decays. \cite{gpp06}


\section{RARE DECAYS} 
The era of positive experimental results for rare charm decays is 
underway.  Happily, there is already a sizable and modern theoretical 
literature on this subject ({\it e.g.} \cite{bghp95,bghp02,fp}).  
There has, however, been a lag in observations because the 
experimental signals are so small.  This is about to change.
\begin{figure}[t]
%\vspace{9pt}
\caption{Contributions to $D^0 \to 
\rho^0 e^+ e^-$.}
%\framebox[55mm]{\rule[-21mm]{0mm}{43mm}}
%\epsfbox{kekfig1.eps}
%\includegraphics[angle=90,width=15pc]{rarefig.ps}
\includegraphics[angle=90,width=15pc]{b06fig.eps}
%\epsfig{figure=pill.ps,height=4.2in,angle=90}
\label{fig:susy}
\end{figure}
%
One noteworthy, if somewhat distressing, theoretical result is that 
not all rare decay modes are of equal interest for detecting New 
Physics interactions at the quark level.  A prime example 
is the sequence of flavor changing radiative decays 
$D \to V \gamma$, where $V = \rho, K^*, etc$ is a neutral spin-one 
particle.  Here, one would hope 
to be probing the underlying quark transition $c \to u \gamma$.  
This mode is, of course, absent at tree level in the SM but can 
occur at higher orders.  Even though the QCD corrections are
relatively large, the $c \to u \gamma$ signal is still unobservably 
tiny. \cite{greub}  Such is not the case for the so-called 
long-distance contributions.  These are calculated in terms of hadronic 
degrees of freedom and are estimated to give branching fractions 
as large as ${\cal O}(10^{-6} \to 10^{-5})$, \cite{bghp95} 
consistent with the scale that 
the PDG data compilation registers for the branching fraction 
${\cal B}_{D^0 \to \phi + \gamma} = (2.5 ^{+ 0.7}_{- 0.6}) 
\cdot 10^{-5}$. This result is welcome but it informs 
us only about details of hadronic dynamics and nothing more.

\begin{table*}[t]
\caption{Current Status of Some Decay Asymmetries ($A_{\rm CP}$)}
\label{table:cpv}
\newcommand{\m}{\hphantom{$-$}}
\newcommand{\cc}[1]{\multicolumn{1}{c}{#1}}
\renewcommand{\tabcolsep}{2pc} % enlarge column spacing
\renewcommand{\arraystretch}{1.2} % enlarge line spacing
\begin{tabular}{@{}llll}
\hline\hline
Neutral & PDG Value & Charged & PDG Value \\
\hline
$D^0 \to K^+K^-$ & $\ 0.005 \pm 0.016$ & $D^\pm \to \phi \pi^\pm$ &
$-0.014 \pm 0.033$\\
$D^0 \to \pi^+\pi^-$ & ~$0.021 \pm 0.026$ & $D^\pm \to \pi^\pm K^+K^-$ &
$0.002 \pm 0.011$\\
$D^0 \to K_s \pi^0$ & \ $0.001 \pm 0.013$ & $D^\pm \to \phi \pi^\pm$ &
$-0.02 \pm 0.05$\\
$D^0 \to \pi^0 \pi^+ K^-$ & $-0.031 \pm 0.086$ & 
$D^\pm \to \pi^\pm \pi^+ \pi^-$ & $-0.02 \pm 0.04$
\\
\hline
\end{tabular}\\[2pt]
\end{table*}

 
Of greater potential for probing New Physics are the decays 
$D \to M \ell^+ \ell^-$ where $M = \pi, K^*, {\it etc}$.  
The output of observing such modes 
is not just a branching fraction, but also a distribution 
(most usually in dilepton invariant mass $q^2 \equiv (p_{\ell^+} 
+ p_{\ell^-})^2$).  Such a distribution could be of real interest, 
but not all parts of it.  Consider the situation depicted in 
Fig.~\ref{fig:susy} for $D^0 \to \rho^0 \ell^+ \ell^-$, 
where the SM contribution is shown in black and the predictions of 
a version of supersymmetry with nonuniversal soft breaking effects 
are shown in color. \cite{bghp02}  This figure has two striking features:

[1] The first is the presence of sharp 
peaks for intermediate values of $q^2$.  These are induced by 
the weak transition $D^0 \to R^0 \rho^0$ ($R^0$ is a 
neutral noncharmed resonance) followed by the electromagnetic conversion 
$R^0 \to \ell^+ \ell^-$.  This part of the graph is clearly a 
manifestation of SM physics, and reflects comments 
made above regarding the flavor-changing radiative decays.  

[2] More interesting from the viewpoint of New Physics is 
the region of small $q^2$.  The SM signal is relatively tiny here, giving 
the NP signal a chance to stand out.  Several 
possible supersymmetric scenarios are shown and we refer the 
reader to Ref.~\cite{bghp02} for details.   

Recent experimental work at FermiLab has begun to make inroads 
on this subject via the decays $D^+, D_s^+ \to 
\pi^+  \mu^+ \mu^-$.  Details of this impressive work is presented 
by Paul Karchin in the following talk. \cite{pk}  It suffices 
to point out that the $\phi$ peak in the intermediate transition 
$D^+, D_s^+ \to \phi \pi^+$ has been observed and that 
for the region sensitive to New Physics the data is about 500 
times above the SM signal, just 10 times above the signal expected 
from the Little Higgs model \cite{fp}, but already constrains a 
version of R-parity violating supersymmetry \cite{bghp02}.

\section{CP-VIOLATIONS} 
To this date, no effects involving CP violation (CPV) have been observed for 
charmed hadrons.  We comment below on two potentially interesting 
areas, involving respectively two-body decay 
modes and three-body decay modes.

\subsection{Direct CPV in Two-body Modes}
On the experimental side, direct CPV for two-body decays of D 
mesons involves measurement of the asymmetry
\begin{eqnarray*}
& & A_{\rm CP} = \frac{\Gamma_{D \to f} 
- \Gamma_{\bar D \to \bar f}}{\Gamma_{D \to f} +
\Gamma_{\bar D \to \bar f}} \ \ .
\label{asym}
\end{eqnarray*}
Direct CPV has been observed for kaons ($\epsilon' /\epsilon$) 
and B$_d$-mesons by studying $K\to \pi\pi$ and $B_d\to K\pi$ decays 
respectively.  Despite years of effort and the presence of sizeable 
branching ratios, attempts to measure CP violating asymmetries in 
D decays have yielded only null results.  The present level of experimental 
sensitivity is indicated by the entries in Table~\ref{table:cpv}. 

What does theory have to say about direct CPV?  In all cases, 
it is QCD which inhibits a complete treatment.  
For $\epsilon' /\epsilon$ in kaon physics, chiral symmetry provides 
a successful means for predicting 
the electroweak penguin contribution \cite{cdgm}, 
but the QCD penguin component remains an enigma.  For heavy 
quark systems, the strong phase shifts generally depend on a mix of 
perturbative and nonperturbative QCD dynamics.  The nonperturbative 
component (surely dominant at the charm scale) 
has thus far precluded a model-independent description.

\subsection{Dalitz Plots of Three Body Modes}
There have been a number of interesting Dalitz studies of charm decays 
over the years and they are listed in Ref.~\cite{asner}.  
Some of these are sensitive to both $D^0$ mixing and CPV.  
A recent example, $D^0 \to K_{\rm S}^0 \pi^+ \pi^-$, 
yields the mixing limits \cite{cleo}
\begin{eqnarray*}
& & - 0.045 < x_{\rm D} < 0.093 \nonumber \\
& & -0.064 < y_{\rm D} < 0.036 \ \ . 
\end{eqnarray*}
Although not yet at the level of the experimental 
bounds listed earlier, they are not that far off.  
It is reassuring that the literature is continuing 
to attract interesting suggestions for further work. \cite{as,aap} 

\section{SUMMARY}
Taking experiment and theory together, it is clear that 
the study of charm electroweak phenomena is quite an active area. 
But there is much left to do, as I summarize in the following. 
\subsection{Mixing}
{\it Experiment}: A number of experimental studies have been 
underway, which is good.
But nothing which could be called a discovery has yet been seen, so 
more sensitivity is needed.  I especially feel that the range 
$0.001 < y_{\rm D} < 0.01$ should be probed in ongoing and 
forthcoming experiments.  Are recent results from Belle and 
BaBar `hints' or just fluctuations? 

{\it Theory}: Crisp Standard Model predictions for $x_{\rm D}$ and 
$y_{\rm D}$ remain frustratingly elusive, but at least we know why. 
At the quark level, what is involved is a triple expansion in 
dimension $D$, QCD coupling $\alpha_s$ and the mass ratio 
$z \equiv m_s^2/m_c^2$.  An NLO analysis with 
$D=6$ gives $x_{\rm D} \simeq y_{\rm D} \simeq 10^{-6}$.  One 
anticipates progress in attacking the problem, but not without 
difficulty.  Performing the theoretical study of $y_{\rm D}$ 
at the hadron level has yielded some interesting insights.  A 
specific model of $|\Delta C| = 1$ decays has 
$y_{\rm D} \simeq 10^{-3}$ whereas an up-to-date phenomenological 
analysis appears to allow $y_{\rm D} \simeq 10^{-2}$.  
Improved $|\Delta C| = 1$ decay data should impact this latter 
approach.

For reasons already explained, $D^0$-${\bar D}^0$ remains a 
possibly fertile area for New Physics studies.  Because the 
field of New Physics is in a state of constant flux (new models, 
constrained parameter space, {\it etc}), there is a need to 
update or re-do the calculations.  A modern treatment of this 
problem is underway.

\subsection{Rare Decays and CP-violations}
Experimental studies of charm rare decays and CPV have been performed 
and as a result we now know what levels of sensitivity are
attainable.  The work thus far has laid the foundations 
for real progress in the field, but the next round of experiments 
will face the challenge of doing even better.  We must bridge 
the gap between current experimental bounds and theoretical predictions.
For theorists, some studies of rare decays are already 
in the literature, but we need more input regarding expectations 
of various CPV signals.

\begin{thebibliography}{9}

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Phys.\ Lett.\ B {\bf 592} (2004) 1. 
\bibitem{hg} H. Georgi, Phys.\ Lett.\ B {\bf 297} (1992) 353.
\bibitem{ohl} T.~Ohl, G.~Ricciardi and E.~H.~Simmons,
  %``D - anti-D mixing in heavy quark effective field theory: The Sequel,''
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\bibitem{bu}
  I.~I.~Y.~Bigi and N.~G.~Uraltsev,
  %``D0 anti-D0 oscillations as a probe of quark-hadron duality,''
  Nucl.\ Phys.\ B {\bf 592} (2001) 92.
\bibitem{gp2005} E. Golowich and A. Petrov, Phys.\ Lett.\ B {\bf 625}
  (2005) 53.
\bibitem{ggp} Y. Gagik, E. Golowich and A Petrov (in progress).
\bibitem{blmps}
  F.~Buccella, M.~Lusignoli, G.~Miele, A.~Pugliese and P.~Santorelli,
  %``Nonleptonic weak decays of charmed mesons,''
  Phys.\ Rev.\ D {\bf 51} (1995) 3478.
\bibitem{dghp}
  J.~F.~Donoghue, E.~Golowich, B.~R.~Holstein and J.~Trampetic,
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\bibitem{falk}
  A.~F.~Falk, Y.~Grossman, Z.~Ligeti, Y.~Nir and A.~A.~Petrov,
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  Phys.\ Rev.\ D {\bf 69} (2004) 114021.
\bibitem{su3}
  A.~F.~Falk, Y.~Grossman, Z.~Ligeti and A.~A.~Petrov,
  %``SU(3) breaking and D0 - anti-D0 mixing,''
  Phys.\ Rev.\ D {\bf 65} (2002) 054034.
  %%CITATION = HEP-PH 0110317;%%
\bibitem{nearby}  E.~Golowich and A.~A.~Petrov,
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  Phys.\ Lett.\ B {\bf 427} (1998) 172.
  %%CITATION = HEP-PH 9802291;%%
\bibitem{ghpp06} E.~Golowich, J.~L.~Hewett, S.~Pakvasa and A. Petrov, 
work in progress.
\bibitem{gpp06} E.~Golowich, S.~Pakvasa and A. Petrov, 
work in progress.
\bibitem{bghp95}
  G.~Burdman, E.~Golowich, J.~L.~Hewett and S.~Pakvasa,
  %``Radiative Weak Decays Of Charm Mesons,''
  Phys.\ Rev.\ D {\bf 52} (1995) 6383.
  %%CITATION = HEP-PH 9502329;%%
\bibitem{bghp02}
  G.~Burdman, E.~Golowich, J.~Hewett and S.~Pakvasa,
  %``Rare charm decays in the standard model and beyond,''
  Phys.\ Rev.\ D {\bf 66} (2002) 014009.
\bibitem{fp}
  S.~Fajfer and S.~Prelovsek,
  %``Effects of littlest Higgs model in rare D meson decays,''
  Phys.\ Rev.\ D {\bf 73} (2006) 054026.
\bibitem{greub}
  C.~Greub, T.~Hurth, M.~Misiak, 
  %``The $c \to u \gamma$ Contribution to Weak Radiative Charm Decay,''
  Phys.\ Lett.\ B {\bf 382}, 415 (1996).
  %%CITATION = HEP-PH 9603417;%%
\bibitem{pk}
P.~Karchin, {\it Recent Results on Charm Physics from the Tevatron 
Collider}, talk at this conference.

\bibitem{cdgm}   
V.~Cirigliano, J.~F.~Donoghue, E.~Golowich and K.~Maltman,
%   ``Improved determination of the electroweak penguin contribution to
  %epsilon'/epsilon in the chiral limit,''
  Phys.\ Lett.\ B {\bf 555}, 71 (2003).
 % [arXiv:hep-ph/0211420].


\bibitem{asner} D.~M.~Asner, {\it Review of Charm Dalitz-plot 
Analyses} appearing in Ref.~\cite{pdg}.


\bibitem{cleo}
  D.~M.~Asner {\it et al.}  [CLEO Collaboration],
%   ``Search for anti-D0 D0 mixing in the Dalitz plot analysis of D0 -->  K0(S)
  %pi+ pi-,''
  Phys.\ Rev.\ D {\bf 72}, 012001 (2005).
  %%CITATION = HEP-EX 0503045;%%

\bibitem{as}
  D.~M.~Asner and W.~M.~Sun,
%   ``Time-independent measurements of D0 - anti-D0 mixing and relative strong
  %phases using quantum correlations,''
  Phys.\ Rev.\ D {\bf 73} (2006) 034024.
\bibitem{aap}
  A.~A.~Petrov,
  %``Hunting for CP violation with untagged charm decays,''
  Phys.\ Rev.\ D {\bf 69} (2004) 111901.

\end{thebibliography}

\end{document}
