text:
\section{Introduction}
The subject of flavour physics is a vast one and I am not going to review the
entire body of
present knowledge. Instead, I would
like to use a few examples to define the problems that we are struggling with
and the
 strategies that we can use to reach a deeper
understanding of this elusive subject.

Our main puzzle was
concisely and effectively put by I.I. Rabi upon the discovery of
the $\mu$: ``Who ordered that?" was his remark.
This question has three distinctive facets. We can start by asking the reason
why there are so many
particles: this can be defined as the ``replication problem." Once we organize
the particles in the
Standard Model
families we have a triplication problem: ``Why are there three families?"
Finally, the
hierarchy in the mass spectrum
of quarks and leptons spans several orders of magnitudes and may provide the
most
distinct clue towards an answer to Rabi's puzzling question.
Even if lepton masses and mixing parameters have recently attracted a lot of
attention,
because of the evidence for $\nu$ oscillations from the
Super-Kamiokande experiment, the quark sector
will be the focus of my discussion. Masses and mixing in the lepton sector are
reviewed in other
excellent contributions to these proceedings \cite{superk}.

In the Standard Model masses are produced via the
Higgs mechanism through the Yukawa couplings. The Yukawa Lagrangian is given by:
\begin{equation}
\begin{array}{ll}
{\cal L} _{Yukawa} = & -G_1 [(\overline{L}_u\overline{\Phi})u_R
+\overline{u}_R(\overline{\Phi}^{\dagger }L_u)]\\
~~ & - G_2 [(\overline{L}_u\overline{\Phi})d_R
+\overline{d}_R(\overline{\Phi}^{\dagger }L_u)] \\
~~ & -G_3 [(\overline{L}_u\overline{\Phi})s_R
+\overline{s}_R(\overline{\Phi}^{\dagger }L_u)] \\
~~ & -G_4 [(\overline{L}_c\overline{\Phi})c_R
+\overline{c}_R(\overline{\Phi}^{\dagger }L_c)] \\
~~ & -G_5 [(\overline{L}_c\overline{\Phi})d_R
+\overline{d}_R(\overline{\Phi}^{\dagger }L_c)]\\
~~ & -G_6 [(\overline{L}_c\overline{\Phi})s_R
+\overline{s}_R(\overline{\Phi}^{\dagger }L_c)],\\
\end{array}
\end{equation}
where $L$ identifies a left-handed SU(2) doublet and the subscript $R$
identifies a right-handed
fermion.
These 6 complex Yukawa couplings are related to 10 independent physical
quantities, the six quark
 masses and  four quark
mixing parameters. The latter can be described by three
Euler-like angles and an imaginary phase. These parameters are
not predicted by the Standard Model, but
are fundamental constants of nature that
need to be extracted from experimental data.

Many theoretical models have tried to uncover a more fundamental
explanation for flavour. For example, some
of the many variations of Supersymmetry \cite{susy} incorporate
the known hierarchy of quark masses and mixing parameters.
In addition, the replication problem has been addressed
by postulating a new deeper level of matter \cite{preons}. In this approach, the
multitude
of quarks can be understood as a sort of periodic table of the composite
structures
that are indeed bound states of more fundamental particles.
In addition, a geometrical origin \cite{string} of flavor has been proposed.

An additional feature of the fundamental interactions explored in
flavour physics is $CP$ violation. The only experimental evidence
  has been obtained  studying neutral $K$ decays. On the
other hand, $CP$ violation is  crucial to our understanding of
the history of the universe.  In particular, it is a necessary ingredient of
our understanding of the origin of the matter dominated universe
\cite{sakharov}. A $CP$ violating
phase is naturally incorporated in the Standard Model within the Cabibbo-
Kobayashi-Maskawa matrix.
Thus several models attempt to explain the baryon asymmetry of the universe as
due
to a $CP$ violating process occurring at the scale of the electroweak symmetry
breaking.
A rough order of magnitude estimate of the expected effect of
the CKM induced $CP$ violation on the baryon asymmetry can be obtained by
constructing a variable $d_{CP}$ that incorporates all the
features of the expected CKM phase: it vanishes when any pair of quarks is
degenerate in mass
and when any CKM angle vanishes
because of the so called ``GIM'' (Glashow, Iliopoulos, Maiani) cancellation.
$d_{CP}$ is defined as:
\begin{equation}
\begin{array}{ll}
d_{CP} = & \sin {\theta _{12}} \sin {\theta _{23}}\sin {\theta _{13}} \sin
{\delta _{CP}}\\
~~&(m_t^2-m_c^2)(m_t^2-m_u^2)(m_c^2-m_u^2)\\
~~&(m_b^2-m_s^2)(m_b^2-m_d^2)(m_s^2-m_d^2),\\
\end{array}
\end{equation}
where $\theta _{ij}$ are three real ``Euler-like''
angles defining the CKM matrix together with the imaginary phase $\delta _{CP}$.

The $d_{CP}$ parameter that we have just defined is a dimensional quantity,
it is conceivable \cite{farrar}
that the natural normalization parameter to transform it into
a pure number  is the temperature at which the electroweak
symmetry breaking occurred. Thus the figure of merit of the strength of the CKM
induced CP violating effect is given by:
\begin{equation}
d_{CP}^T = d_{CP}/kT_{ew}^{12}  \approx 10^{-18},
\end{equation}
where $T_{ew}$ represents the temperature at the time the electroweak symmetry
breaking occurred and
$k$ is the Boltzmann constant.
This suggests that CKM CP violation is an effect too small to account for the
known baryon asymmetry of the universe,
\begin{equation}
\left|\frac{N_{B}-N_{\overline{B}}}{N_{B}+N_{\overline{B}}}\right| _{t\approx
10^{-6} s}\approx
\left|\frac{N_B}{N_{\gamma }}\right| _{now}\approx 10^{-10}.
\end{equation}
This discrepancy is very qualitative in nature and may have a number of
explanations. However a
very tantalizing hypothesis is the presence of additional $CP$ violating phases
produced by
mechanisms beyond the Standard Model. Thus, the experimental exploration of $CP$
violation observables
has a good chance to
uncover evidence for new physics.
\section{Quark Masses}
The hierarchy of the quark masses is very puzzling. The mass interval between
the lightest
and the heaviest quark  spans the huge interval between a few MeV and hundreds
of GeV. The
determination of these masses has many challenges and a good illustration of the
different roles
played by QCD in different hadronic processes. The parameter that defines how
QCD affects our ability of
measuring fundamental properties is the mass scale $\Lambda _{QCD} \approx 500$
MeV. Thus, for very
heavy mass scales QCD corrections are not very important and can be evaluated
using perturbative
methods. As the mass decreases, non-perturbative effects become more important
and the extrapolation
process becomes more uncertain. This interplay will be illustrated below.
\subsection{The top quark mass}

The top quark is the heaviest and thus the least affected by the strong
interaction. In fact, it is so heavy
that it has the unique property of decaying before hadronizing in a top-flavored
hadron. It was discovered
at Fermilab \cite{topdiscovery}, at the Tevatron proton-antiproton collider. Its
properties have been
studied by  CDF and D0. In
particular, one of the finest achievements by these groups is a very accurate
determination of the quark
mass $m_t$ . Several different techniques are used. Recently, these two
experiments have
formed a working group to obtain a world average for $m_t$ , considering the
correlations in their
measurements.

The top quark decays into a $b$ quark and a $W$ boson with a probability close
to one. In some
cases this $b$ quark
undergoes semileptonic decays. In both CDF and D0 the dominant contribution to
the $m_t$\ measurement comes from
samples containing one high $p_t$\ lepton and one jet. CDF also uses a sample
including only hadrons in the final state, whereas D0 has a secondary data set
containing two
leptons.

The value of the measured top quark mass is $(174.3 \pm 3.2  \pm 4.0)$ GeV. This
is the heaviest
measured mass of a fundamental particle. The interest in studying the properties
of the top
quark is largely motivated by the unique closeness of $m_t$ to the mass defining
the scale of the
electroweak symmetry breaking. The mass $m_t$\ is related to the vacuum
expectation value of the
Higgs field through the relationship:
\begin{equation}
m_t = \lambda _t v/\sqrt{2},
\end{equation}
where $\lambda _t$ is the Yukawa coupling and $v$ is the vacuum expectation
value of the Higgs
field. Note that the Yukawa coupling is of order one. This property can be
accomodated in
a natural way in some supersymmetric theories that encompass a very heavy top
quark at the GUT
scale \cite{susy-guts}.
\begin{figure}[hbt]
\begin{center}
\epsfig{figure=mw-mt.eps,width=2.7in}
\caption{ Relation between the W and top masses for some values
    of the Higgs mass \cite{galtieri}. The cross hatched area to the
left represents the
    allowed region from an overall Standard Model fit. The other two regions
    are obtained from direct measurements of M$_W$ and M$_{top}$.}
\label{fig:mhiggs}
\end{center}
\end{figure}

The measured $W$ and top masses can give some constraint on the mass scale for
the last particle in the
Standard Model to elude our discovery, the Higgs scalar. Fig.~\ref{fig:mhiggs}
shows a summary of the constraints
on the Higgs mass from the $W$ mass measurements at LEP II and the combined
$m_W$ and $m_t$ at the Tevatron.
These data favor a light Higgs, leading to the hope that we are on the verge of
learning more
about the mechanism of electroweak symmetry breaking.

\subsection{The $b$ quark mass}
The interest in an accurate
measurement of the $b$ quark mass has a two-fold motivation. On the one hand its
measurement helps to
pin down the quark mass hierarchy as discussed before. On the other
hand, renewed attention to $m_b$\ has been motivated by the
suggestion that the CKM matrix elements $|V_{cb}|$\ and $|V_{ub}|$\
 can now be obtained from inclusive measurements with great accuracy using
the so
called ``Heavy Quark Expansion'' \cite{ope}. A precise determination
 of $m_b$ is a ``sine qua non'' for most inclusive methods to study $B$
decays.
Since the mass of the beauty quark is about 5 GeV, thus its derivation from
experimental observables is
affected by the strong interaction to a much higher degree that in the $t$ quark
case.
In fact, before we discuss any theoretical estimate or experimental
determination of the $b$ quark mass
we need to define its meaning carefully.
The widely used  ``pole mass,'' namely the parameter appearing in the quark
propagator, has
been demonstrated to be inadequate \cite{bigietal} for an accurate description
of
$b$ quark phenomenology. These
authors point out the existence of an infrared renormalon generating a factorial
divergence in the high-order cofficients in the $\alpha _S$ series producing an
intrinsic uncertainty
of the order $\Lambda _{QCD}/m_Q$.

An alternative, that appears to be quite a good candidate to describe $b$ quark
properties in a regime
where perturbative effects are important, is the $\overline{MS}$\ mass
$\overline{m}_b(\mu )$. This
is a short distance mass, and therefore does not contain ambiguities of the
order of $\Lambda _{QCD}$ like
the pole mass. This definition is adequate for observables where perturbative
effects are dominant,
such as recent measurements of the $b$ quark mass at the $Z^0$ energy.
As this quantity is not defined for scales $\mu$ below $m_b$, alternative
definitions of the running mass
have been proposed that can be normalized at a scale $\mu$ smaller than $m_b$.
Most of the authors refer
to the mass defined with this procedure as ``kinetic mass.''

Table~\ref{bmass} summarizes the most recent theoretical evaluations of $m_b$.
The calculations using
the $m_{kin}$ prescription or an equivalent subtraction scheme are in
closer agreement. However other evaluations of the pole mass and the
$\overline{MS}$ mass
have shown frequent disagreement in the methodology of assessing errors. In
addition,
recent lattice data \cite{yashimoto} seem to imply an even lighter $m_b$ . It is
clear that
there is still work to be done before quantities sensitive to $m_b$\ can be
determined
accurately.

\begin{table}
\begin{center}
\caption{\label{bmass} Theoretical estimates of $m_b$ (GeV/c$^2$). The first
column gives the
theoretical predictions for the pole mass $m_b$, the second column the predicted
value of the $\overline{MS}$ mass $\overline{m}_b(m_b)$ at
the scale of the $b$ meson mass and the third column corresponds to the
prediction for the {\it kinetic} or {\it potential subtracted}
mass defined at a scale $\mu \approx 1$ GeV.}
\begin{tabular}{lccc}
\br
$m_b$ & $\overline{m}_b$ & $m_{kin}$ & Ref. \\
\hline
\multicolumn{4}{c}{\it QCD sum rule evaluations}\\
\hline
-- & $4.20\pm 0.1$ & $ 4.56\pm 0.06$ &\cite{my98}  \\
-- & $4.20\pm 0.06$ &$4.71\pm 0.06$  & \cite{h98}\\
  $4.97\pm 0.17$ & $4.26\pm 0.12$ & $4.60 \pm 0.18$ &\cite{bs} \\
 $4.75 \pm 0.04$ & -- & -- & \cite{kpp} \\ \hline
\multicolumn{4}{c}{\it $\Upsilon$ sum rule evaluations}\\
\hline
$4.604\pm 0.014$ & $4.13\pm 0.06$& --& \cite{jp978}\\
$5.015 ^{+0.110}_{-0.070}$ & $4.453 ^{+0.050}_{-0.032}$& --   &\cite{py98}
 \\
\hline
\multicolumn{4}{c}{\it Lattice QCD evaluations}\\
\hline
 $5.0\pm 0.2$ & $4.0\pm 0.1$ & -- &  \cite{deta} \\
 -- & $4.41\pm 0.15$ &-- & \cite{ms98} \\
\br
\end{tabular}
\end{center}
\end{table}

\section{Quark Mixing}
In the framework of the Standard Model the gauge bosons, $W^{\pm}$,
$\gamma$ and
$Z^o$ couple to
mixtures of the physical $d,~ s$ and $b$ states. This mixing is described
by the Cabibbo-Kobayashi-Maskawa (CKM) matrix:
\begin{equation}
V_{CKM} =\left(\begin{array}{ccc}
V_{ud} &  V_{us} & V_{ub} \\
V_{cd} &  V_{cs} & V_{cb} \\
V_{td} &  V_{ts} & V_{tb}  \end{array}\right).
\end{equation}
A commonly used approximate parameterization was originally proposed by
Wolfenstein \cite{wolf}.
It reflects the hierarchy between the magnitude of matrix elements
belonging to different
diagonals. It is:
\begin{equation}
\scriptsize
{\begin{array}{ccc}
1-\lambda^2/2 &  \lambda & A\lambda^3(\rho-i\eta(1-\lambda^2/2)) \\
-\lambda &  1-\lambda^2/2-i\eta A^2\lambda^4 & A\lambda^2(1+i\eta\lambda^2) \\
A\lambda^3(1-\rho-i\eta) &  -A\lambda^2& 1
\end{array}}
\end{equation}

The CKM matrix must be unitary and the relation between elements of different
rows dictated by this property can be graphically represented as
so called `unitarity triangles'.   Fig.~\ref{six_tri} shows the 6 unitarity
triangles
that can be constructed to check this property. The expected lengths of the
sides
are suggested. The bottom two triangles give a hint on the optimal strategy
to test the CKM sector of the Standard Model.
The three sides are of comparable length and thus all the angles and sides are
more amenable to experimental measurement. The CKM matrix is characterized by
four independent parameters. Aleksan, Kayser and London \cite{alk} pointed out
that
we can express the CKM matrix as a function of four phases that can be
determined
by $CP$ observables. These phases are:
\begin{eqnarray}
\beta=arg\left(-\frac{V_{tb}V_{ts}^{\star }}{V_{cb}V_{cd}^{\star }}\right) \\
\gamma =arg\left(-\frac{V_{ub}^{\star }V_{ud}}{V_{cb} ^{\star }V_{cd}}\right) \\
\chi = arg\left(-\frac{V_{cs}^{\star }V_{cb}}{V_{ts}^{\star }V_{tb}}\right) \\
\chi ^{\prime }=arg\left(-\frac{V_{ud}^{\star }V_{us}}{V_{cd}^{\star
}V_{cs}}\right)
\end{eqnarray}
 Silva and
Wolfenstein \cite{wol-si} emphasized that we can use these
phases to identify new physics effects in $B$
decays. The details of an
experimental program capable of making these
measurements with the needed accuracy will be discussed below.

\begin{figure}[hb]
\centerline{\epsfig{figure=six_tri.eps,height=2.3in}}
\caption{\label{six_tri}The six CKM triangles. The bold labels, i.e {\bf ds}
refer to the rows or columns used in the unitarity relationship.}
\end{figure}

The experimental information presently available consists of $CP$ violation
observables
in the $K$ system, discussed by G. Buchalla \cite{Gerhard} in these
proceedings, and by a variety
of constraints on the sides of the unitarity triangles. Very often the dominant
uncertainty
in the extraction of the magnitude of the CKM parameters from the data is the
relationship
between experimental observables and the quark mixing parameter to be measured.
This relationship is governed by a matrix element involving strong interaction
effects. The challenges
and possible pitfalls in the evaluation of the relevant matrix elements are
discussed below.

\subsection{The determination of $V_{cb}$ from the decay $B\rightarrow D^{\star } \ell
\overline{\nu}$.}
Heavy Quark Effective Theory (HQET) \cite{isgur} has been a very important
breakthrough in
our understanding of $B$ meson decays. It is an effective theory that
gives very definite predictions in the limit of infinite quark masses. In
addition,
corrections for finite quark masses can be accounted for  with a systematic
study
of non-perturbative effects using a 1/$m_Q$\ expansion, where $m_Q$ represents
the mass of the heavy quarks involved in the process. One of the first
implication of the theory
\cite{luke} has been the advantage offered by the decay $B\rightarrow D^{\star } \ell
\nu$. The differential
decay width $\Gamma (B\rightarrow D^{\star } \ell \overline{\nu})$ is a function of the
invariant 4-velocity
transfer $w=\vec{v}\cdot \vec{v^{\prime}}$, where $\vec{v}$ and
$\vec{v^{\prime}}$
are the 4-velocities of the incoming and outgoing heavy hadron respectively. It
is given by:
\begin{eqnarray}
\frac{d\Gamma}{dw}= {\cal K}(w){\cal F}^2(w)|V_{cb}| ^2,\\
{\cal F}(w) = {\cal F}_{D^ {\star }}(1){\cal G}(w)
\end{eqnarray}
where ${\cal K}(w)$ is a known phase space factor, ${\cal G}(w)$ is the shape of
the Isgur-Wise function and
${\cal F}_{D^ {\star }}(1)$ is a normalization factor that is predicted from
this effective theory.
It is generally expressed as:
\begin{eqnarray}
{\cal F}(1) =\eta _A ( 1 + const
\times  \frac{\Lambda _{QCD}^2}{m_Q^2}+ \cdots )
\\ \nonumber \equiv
\eta _A (1+\delta _{1/m_Q^2})
\end{eqnarray}
Note, the $1/m_Q$ term vanishes.
The parameter $\eta _A$ is the short distance correction arising from the finite
renormalization of the flavour changing
axial current at zero recoil and $\delta _{1/m_Q^2}$ parametrizes the second
order term (and higher) order
corrections in the $1/m_Q$ expansion including the effects of finite heavy quark
masses.
There has been a lot of theoretical activity on both $\eta _A$ and $1/m_Q^2$
corrections. The $\eta _A$ factor
has been calculated by Czarnecki at two loop order \cite{cza} to be $0.960\pm
0.007$. The $1/m_Q^2$ correction has been
evaluated in different approaches and is more subjected to the author bias
because it involves non-perturbative effects
\cite{variety1}, \cite{variety2}, \cite{variety3},
\cite{variety4}, \cite{variety5}.
These different estimates have been combined into \cite{babar}:
\begin{equation}
{\cal F}(1)=0.913\pm 0.007\pm 0.024 \pm 0.011,
\end{equation}
where the first error accounts for the remaining perturbative uncertainty,
the second one reflects the uncertainty in the calculation of the $1/m_Q^2$
corrections and the third one gives an estimate of the higher-order power
corrections.
 A very interesting recent development
is that Lattice Gauge theory has produced a preliminary
result on ${\cal F}(1)$. They obtain \cite{simone}, \cite{dlnu} :
\begin{equation}
{\cal F}(1)=0.935\pm 0.022 ^{+0.008}_{-0.011}\pm 0.008 \pm 0.020,
\label{normds}
\end{equation}
where the first error is statistical, the second is due to the uncertainty in
the
quark masses, the third is the uncertainty in radiative corrections beyond 1
loop and
the last represent $1/m_Q^3$ effects. Errors not yet estimated include the
sensitivity to
the lattice spacing adopted and to the quenching approximation.
The calculation is in its initial stage, but this is a promising hint that
an accurate value for
${\cal F}(1)$ will be available soon.

The present status of the experimental determination of the product
${\cal F}(1) V_{cb}$ is summarized in Table \ref{vcbexcl}.
\begin{table}
\begin{center}
\caption{\label{vcbexcl}Determination of $|V_{cb}|$\
from $B\rightarrow D^{\star}\ell \overline{\nu }$.
The first error in the $|V_{cb}|$\ estimate is the experimental error, obtained
adding in quadrature statistical and systematic errors. The last error is due to
theoretical
uncertainties in ${\cal F} (1)$.}
\begin{tabular}{lll}
\br
Experiment & ${\cal F}(1) V_{cb}\times 10^{-3}$ & $V_{cb}\times 10^{-3}$ \\
\hline
ALEPH \cite{alds}
  & $31.9\pm 1.8\pm 1.9$ & $34.9 \pm 2.9 \pm 1.6$   \\
DELPHI\cite{del99} & $37.7\pm 1.7 \pm 1.7$ &$ 41.3 \pm 2.6 \pm 1.9$\\
OPAL\cite{opl96}
& $32.8\pm 1.9 \pm 2.2$ & $35.9 \pm 3.2 \pm 1.5 $\\
\hline
CLEO $\dagger$ & $36.1 \pm 1.9 \pm 1.9$ & $39.5 \pm 2.9 \pm 1.8$ \\
\hline
AVERAGE &  $34.8\pm 0.91\pm 0.95$& $38.2\pm 1.4 \pm 1.8 $\\
\hline
\end{tabular}
\end{center}
$\dagger$ The published CLEO result \cite{dscleo} has been scaled up by
3\% according to the calculation performed by Stone \cite{albuquerque} to
account
for the curvature of the form factor.
\end{table}

If we average these results, we obtain $V_{cb}=(38.2 \pm 1.40 _{exp}
+1.8_{th})\times
10^{-3}$.
The experimental error is obtained by adding in quadrature the statistical and
systematic errors.  The
theoretical
error is based on Eq.~\ref{normds}.

\subsection{The determination of $|V_{cb}|$\ from inclusive semileptonic decays.}

An alternative determination of $V_{cb}$ has been obtained using the inclusive
semileptonic branching fraction. This quantity has been studied both at the
$\Upsilon ({\rm 4S})$\ from CLEO and ARGUS and at LEP. The most accurate measurement at
the $\Upsilon ({\rm 4S})$\
has been reported by CLEO from a small subset of their full data sample
\cite{dilep} using a lepton tagged sample. This method of extracting the
branching fraction is less model dependent as it can measure a larger portion
of the electron spectrum as shown in Fig.~ \ref{sldile}.

\begin{figure}
\begin{center}
\epsfig{file=sl.eps,width=2.7in}
 \caption{Spectra of electrons from
$B\rightarrow  X e \overline{\nu }$ (filled circles) and $b\rightarrow  c \rightarrow y l
\overline{\nu}$
(open circles) identified with
lepton tags. The curves show the best fit to the modified ISGW model, with 23\%
$B\rightarrow D^{\star \star}\ell \overline{\nu}$.}
\label{sldile}
\end{center}
\end{figure}

 All the four LEP
experiments reported measurements of the semileptonic branching fractions.
The experimental information is summarized in Table \ref{semil}. The
measured semileptonic widths, obtained using the most recent average values
for the $b$ quark  and the $B$ meson lifetimes, are shown also. Note that the
partial width measurements from LEP and the $\Upsilon ({\rm 4S})$\ are still mildly
inconsistent. In addition, the
systematic
errors in different LEP experiments are evaluated using different methods and
assumptions.
A working group has been established to address this issue \cite{lepwg}, but
their
work is still in progress. As the dominant error in these analyses is
systematic, until
these issues are settled it appears premature to use a weighted average of these
results.

\begin{table}
\begin{center}
\caption{\label{semil}Summary on semileptonic width data from CLEO and LEP.
The lifetimes $\tau _B=1.605\pm 0.021$ ps and $\tau_b=1.564\pm 0.014$ ps are
used to obtain
$\Gamma _{SL}$ for CLEO and LEP respectively.}
\begin{tabular}{lll}
\br
Exp. &  ${\cal B}_{SL}$(\%) & $\Gamma _{SL}$ \\
  &  & $\times 10^{10} {\rm s}^{-1}$ \\
\hline
ALPH \cite{alsl} & $11.01\pm 0.10\pm 0.30$ & $7.04 {\scriptsize \pm 0.21} $ \\
DPHI \cite{delsl} & $10.65\pm 0.11 \pm 0.23 ^{+0.43}_{-0.27}$ & $6.81
^{+0.32}_{-0.23}$ \\
L3\cite{l3sl}& $10.16 \pm 0.13 \pm 0.29 $ & $6.50 {\scriptsize \pm 0.20}$ \\
OPAL\cite{opalsl} & $10.83 \pm 0.10 \pm 0.20 ^{+0.20}_{-0.13}$ & $6.92
^{+0.19}_{-0.17}$\\
\hline
CLEO\cite{dilep} & $10.49 \pm 0.17 \pm 0.43$ & $6.54 {\scriptsize \pm 0.29}$\\
\br
\end{tabular}
\end{center}
\end{table}

Recently  proponents
of the heavy quark expansion (HQE) \cite{ope-sl} have suggested that inclusive
quantities are the most promising avenue to perform a precise determination
of the CKM parameters. The semileptonic width is related to $|V_{cb}|$\ and
to the matrix element calculated by HQE through:
\begin{equation}
\begin{array}{ll}
|V_{cb}| = & 0.0411 \sqrt {{\cal B}(B\rightarrow X_c\ell \overline{\nu})/0.105} \\
~~ &\times \sqrt{1.55/\tau _B ({\rm ps})}\\
~~ &\left[1-0.024\left(\frac{\mu_{\pi }^2-0.5}{0.1}\right)\right]\times \\
~~ & (1\pm 0.01 (pert.)\pm 0.01 (m_b) \\
~~ & \pm 0.015 (1/m_b^3))
\end{array}
\end{equation}
where $\mu _{\pi}^2$ is a kinetic energy contribution which is a gauge-covariant
extension of the square of the $b$ quark momentum inside the
heavy hadron, $\mu _G$ is the chromomagnetic matrix element defined to a
given order in perturbative theory. Alternative formulations of this
relationship
have been proposed, either using slightly different parameterizations of the
correction
terms \cite{falk-incl}, or relating the semileptonic width to the $\Upsilon$
mass
in order to reduce the uncertainties associated with quark masses \cite{zoltan}.
If, for illustration purpose, we use the CLEO semileptonic width to extract
$|V_{cb}|$\ with this
method, we obtain $|V_{cb}| = 0.041 \pm 0.001_{exp} \pm 0.0025_{th}$.

 One very important concern is the dependence upon the quark
masses. Bigi \cite{bigiwg}
assumes an uncertainty of 10\%. Recent theoretical estimates of $m^{kin}_b$
seem to support this view, but more experimental data confirming
this picture is needed.  The
semileptonic width in the heavy quark expansion is dependent upon $m_c$\ and
$m_b$\ though the relationship:
\begin{equation}
\Gamma(B\rightarrow X_c\ell \overline{\nu}) \propto G_F^2(m_b-m_c)^2m_b^3
\end{equation}

The difference $m_b-m_c$ can be inferred according to several
authors \cite{hqe}
through the relationship:
\begin{equation}
\begin{array}{ll}
m_b - m_c = & <M_B> - <M_D> + \\
~~ & \mu ^2_{\pi }\left(\frac{1}{2m_c}-\frac{1}{2m_b}\right) + \\
~~&{\cal O}(1/m_{b,c}^2),
\end{array}
\end{equation}
where $<M_B>$ and $<M_D>$ represent the spin averaged beauty and charm meson
masses.
This formula gives $m_b - m_c \approx 3.5$ GeV, corresponding to an
uncomfortably low value of
the $c$ quark mass \cite{bigiwg}.

Finally it is hard to give a reliable estimate of the possible quark hadron
duality
violation in inclusive decays. In fact there are some arguments that suggest a
potential for significant violations of this assumption \cite{nathan}.
Until these issues are resolved, an average value of $|V_{cb}|$\ based on the
$D^{\star }\ell \overline{\nu}$ method
and the inclusive semileptonic widths does not seem appropriate.

Additional experimental
constraints are crucial to achieve a better understanding of these sources of
errors. The study of the
moments of the lepton spectrum and of the hadronic mass spectrum provides in
principle an additional
constraint that allows the extraction of some of the theoretical parameters
described above from
data. The moments of the hadronic mass spectrum are defined as:
\begin{equation}
<(s_H-\overline{m}_D^2)^n)>\equiv\frac{1}{\Gamma _{SL}}\int ds \frac{d\Gamma
}{ds}(s- \overline{m}_D^2)^n,
\end{equation}
where $s$ represent the hadronic mass recoiling against the lepton-neutrino pair
and $\overline{m}_D$ represents the
spin averaged mass of the $D$ meson.
If we use the heavy quark expansion result for $\Gamma _{SL}$, we obtain
for the
first moment \cite{falk-incl} :
\begin{equation}
\begin{array}{ll}
<(s_H-\overline{m}_D^2)> =& m_B^2 [ 0.051 \frac{\alpha _S}{\pi} +\\
~~ & 0.23 \frac{\overline{\Lambda}}{m_B}(1+0.43\frac{\alpha _S}{\pi})\\
~~ &+0.26\frac{\overline{\Lambda }^2}{m_B^2} +1.01 \frac{\lambda _1}{m_B^2}\\
~~ & -0.31
 \frac{\lambda _2}{m_B^2}]
\end{array}
\end{equation}
where the two matrix elements $\lambda _1$ and $\lambda _2$, characterizing the
corrections of
order $\Lambda _{QCD}/m_b^2$ are given by:
\begin{eqnarray}
\lambda _1 =-\frac{1}{2m_B}<B|\overline{h}_{\nu }(i\vec{D})^2 h_{\nu}| B>, \\
\lambda _2 =\frac{1}{3}<B| \overline{h}_{\nu }\frac{g}{2}\sigma _{\mu
\nu}G^{\mu\nu}h_{\nu}| B>,
\end{eqnarray}
where  $h_{\nu}$ is the heavy quark field in the effective theory with velocity
$\vec{v}$.
The parameter $\overline{\Lambda}$ is related to the $b$ quark mass through the
relationship:
\begin{equation}
m_B =m_b +\overline{\Lambda} -\frac{\lambda _1+3\lambda _2}{2m_b}.
\end{equation}
The $B^{\star}-B$ mass splitting determines $\lambda _2=0.12\
{\rm GeV}^2$. The parameters $\overline{\Lambda}$
and $\lambda _1$ can be extracted from the measured moments. Each measured
moment corresponds
to a band in the $\lambda _1 -\overline{\Lambda}$ plane. The CLEO collaboration
\cite{poling-vanc} measured first and second moments of the hadronic
mass have a region of intersection that implies:
\begin{eqnarray}
\overline{\Lambda} = 0.33\pm 0.02 \pm 0.08 {\rm GeV}\\
\lambda _1 = -0.13 \pm 0.01 \pm 0.06 (\rm (GeV/c)^2.
\end{eqnarray}

\begin{figure}[hbt]
\vspace{-5mm}
\centerline{\epsfig{figure=moments.eps,width=2.1in}}
\vspace{5mm}
\caption{\label{moments}Bands in $\overline{\Lambda}-\lambda_1$ space found
by CLEO in analyzing first and second moments of hadronic mass squared and
lepton energy. The intersections of the two moments for each set determines
the two parameters. The one standard deviation error ellipses are shown.}
\end{figure}

The two curves are shown in Fig.~\ref{moments}, that shows also the constraints
derived from a similar analysis
of the experimental moments of the lepton spectrum. It can be seen that the two
sets of constraints do not intersect at
a common point as they should. These data are still preliminary and we cannot
draw definite conclusions from them.
However until this discrepancy is resolved, this
is yet another reason not to use
an average value for $V_{cb}$ based
on the inclusive and exclusive determinations.

\subsection{The determination of $|V_{ub}|$\ from exclusive charmless semileptonic
decays}
Unfortunately, in the case of $|V_{ub}|$\ HQET does not help to
normalize the relevant
form factors. A variety of
calculations of such form factors exist, based on lattice gauge theory
\cite{ukqcd}, light cone sum rules  (LCSR) \cite{lcsr},
and quark models \cite{isgw}. The CLEO
collaboration has reported the first
convincing evidence for the decays $B\rightarrow \rho \ell \overline{\nu}$ and $B\rightarrow
\pi \ell \overline{\nu }$ \cite{buprl}.
CLEO has recently reported a measurement of the decay $B \rightarrow \rho \ell
\overline{\nu }$ with a different technique and a bigger
data sample \cite{summerrho}. They have used several
different models to extract
the value of $|V_{ub}|$ . Their results are summarized
in Table \ref{vubrho}.

\begin{table}
\begin{center}
\caption{\label{vubrho} Values of $|V_{ub}|$\ using  $B\rightarrow \rho \ell \overline{\nu }$
and some theoretical models. The $|V_{ub}|$\ data
include the results of a recent CLEO analysis \cite{summerrho} and a previous
CLEO result on exclusive charmless semileptonic
decays \cite{rhoprl}. The average $|V_{ub}|$\ includes an additional contribution
representative of the theoretical uncertainty
in the measurement.}
\begin{tabular}{ll}
\br
Model & $|V_{ub}|$\ ($\times 10^{-3}$)\\
\hline
UKQCD \cite{ukqcd} & $3.32\pm 0.14 ^{+0.21}_{-0.26}$ \\
LCSR \cite{lcsr} & $3.45 \pm 0.15 ^{+0.22}_{-0.31}$ \\
ISGW2 \cite{isgw} & $ 3.24 \pm 0.14 ^{+0.22}_{-0.29}$ \\
Beyer-Melikhov \cite{bm} & $ 3.32 \pm 0.15 ^{+0.21}_{-0.30}$ \\
Wise/Ligeti \cite{wl} & $2.92 \pm 0.13 ^{+0.19}_{-0.26}$ \\
\hline
Average & $3.25\pm 0.14 ^{+0.21}_{-0.29}\pm 0.55$ \\
\br
\end{tabular}
\end{center}
\end{table}

The first three calculations are based on quark models and their uncertainties
are guessed to be in the 25-50\%
range in the rate, corresponding to a 12.5-25\% uncertainty for $|V_{ub}|$ . The other
approaches, light cone sum rules and lattice
QCD, estimate their errors in the range of 30\%, leading to a 15\% error in $|V_{ub}|$
. We can conclude that the average value
of $|V_{ub}|$\ extracted with this method is $| V_{ub}| = (3.25 \pm 0.14 ^{+0.21}_{-
0.31}\pm 0.5)\times 10^{-3}$. This corresponds
to a value of $|V_{ub}/V_{cb}| = 0.085 \pm 0.023$. The statistical and
systematic errors have been added in quadrature
and the theoretical error has been added linearly to be conservative. Note that
the theoretical error is somewhat arbitrary,
as the spread between the models considered does not necessarily
represent the uncertainty in $\Gamma _u^{th}$ nor may it properly reflect the
effect of the lepton momentum cut of $>2.3$ GeV/c used in the analysis.

An alternative
 approach used by CLEO has been the investigation of the inclusive lepton
spectrum beyond the kinematic
endpoint of $B\rightarrow X_c \ell \overline{\nu}$ decays \cite{cleoinc}. This method
gave the first unambiguous evidence
for charmless semileptonic decays, however its use to extract $|V_{ub}|$\ is plagued
by several theoretical
uncertainties. In addition to the errors discussed above, there is the
additional problem that very few
models can be used to relate $\Gamma _u ({\rm endpoint})$ with $\Gamma _u$. In
fact, most of the models
discussed above study only final states like $\rho \ell \overline{\nu}$ and $\pi
\ell \overline{\nu}$, whereas
it is likely that $\Gamma _u$ is composed of several different hadronic final
states. The Operator Product
Expansion (OPE) cannot give reliable predictions either, because when the
momentum region considered is of the
order of $\Lambda _{QCD}$ an infinite series of terms in this expansion may be
relevant. Nonetheless the model
dependent value extracted from these data has a central value of $|V_{ub}/V_{cb}|$ =0.079
\cite{beauty96}, very close to the
exclusive result.

Recently, interest has been stirred by a new approach
\cite{vub-bdu} to the extraction of $|V_{ub}|$\
based on the OPE
approach. The idea is that if the semileptonic width $\Gamma _u$ is extracted by
integrating over the hadronic mass $X_u$ recoiling
against the lepton neutrino pair in a sufficiently large region of phase space,
the relationship between $|V_{ub}|$\ and the
measured value of the charmless semileptonic branching fraction can be reliably
predicted. All the LEP experiments
but OPAL attempted
to use this technique to determine $|V_{ub}|$ . An example of the lepton spectrum
obtained by cutting on the measured $X_u < 1.5$ GeV is shown in
Fig.~\ref{vubdelphi}. Note that the claimed $|V_{ub}|$\ signal is accompanied by a
dominant $b\rightarrow c$ background.
The three experiments combine their analyses and quote
$|V_{ub}|= (4.05
^{+0.39}_{-0.46}(stat+det)^{+0.43}_{-0.51} (b\rightarrow c)
^{+0.23}_{-0.27}(b\rightarrow u) \pm 0.02
(\tau _b) \pm 0.16 (HQE)\times 10^{-3}$ \cite{vubwg}. These results raise
several concerns. First of all
the small error on the $b\rightarrow c$ background component is not adequately
justified. It implies a knowledge of
the $b\rightarrow c$ background to better than 1\%. Moreover the validity of the
theoretical input applies only
if the full phase space for the $b\rightarrow u \ell \overline{\nu}$ is measured. Even
if the mass cut $M_X<1.5$ GeV
should include most of the $\Gamma _u$ width, the complex set of event selection
criteria
applied may bias the phase space and make the errors in the $|V_{ub}|$\ determination
bigger than
expected \cite{ligeti-dpf}.

\begin{figure}[bt]
\vspace{-9mm}
\centerline{\epsfig{figure=delphi_vub.eps,width=2.in}}
\vspace{-4mm}
\caption{\label{vubdelphi}The lepton energy distribution in the $B$ rest
frame from DELPHI. The data have been enriched in $b \to u$ events, and the
mass of the recoiling hadronic system is required to be below 1.6 GeV. The
points indicate data, the light shaded region, the fitted background and the
dark shaded region, the fitted $b \to u \ell \nu$ signal. }
\end{figure}

Much work needs to be done to achieve a precise measurement of $|V_{ub}|$ . This
is a quite important element of our strategy to pin down the CKM sector of the
Standard Model.
On the theoretical side, large efforts are put in developing more reliable
methods to determine
the heavy to light form factors. A combination of several
methods \cite{neub-buras}, all with a limited range of applicability,
seem to be the strategy more likely to succeed. For instance, lattice QCD can
provide reliable estimates
of the form factors at large momentum transfer \cite{excl-lat}, where the
discretization errors
are under control.
HQET predicts a relationship between semileptonic $D$ decays and semileptonic
$B$ decays. To check
these predictions and apply them to $|V_{ub}|$\ estimates, large data sample with
reconstructed neutrino momentum
are necessary. For now, I use the $\rho \ell \overline{\nu}$ result as the best
estimate of $|V_{ub}/V_{cb}|$ .
I take $|V_{ub}/V_{cb}|= 0.085 \pm 0.023$.

\subsection{The present knowledge of the CKM parameters}
In addition to the measurement of $|V_{ub}/V_{cb}|$, other experimental
constraints can be used
to check the  $bd$ unitarity triangle.

\begin{figure}[htb]
\centerline{\epsfig{figure=ckm_tri_7.eps,height=2in}}
\vspace{-0.2cm}
\caption{\label{stone-const}The CKM triangle
shown in the $\rho-\eta$ plane. The
shaded regions show $\pm 1\sigma$ contours given by
$|V_{ub}/V_{cb}|$, neutral $B$ mixing, and CP violation in $K_L^o$ decay
($\epsilon$) \cite{stone}. The dashed region
is excluded by $B_s$ mixing limits.
The allowed region is defined by the overlap of
the 3 permitted areas, and is where the apex of the CKM triangle  sits.}
\end{figure}

An important input is the
$\epsilon$ parameter
describing
$CP$ violation effects in $K$ decays \cite{kcp}.
Note that the $\epsilon$ parameter is the only constraint that
forces $\eta$
to be positive. It is related to $\eta$ and $\rho$ through the relationship:
\begin{displaymath}
\eta\left[(1-\rho)A^2(1.4\pm 0.2)+0.35\right]A^2{B_K \over 0.75}=\\
(0.30\pm 0.06),
\end{displaymath}
where the errors arise mostly from uncertainties on $|V_{cb}|$ and $B_K$. Recall
that $A$ is
one of the Wolfenstein parameters:
\begin{equation}
A = V_{cb}/\lambda ^2,\\ |\lambda| =|V_{us}| =0.220\pm 0.002.
\end{equation}
$B_K$
is taken as 0.75$\pm$0.15 according to Buras \cite{Buras_bk}.
Also the parameter $Re(\epsilon ^{\prime}/\epsilon )$, recently measured with
increased
accuracy by KTeV \cite{ktev} and NA48 \cite{na48} can be used. Several
phenomenological calculations give $\eta$ as positive \cite{buras-eta}.
Note that a
recent
lattice calculation \cite{soni-epsilonp}, using a novel algorithm involving
domain wall fermions (DWF),
obtains for the parameter $Re(\epsilon ^{\prime}_{DWF}/\epsilon _{exp})$,
a negative value of $-(3.3\pm 0.3 _{stat}\pm 1.6_{sys})\times 10^{-2}\eta$,
where $\eta$ is the CP violation parameter in the Wolfenstein parameterization
of the CKM matrix.
This result is quite recent and needs further studies \cite{martinelli}, but it
may imply a
constraint in the $\rho - \eta$
plane not overlapping with the others and implies a violation of the Standard
Model.

Finally neutral $B$ meson oscillations provide additional constraints,
semicircles in the $\rho -\eta$ plane
centered at $(\rho,\eta)=(1,0)$.
The neutral $B_d$ oscillations
are measured rather well \cite{lep-osc}. The world average, including data from
LEP, CDF, and SLD, gives
$\Delta M_d=0.481 \pm 0.017 {\rm ps}^{-1}$. Only lower limits exist for $\Delta
M_s$. The LEP average
is 9.6 ps$^{-1}$, dominated by the 1998 ALEPH inclusive
lepton analysis corresponding to a 95\% C.L. lower limit of 9.5 ps$^{-1}$. The
world average
presented at Tampere is 12.4 ps$^{-1}$, whereas the most recent preliminary
world average is 14.3 ps$^{-1}$.
I will take as the world average the value of 12.4 ps$^{-1}$, because I believe
that a preliminary
value that is so much bigger than any individual measurement needs further
scrutiny.

The constraints on
$\rho$ versus $\eta$ from the $|V_{ub}/V_{cb}|$ determination,
$\epsilon$ and $B$
mixing are shown in Fig.~\ref{stone-const}. The bands represent $\pm1\sigma$ errors,
for the measurements and a 95\% confidence level upper limit on $B_s$ mixing.
 The width of the $B_d$ mixing band
is caused mainly by
the uncertainty on $f_B$, taken here as $240> f_B > 160$ MeV.

\begin{figure}[hbt]
\begin{center}
\epsfig{figure=haricot_new1999.EPS,
bbllx=80pt,bburx=503pt,bblly=8pt,bbury=249pt,height=4cm}
\caption{ The allowed region for $\overline{\rho}$ and $\overline{\eta}$
according to Ref. \cite{sr}.
The contours at 68 $\%$ and 95 $\%$ are shown. The full lines correspond to the
central values of the constraints given by
the measurements of  $  \frac{\left | V_{ub} \right |}{\left | V_{cb} \right |}
$, $\epsilon$ and $\Delta m_d$.
The dotted curve corresponds to the 95 $\%$ C.L. upper limit obtained from the
experimental limit on
$\Delta m_s$. The variables $\overline{\rho}$ and $\overline{\eta}$ are
defined as
 $\overline{\rho}\equiv \rho(1-\lambda^2)$ and  $\overline{\eta}\equiv \eta(1-
\lambda^2)$. }
\label{fairytale}
\end{center}
\end{figure}
Some authors have taken the data discussed above as the input of a global fit
that is supposed to generate
confidence level contours defined the Standard Model allowed region in the
$\rho-\eta$ plane. Fig.~\ref{fairytale}
shows a recent example of such an analysis \cite{sr}. The big problem in works
of this nature is how
to combine in a reliable fashion results often dominated by theoretical
uncertainties. Theoretical
errors are often educated guesses \cite{bigiwg} and thus not easily amenable to a
rigorous statistical analysis.
The relevance of the small contour that defines the Standard Model allowed
region in this plot is questionable.
For example, it will be very hard to attribute to a Standard Model failure any
discrepancy between these
results and new data coming from the next generation $b$ experiments that will
be discussed later.

\begin{figure}[hbt]
\begin{center}
\epsfig{figure=ckm-mass-3.ps,bbllx=80pt,bburx=550pt,bblly=400pt,
bbury=534pt,width=3in}
\vspace{2cm}
\caption{\label{bhrplot} Fit 1 (smaller region) from Ref. \cite{bhr}: prediction
for $\rho$ and $\eta$ using the quark mass constraints
from Eq.~\ref{c1} and~ \ref{c2}. Fit. 2 (larger region) corresponds to a
SM fit using $|V_{ub}/V_{cb}|$ , $\Delta m_s$ , $\Delta m_d$\ but not $\epsilon$.
For both fits the countours are 68, 95 and 99 \% C.L. respectively. The
variables $\overline{\rho}$ and $\overline{\eta}$ are defined as
 $\overline{\rho}\equiv \rho(1-\lambda^2)$ and  $\overline{\eta}\equiv \eta(1-
\lambda^2)$.}
\end{center}
\end{figure}

There is one interesting idea that was proposed originally by H. Fritzsch
\cite{harald} and is explored in
several recent papers. Its starting point is the observation that both the quark
masses and the quark mixing
follow specific hierarchies. Perhaps these patterns contain a clue that can lead
us to the more complete theory
that we are so eagerly pursuing. In particular quark mass textures,
i.e. specific patterns of zeros in quark mass matrices, that are motivated
by attempts to understand the origing of flavour assuming a spontaneously
broken symmetry, predict relationship between quark masses and quark mixing
parameters. For example, Barbieri, Hall and Romanino \cite{bhr} explored
the constraints in the $\rho-\eta$ plane produced by the relationships:
\begin{eqnarray}
\left| \frac{V_{ub}}{V_{cb}} \right| =\left(\frac{m_u}{m_c}\right)^{1/2}\\
\label{c1}
\left| \frac{V_{td}}{V_{ts}} \right| =\left(\frac{m_d}{m_s}\right)^{1/2}
\label{c2}
\end{eqnarray}
Fig.~\ref{bhrplot} shows the results from their analysis. Also in this case
the contour plots should be taken with some reservations. It should be noted
that
their results are consistent with a Standard Model fit performed with
the same technique as Roudeau {\it et al.} . The consistency is modest. This analysis
illustrates another handle that we may use in the future more
effectively to reach a more complete understanding of the mystery of flavour.

\section{Rare $b$ Decays}

``Rare" $b$ decays encompass a large class of decay modes, with
branching fractions not necessarily exceedingly small, where a suppression
mechanism reduces the rate compared to the dominant ``tree diagram.''
Fig.~\ref{rareb} shows the Feynman diagrams for the various decay processes
considered. Fig~\ref{rareb} (a) shows a tree amplitude that is associated
with $b\rightarrow u$ CKM suppressed decays.

$B^0-\bar{B^0}$
mixing occurs via a
``box" diagram with virtual $W$ bosons and $t$ quarks inside the box
[Figure \ref{rareb}(b)].
The box diagram gives rise
to large fractions of mixed events: 17\% for $B^0$ and 50\% for $B_s$ mesons.

Flavor-changing neutral currents lead to the transitions $b\to s$ and
$b\to d$.
These can be described in the Standard Model by one-loop diagrams,
known as ``penguin" diagrams, where a $W^-$ is emitted and reabsorbed.
The first such process to be observed was $b\to s\gamma$, described by the
diagram in Figure \ref{rareb}(c), where the $\gamma$ can be radiated from any
charged particle line. Another process which is important in rare $b$ decays
is $b\to s g$, where $g$ designates a gluon radiated from a quark line
[Figure \ref{rareb}(d)]. A third example of such processes is the transition
$b\to s\ell^+\ell^-$ which can occur through the diagrams shown in Figures
\ref{rareb}(e) and \ref{rareb}(f). We consider the loop processes shown in
 Figures \ref{rareb} (c)-(f)
to be among the most interesting and important rare $b$ decays.

\begin{figure}[hbt]
\centerline{\epsfig{figure=rare_b_decay.eps,
height=5.0in,bbllx=0bp,bblly=0bp,bburx=600bp,bbury=800bp,clip=}}
\vspace{-2.5cm}
\caption{Feynman Diagrams for $b$ Decays}
\label{rareb}
\end{figure}

\subsection{The decays $b\rightarrow s \gamma$ and $b\rightarrow s \ell ^+\ell ^-$}

There are several reasons why the study of rare $b$ decays is very important.
First of all, the suppression involved in loop diagrams makes it possible for
these
Standard Model processes to interfere with decay diagrams mediated by exotic
mechanisms due to `beyond Standard Model' interactions. In addition, loop
diagrams and CKM suppression can affect our ability of measuring CP violation
asymmetries.

CLEO has recently reported an updated value of
this branching fraction, ${\cal B}(b\rightarrow s \gamma)=(3.15\pm 0.35 \pm 0.32 \pm
0.26)\times 10^{-4}$ \cite{sgleppho}, where the first uncertainty is
statistical, the second
is systematic and the third accounts for model dependence.
ALEPH measured ${\cal B}(b\rightarrow s \gamma)=(3.11\pm 0.8 \pm 0.72 \pm
0.26)\times 10^{-4}$ \cite{sgaleph}, where the first error is statistical and
the second is systematic, providing a nice confirmation of the CLEO
result. In parallel a new
theoretical estimate of the Standard Model prediction with a full
next-to-leading-order-log calculation \cite{n3} has been performed, giving
a predicted ${\cal B}(b\rightarrow s \gamma)=(3.28\pm 0.33)\times 10^{-4}$, in
excellent agreement with the measured values.

The decay $b\rightarrow s \gamma$ was the first inclusive rare $b$ decay to be
measured \cite{bsgamma} and stirred a lot of theretical interest. It is
a powerful  constraint of theories ``beyond the
Standard Model." For example, Masiero \cite{antonio-b96} identifies this
process as ``the most relevant place in flavor changing neutral current $B$
physics to constrain SUSY, at least before the
advent of $B$ factories.''

The Standard Model predicts no CP asymmetry in $b\rightarrow s\gamma$. However recent
theoretical work \cite{n8} suggested that non-Standard Model physics may
induce a significant CP aysmmetry. Thus a search for CP asymmetry has been
performed by CLEO. A preliminary results of ${\cal A} = (0.16\pm 0.14\pm 0.05)
\times (1.0\pm 0.04)$ has been reported by CLEO \cite{sgleppho}. The
first number is the central value,
followed by the statistical error and an additive systematic error. The
multiplicative error is related to the uncertainty in the
mistagging rate correction. From this result a 90\% C.L. limit on the CP
asymmetry ${\cal A}$ of $-0.09<{\cal A}<0.42$ is derived. These results are
based on $\approx 3.1\ {\rm fb}^{-1}$ of data.

Another related decay mode that is quite important in constraining new
physics is the decay $b\rightarrow s\ell ^+ \ell ^-$ and the related exclusive
channels $B\rightarrow K^{(\star )} \ell ^+ \ell ^-$. These processes have been
studied both at CLEO and at CDF and D0. Table~\ref{lpluslmin} summarizes
the searches for these decays.

\begin{table}
\begin{center}
\caption{\label{lpluslmin} Searches for $b\rightarrow \ell ^+ \ell^-$ decays
compared with Standard Model theoretical predictions \cite{alill}.}
\begin{tabular}{lclc}
\br
$b$ decay & 90\% C.L. & Group & Prediction \\
mode & $\times 10^{-5}$ & ~~ &  $(\times 10 ^{-6})$ \\
\hline
$s\mu ^+ \mu^-$ & $32$ & D0 \cite{d02l} &  $(8\pm 2)$\\
~~ &5.7 &CLEO \cite{cleo2l} &~~\\
$K^{\star o}\mu ^+\mu ^-$ & 0.4 &CDF \cite{cdf2l}
& $2.9$ \\
~~ & $1.1$ &CLEO \cite{cleokse}&~~\\
$K^{\star o} e^+e^-$ & $1.3$ & CLEO \cite{cleokse} &
$5.6$ \\
$K^-\mu ^+\mu  ^-$ & $0.83$ & CLEO \cite{cleokse} & $0.6$\\
~~ & $0.52$ & CDF \cite{cdf2l} & ~~\\
$K^-e^+e^-$ &$1.1$ & CLEO \cite{cleokse}&$0.6$\\
\br
\end{tabular}
\end{center}
\end{table}

\subsection{Rare Hadronic $b$ Decays}
Fig.~\ref{rareb} includes the dominant diagrams mediating
rare $B$ hadronic decays.
The interplay between penguin and loop diagrams may affect our ability of
measuring CP asymmetries in two different ways. On one hand, loops and
CKM suppressed diagrams
can lead to final states accessible to both $B$ and $\overline{B}$ decays,
making it possible to measure interference effects without neutral
$B$ mixing. On the
other hand, the interplay between these two processes can cloud the
relationship between measured $CP$ asymmetries and the CKM phase when mixing
induced CP violation is looked for. A classical
example
of this effect is the decay $B^o\rightarrow \pi^+\pi^-$. The main Standard Model
diagrams contributing to this decay process are shown in Fig.~\ref{rareb}
(a) and (d).
If the $b\rightarrow u$ diagram is dominant, the angle $\alpha$ can be extracted
from the measurement of the asymmetry in the decay $B^o\rightarrow \pi^+
\pi ^-$.  On the other hand, if these two diagrams
have comparable amplitude, the extraction of $\alpha$ from this decay channel is
 going to be a much more difficult task.

CLEO has studied several decays that can lead to a more precise understanding
of the interplay between penguin diagrams and $b\rightarrow u$ diagrams in $B$ meson
decays. The analysis technique used has been extensively refined in order to
make the best use of the limited statistics presently available. In most of the
decay channels of interest, the dominant source of background are continuum
events; the fundamental difference
between $e^+e^-\rightarrow q\overline{q}$ and $B$ decays is the shape of the underlying
event. The
latter decays tend to produce a more `spherical' distribution of particles
whereas continuum events tend to be more `jet-like', with most of the particle
emitted into two narrow back to back `jets'. This property can be translated
into
several different shape variables.
 CLEO constructs a Fisher discriminant
${\cal F}=\Sigma _i \alpha_ iy_i$, a linear combination of several
variables $y_i$. The variables used are $|\cos{\theta _{cand}}|$, the
cosine of the angle between the candidate $B$ sphericity axis and the beam
axis, the ratio of Fox-Wolfram moments $R_2=H_2/H_0$, and nine
variables that measure the scalar sum of the momenta of the tracks and showers
from the rest of the event in 9 angular bins, each of 10$^{\circ}$,
around the candidate sphericity axis. The coefficients $\alpha _i$ have
been chosen to optimize the separation between signal and background Monte
Carlo samples \cite{rareb}. In
addition, several kinematical constraints allow a more precise determination of
the final state. First of all  they consider the energy difference $\Delta
E=E_{cand}-E_B$, where $E_{cand}$ is
the reconstructed  candidate mass  and $E_B$ is the known beam
energy ($\Delta E =0$ for signal events) and the
beam constrained mass $M_B$ calculated from $M_B^2=E_{beam}^2-\left(\Sigma _i
\vec{p}_i\right)^2$. In addition, the $B$ decay angle with
respect to the beam axis has a $\sin ^2 (\theta _B )$ angular distribution.
Finally,
to improve the separation between the final states $K\pi$ and $\pi\pi$
the specific energy loss in the drift chamber, $dE/dx$ is used.

CLEO uses a
sophisticated unbinned maximum likelihood (ML) fit to optimize the precision of
the
signal yield obtained in the analysis, using
$\Delta E$, $M_B$, ${\cal F}$, $|\cos{\theta _B}|$, and $dE/dx$ wherever
applicable. In each of these fits the likelihood of the event is parameterized
by the sum of probabilities for all the relevant signal and background
hypotheses, with relevant weights determined by maximizing the likelihood
function (${\cal L}$). The probability of a particular hypothesis is calculated
as the product of the probability density functions for each of the input
variables determined with high statistics Monte Carlo samples.
The likelihood function is defined as:
\begin{equation}
{\cal L} = \Pi _k \Sigma _i P^i_k(\Delta E, M_B,{\cal F}, dE/dx,
\cos{\theta _B}) \times f_i
\end{equation}
where the index $k$ runs over the number of events, the index $i$ over
the hypotheses considered, $P^i_k$ are the probabilities for
different hypotheses obtained from Monte Carlo
simulations of the signal and background channels considered and
independent data samples, and $f_i$ are
the fractional yields for
 hypothesis $i$, with the constraint:
\begin{equation}
\Sigma _i f_i =1
\end{equation}

Further details about the likelihood fit can be found elsewhere \cite{rareb}.
 The fits
include all the decay channels having a similar topology. For example, in the
final state including two charged hadrons, the final states considered were
$K^{\pm}\pi^{\mp }$, $\pi^+\pi^-$ and $K^+K^-$.

\begin{figure}[htb]
\centering
\leavevmode
\epsfxsize=3.0in
\epsffile{contkpi_prl.ps}
\vspace{-1in}
\caption{Contours of the $-2\ln{\cal L}$ for the ML fit to
$N_{K^{\pm}\pi^{\mp}}$ and $N_{\pi^+\pi^-}$, the $K^\pm\pi^\mp$
and $\pi^+\pi^-$ yields respectively. }
\label{fig:contourkpi}
\end{figure}

\begin{figure}[htb]
\centering
\leavevmode
\epsfxsize=3in
\epsffile{pipi_lp99.ps}
\caption{Projections of $K\pi$ and $\pi\pi$ events
onto $M$ and $\Delta E$ with cuts.
Upper left: $M$ distribution of $K\pi$-like events;
upper right: $M$ distribution of $\pi\pi$-like events.
Lower left: $\Delta E$ distribution of events prior
to $\pi\pi$ vs $K\pi$ vs $KK$ selection according to dE/dx;
Lower right: $\Delta E$ distribution of events that are
more likely to be $\pi\pi$ than $K\pi$ or $KK$ based on dE/dx.
Overlays in the lower plots are the results of the likelihood
fit scaled by the efficiency of the cuts used to project
into these plots. Solid line: total fit; dashed: $K\pi$;
dotted: $\pi\pi$; dot-dash: continuum background.}
\label{fig:kpi-pipi-projections}
\end{figure}

Fig. \ref{fig:contourkpi} shows contour plots of the ML fits for the signal
yields
in the  $K^{\pm}\pi^{\mp}$ and $\pi^+\pi^-$ final states. The other
channels included in the likelihood function have $f_i$ fixed to their most
probable value extracted from the fit. It can
be seen that there is a well defined signal for both the final states
$K^{\pm}\pi^{\mp}$ and
$\pi^+\pi^-$. The ratio between the most probable yields in
the two channels shows that the $b\rightarrow u$ diagram
is suppressed with respect to the penguin diagram in $B$ decays to two
pseudoscalar mesons.  Fig. \ref{fig:kpi-pipi-projections}
shows distributions in $M_B$ and $\Delta E$ for events after cuts on the
Fisher discriminant and whichever of $M$ and $\Delta E$ is not being
plotted, plus an exclusive classification into $K\pi$-like and $\pi\pi$-like
candidates
based on the most probable assignment with $dE/dx$ information. The
likelihood fit, suitably scaled to account for the efficiencies of the
additional cuts,
is overlaid in the $\Delta E$ distributions to illustrate the separation
between $K\pi$ and $\pi\pi$ events.

Table \ref{twops} summarizes the CLEO results for the
$B\rightarrow K\pi,~\pi \pi,~ KK$ final states. Unless explicitly stated, the
preliminary results are
based on 9.66 million $B\overline{B}$~pairs collected with the CLEO
detector.

There is a consistent
pattern of penguin dominance in $B$\ decays into two charmless
pseudoscalar
mesons that makes the prospects of extracting the angle
$\alpha$ from the study of the CP asymmetry in
the $B\rightarrow \pi^+\pi^-$ mode less favorable than originally expected.

\begin{table}
\begin{center}
\caption{Experimental results.
Branching fractions
(${\cal B}$) and 90\% C.L. upper limits are given in units
of $10^{-6}$.}
\begin {tabular}{lll}

\br
Mode&
${\cal B}$($10^{-6}$) & Signif.($\sigma$) \\
\hline
$\pi^+\pi^-$ &
   $4.7^{+1.8}_{-1.5}\pm 0.6$ &4.2      \\

$\pi^+\pi^0$

&$<12$  & 3.2        \\
\br
$K^+\pi^-$
 & $18.8^{+2.8}_{-2.6} \pm 1.3$  &11.7      \\
$K^+\pi^0$
& $12.1^{+3.0+2.1}_{-2.8-1.4}$  & 6.1        \\
$K^0\pi^+$  &
$18.2^{+4.6}_{-4.0} \pm 1.6$
 & 7.6 \\
$K^0\pi^0$
&$14.8^{+5.9+2.4}_{-5.1-3.3}$    & 4.7            \\
\br
$K^+K^-$
& $<2.0$ & --  \\
$K^+\overline{K}^0$   &
 $<5.1$   & 1.1  \\
\br
\end {tabular}
\label{twops}
\end{center}
\end {table}

\begin{figure}[htb]
\centerline{\epsfig{figure=pirho.ps, width=2.8 in}}
\caption{$n\sigma$ contours for the decays $B^+ \rightarrow \rho ^0 \pi^+$
and $B^+\rightarrow \rho ^0 K^+$. The cross identifies the most
probable values of the yields
for these two channels.
\label{pirho}}
\end{figure}

 Recent
CLEO data suggest that final states involving a vector and a pseudoscalar meson
offer a different picture. In fact,
$B^+ \rightarrow \pi ^+ \rho^o$ and $B \rightarrow \rho ^{\pm} \pi ^{\mp}$ \cite{gao}
have been observed, while the penguin dominated final states $B^+ \rightarrow K  \rho$
and $B \rightarrow K^{\star} \pi$ have
not.
 The analysis procedure is similar to the one
adopted for the charmless pseudoscalar-pseudoscalar exclusive decays. In this
quasi two-body case, there are three
particles in the final state and some additional constraints are provided
by the vector particle decay kinematics. The invariant mass of its decay
products must be consistent with the vector meson mass. In addition, the
vector meson is polarized, thus its helicity angle
$\theta _h$ has a $\cos ^2{\theta _h}$ distribution. The
maximum likelihood fit
includes $\pi\rho^0$ and $K\rho ^0$ signal channels and continuum samples. The
$n\sigma$ contour
 plot for this analysis is shown
in Fig. \ref{pirho} and gives solid evidence for a $B^+ \rightarrow \pi ^+\rho ^o$
signal, while the $B^+\rightarrow K^ +\rho ^o$ channel appears to be suppressed.
Table~\ref{results2} shows the results for each decay mode
 investigated. For observations the final
 result is reported as a branching fraction central value, while for modes
 where the yield is not sufficiently significant the 90\% confidence
 level upper limit is quoted. Also listed in the Table are
theoretical
 estimates.

\begin{table*}[htb]
\caption{ Summary of CLEO results on charmless hadronic
decays to a final state including a vector
and a pseudoscalar meson compared with expectations from theoretical models.}
\vspace{0.4cm}
\begin{center}
\begin{tabular}{llll}
\br
Decay mode & ${\cal B} (10^{-6})$  & Theory {\cal B}\ ($10^{-6}$)&References\\
\hline
\mbox{$B^+\rightarrow\omega\pi^+$}   & $11.3^{+3.3}_{-2.9}\pm{1.5}$ & $0.6-11$        &
    \cite{chau,dean,kps,du,oh,ciuchini,ali,cheng}     \\
\mbox{$B^0\rightarrow\omega \pi^{0}$}  &          $< 5.8 $            & $0.01-12$       &
    \cite{chau,dean,du,oh,ciuchini,ali,cheng}         \\
\mbox{$B^+\rightarrow\omega K^+$}    &          $< 8.0$             & $0.2-13$        &
    \cite{chau,dean,kps,du,oh,ciuchini,ali,cheng}     \\
\mbox{$B^0\rightarrow\omega K^{0}$}   &          $< 21$               & $0.02-10$       &
    \cite{chau,dean,du,oh,ciuchini,ali,cheng}         \\
\mbox{$B^+\rightarrow\omega h^+$}    & $14.3^{+3.6}_{-3.2}\pm 2.1$  &                 &
                        \\
\mbox{$B^+\rightarrow\omega \rho^+$} &          $< 47$               & $7-28$          &
    \cite{chau,dean,kpsvv,ciuchini,ali,cheng}         \\
\mbox{$B^0\rightarrow\omega \rho^0$} &          $< 11$               & $0.005-0.4$     &
    \cite{chau,ciuchini,ali,cheng}                    \\
\mbox{$B^+\rightarrow\omega K^{*+}$} &          $< 52$              & $0.9-15$        &
    \cite{chau,dean,kpsvv,ciuchini,ali,cheng}         \\
\mbox{$B^0\rightarrow\omega K^{*0}$} &          $< 19$              & $0.3-12$        &
    \cite{chau,dean,ciuchini,ali,cheng}               \\
\mbox{$B^+\rightarrow\rho^0 \pi^+$}    &    $15^{+5}_{-5} \pm 4$       & $0.4-8$      &
  \cite{chau,ebert,dean,kps,du,oh,ciuchini,ali,cheng} \\
\mbox{$B^0\rightarrow\rho^- \pi^+$}    &    $35^{+11}_{-10} \pm 5$    & $26-52$      &
  \cite{chau,ebert,dean,du,oh,ciuchini,ali,cheng}     \\
\mbox{$B^0\rightarrow\rho^0 \pi^0$}   &          $<5.1$              & $0.9-2.3$       &
  \cite{chau,ebert,du,oh,ciuchini,ali,cheng}          \\
\mbox{$B^+\rightarrow\rho^0 K^+$}     &          $<22 $              & $0.1-1.7$    &
  \cite{desh,chau,dean,kps,du,oh,ciuchini,ali,cheng}  \\
\mbox{$B^0\rightarrow\rho^- K^+$}     &          $<25 $              & $0.2-2.5$    &
  \cite{desh,chau,dean,du,oh,ciuchini,ali,cheng}      \\
\mbox{$B^0\rightarrow\rho^0 K^0$}    &          $<27 $              & $0.04-1.7$   &
  \cite{desh,chau,dean,du,oh,ciuchini,ali,cheng}      \\
\mbox{$B^+\rightarrow K^{*0} \pi^+$}    &          $<27 $              & $4-12$       &
  \cite{desh,chau,fl,du,oh,ciuchini,ali,cheng}        \\
\mbox{$B^0\rightarrow K^{*+} \pi^-$}    & $22^{+8 \; +4}_{-6 \; -5}$   & $1.2-19$     &
  \cite{desh,chau,dean,du,oh,ciuchini,ali,cheng}      \\
\mbox{$B^0\rightarrow K^{*0} \pi^0$}   &          $<4.2$              & $1.1-5$         &
  \cite{desh,chau,dean,du,oh,ciuchini,ali,cheng}      \\
\mbox{$B^0\rightarrow K^{*+} K^-$}     &          $<6  $              &              &
                                                      \\
\mbox{$B^+\rightarrow K^{*0} K^+$}     &          $<12 $              & $0.2-1$      &
  \cite{chau,kps,du,oh,ali,cheng} \\
\mbox{$B^+\ra\phi\pi^+$}     &          $<4.0$              & $0.001-0.4$  &
    \cite{xing,dean,fl,kps,du,oh,ciuchini,ali,cheng}  \\
\mbox{$B^0\ra\phi\pi^0$}    &          $<5.4$              & $0.0004-0.2$ &
    \cite{xing,dean,fl,du,oh,ciuchini,ali,cheng}      \\
\mbox{$B^+\ra\phi K^+$}      &          $< 5.9$             & $0.3-18$     &
    \cite{desh,chau,dean,fl,dav,kps,du,oh,ciuchini,ali,cheng} \\
\mbox{$B^0\ra\phi K^0$}     &          $< 28$              & $0.3-18$     &
    \cite{desh,chau,dean,fl,dav,du,oh,ciuchini,ali,cheng}     \\
\br
\end{tabular}
\end{center}
\label{results2}
\end{table*}

The stronger $b\rightarrow u$ component in vector to pseudoscalar final states suggests
that
an approach, proposed by Snyder and Quinn \cite{sq} can lead to
a precise measurement of the angle $\alpha$.
The interference between Tree and Penguin diagrams can be measured
 through the time dependent CP violating
 effects in the decays $B^o\to\rho\pi\to\pi^+\pi^-\pi^o$.
 Since the
$\rho$ is spin-1, the $\pi$ spin-0 and the initial $B$ also spinless, the
$\rho$
is fully polarized in the (1,0) configuration, so the helicity angle has a
$\cos^2{\theta}$
distribution.
 This causes the periphery of the Dalitz plot to be
heavily populated, especially the corners. A sample Dalitz plot is shown in
Fig.~\ref{dalitz}.
\begin{figure}[htb]
\vspace{-0.4cm}
\centerline{\epsfig{figure=dalitz3pi.eps,height=2.3in}}
\vspace{-.6cm}
\caption{\label{dalitz} The Dalitz plot for
$B^o\to\rho\pi\to\pi^+\pi^-\pi^o$ from Snyder and Quinn.}
\end{figure}
 Snyder and Quinn performed an idealized analysis that showed that a background
free 1000 or
2000 flavor tagged event samples is sufficient to measure $\alpha$.

These charmless hadronic decays can, in principle, provide also
some information on the phase $\gamma$, conventionally defined as
the argument of $V_{ub}$. This phase can cause asymmetries in decay rates to
charge conjugate pairs. CLEO has taken a first look at possible evidence for
these rate asymmetries. No positive signal has been seen and the present
sensitivity
is shown in Table~\ref{tbl:sum} summarizing their preliminary results.
\vskip 0.5cm
\begin{table*}[ht]
\begin{center}
\caption{\mbox{${{\cal A}_{\rm CP}}$}\ measurements in five charmless $B$ decay modes. CLEO 1999
Preliminary.}
\begin{tabular}{lllll}
\br
Mode &  $\mbox{${ \cal S   }$}$              & $\mbox{${ \overline{\sig} }$}$            & $\mbox{${{\cal A}_{\rm CP}}$}$ & 90\% CL
\cr
\hline
$K\pi^0$         &  $16.8\pm 7.5$      & $28.9\pm 7.5$        & $-0.27\pm
0.23\pm 0.05$          & $[-0.70, 0.16]$   \cr
$K^0_S\pi$       & $14.5 \pm 4.4$      & $10.2 \pm 4.0$       & $0.17\pm 0.24\pm
0.05$           & $[-0.27, 0.61]$   \cr
$K\pi$           &$38.6_{-8.1}^{+9.0}$ &$41.6_{-8.0}^{+8.9}$  & $-0.04\pm
0.16\pm 0.05$          & $[-0.35, 0.27]$   \cr
$\mbox{$\eta^\prime$} K$       & $51.7\pm 9.2$       & $48.7\pm 8.9$        & $0.03\pm 0.12\pm
0.05$           & $[-0.22, 0.28]$  \cr
$\omega\pi$     &$\aerr{9.4}{4.9}{4.0}$&$\aerr{19.1}{6.8}{5.9}$& $-0.34\pm
0.25\pm 0.05$         & $[-0.80, 0.12]$  \cr
\hline
\end{tabular}
\label{tbl:sum}
\end{center}
\end{table*}

\begin{table*}[htb]
\caption{Summary of CLEO results for $B$\ branching fractions
to charmless final states involving an $\eta$ or $\eta^{\prime}$
mesons. The second  column gives recent
preliminary result \cite{leppho}, unless otherwise stated. The central value
followed by statistical and
systematic error is given if significantly above zero, otherwise as a 90\%
confidence level upper limit is quoted.  Estimates from various theoretical
sources are shown for comparison.}
\begin{center}
\begin{tabular}{llll}
\br
Decay mode
&  ${\cal B} (10^{-6})$ & Signif. ($\sigma$) &
 Theory {\cal B}($10^{-6}$)\cr
\hline
$B^+\rightarrow\mbox{$\mbox{$\eta^\prime$} K^+$}$     &  \mbox{$80^{+10}_{-9}\pm8$} &
                        16.8 &
                        7 -- 65 \cite{chau,du}\\
$B^0\rightarrow\mbox{$\mbox{$\eta^\prime$} K^0$}$    & \mbox{$88^{+18}_{-16}\pm9$} & 11.7  &
                       9 -- 59 \cite{chau,du}\\
$B^+\rightarrow\mbox{$\mbox{$\eta^\prime$}\pi^+$}$    & $<11$ & $0.2$ &
                        1 -- 23 \cite{chau,du}\cr
$B^0\rightarrow\mbox{$\mbox{$\eta^\prime$}\mbox{$\pi^0$}$}$\cite{etapprl}   & $<11$ & --
                         & 0.1 -- 14 \cite{chau,du}\cr
$B^+\rightarrow\mbox{$\mbox{$\eta^\prime$} K^{*+}$}$\cite{cleoDPF}  &$<87$ &   1.2 &
                          0.1 -- 3.7 \cite{chau,du}\cr
$B^0\rightarrow\mbox{$\mbox{$\eta^\prime$} K^{*0}$}$\cite{cleoDPF}  & $<20$   &1.0 &
                         0.1 -- 8.0 \cite{chau,du}\cr
$B^+\rightarrow\mbox{$\mbox{$\eta^\prime$}\rho^+$}$ \cite{etapprl}  & $<47$ & --
                        & 3 -- 24 \cite{chau,du}\cr
$B^0\rightarrow\mbox{$\mbox{$\eta^\prime$}\rho^0$}$   \cite{etapprl}&  $<23$ & --
                       & 0.1 -- 11 \cite{chau,du}\cr
$B^+\rightarrow\mbox{$\eta K^+$}$      & $<7.1$   & 1.0 &
                   0.2 -- 5.0 \cite{chau,du}\cr
$B^0\rightarrow\mbox{$\eta K^0$}$      & $<9.5$ &--&
                        0.1 -- 3.0 \cite{chau,dean,du}\cr
$B^+\rightarrow\mbox{$\eta\pi^+$}$      & $<6.0$ & 0.6 &
                       1.9 -- 7.4 \cite{chau,dean,du}\cr
$B^0\rightarrow\mbox{$\eta\mbox{$\pi^0$}$}$      & $<3.1$ & -- &
                        0.2 -- 4.3 \cite{chau,du}\cr
$B^+\rightarrow\mbox{$\eta K^{*+}$}$   & \mbox{$27.3^{+9.6}_{-8.2}\pm 5.0$} &   4.8 &
                       0.2 -- 8.2 \cite{chau,du}\cr
$B^0\rightarrow\mbox{$\eta K^{*0}$}$    &\mbox{$13.8^{+5.5}_{-4.4}\pm 1.7$} &  5.1 &
                        0.1 -- 8.9 \cite{chau,dean,du}\cr
$B^+\rightarrow\mbox{$\eta \rho^+$}$  & $<16$ &  1.3 &
                       4 -- 17 \cite{chau,dean,du}\cr
$B^0\rightarrow\mbox{$\eta \rho^0$}$   & $<11$  & 1.3
                       & 0.1 -- 6.5 \cite{chau,dean,du}\cr
\br
\end{tabular}
\end{center}
\label{combtab}
\end{table*}

The branching fractions themselves can be used to constraint the angle
$\gamma$. Several approaches have been pursued and they are
more or less model dependent \cite{gamma-lit}. Atwood and Soni
performed a general analysis
of $B$ decays involving 10 $B$ decay modes to pseudoscalar final states
\cite{as98} for the charged
and neutral $B$\ mesons respectively. Their
analysis has been recently updated to include the results discussed in this
paper.  Conjugate
pairs have been taken together since the experimental data are not yet
sensitive to CP violation effects. Rescattering effects are attributed to a
single complex
parameter $\kappa$. This analysis determines 8 parameters,
tree amplitude $t$, color suppressed
amplitude $\hat{t}$, penguin amplitude $p$, electroweak penguin amplitude
$e$, real $\kappa =\kappa _R$, imaginary  $\kappa =\kappa _I$, and the
CKM parameters $\rho$ and $\eta$. A self-consistent solution
is sought for using a $\chi ^2$ minimization. Several fits are performed
using different simplifying assumptions. The best fits are obtained
assuming that electroweak penguin and rescattering effects are negligible. In
this case the authors obtain a value of
$\gamma = 92\pm 20$ degrees.

Recently Hou, Smith and W\"uerthwein \cite{hsw} have performed a
similar analysis, including final states
 composed by two pseudoscalar mesons and a vector and a pseudoscalar
 meson. They perform a fit with the same procedure
as one of the fits by Atwood and Soni, with the restrictive assumption of
factorization. They obtain $\gamma = 114 ^{+25}_{-21}$ degrees. The
$VP$ final states have been studied with flavor SU(3) by Gronau
and Rosner \cite{gr99} and they found that several processes are consistent
with $\cos{\gamma}<0$.  These results are preliminary.
These studies illustrate the increasing interest in these decays to measure
fundamental Standard Model parameters. However to reach definite
conclusion, a deeper understanding of hadronic physics must be achieved.

The CLEO study of $B$ decays to final states including two charmless hadrons
has presented some other interesting surprises. A large branching ratio
has been discovered for final states including a $\eta ^{\prime}$ meson. The
analysis technique in this case is essentially the same as the one discussed
above. The $\eta ^{\prime}$ is reconstructed both in its
$\eta \pi^+\pi^-$ and $\rho \gamma$ decay channels. The results for different
decay modes including
$\eta$ and $\eta ^{\prime}$
are summarized in Table~\ref{combtab}. The most notable
feature is the astonishing large rate for the
$\eta ^{\prime} K$
final state. While several theoretical interpretations have
been proposed to explain this enhancement \cite{etap-th}, a very
plausible explanation  still points to a dominance of penguin effects.

\section{The lesson from charm}
Charm is a unique probe of the Standard Model in the up quark sector,
thus providing a window of opportunity to discover new physics complementary
to that attainable from the down-quark sector. Due to the effectiveness of
the GIM mechanism, short distance contribution to
rare charm processes
are extremely small. Thus very often long range effects, for which reliable
calculations are rarely available, dominate the rates. On the other hand the
fact that the Standard Model predictions are so small for flavor changing
neutral currents in the charm sector provides a unique opportunity
to discover new physics in charm rare decays, $D^o\bar{D}^o$ mixing and
CP violation in the decays of charmed mesons.
\subsection{Rare and Forbidden decays of charmed mesons}
Flavor changing neutral current (FCNC) decays of the $D$ meson include the
processes $D^o\rightarrow \ell ^+\ell ^-,\ \gamma\gamma$, and $D\rightarrow X_u \gamma,\
X_u\nu\overline{\nu},\ X_u \ell ^+\ell ^-$.
They proceed via electromagnetic or weak penguin diagrams, with contributions
from box diagrams in
some cases. Calculations of short distance contributions to these decays are
quite reliable \cite{joanne96}, however the long range contribution estimates
are plagued with hadronic uncertainties and are mentioned here
to give an approximate upper limit of the size of these effects.

Table~\ref{rared} summarizes some theoretical predictions together with the
experimental upper limits
coming from fixed target charm experiments, most notably E791 \cite{e791r},
 and CLEO.  Soon another fixed target experiment at Fermilab, FOCUS, should
provide an improvement of about a factor of 10 \cite{daniele}. These decays
are usually classified into three categories:
\begin{itemize}
\item[1)] Flavor changing neutral current (FCNC) decays, such as
$D^o\rightarrow \ell ^+\ell^-$ and $D^o\rightarrow X\ell ^+\ell ^-$,
\item[2] Lepton family number violating (LFNV) such as
$D^+\rightarrow h^-\mu^{\pm} e^{\mp})$,
\item[3)]Lepton number violating (LNV) decays such as
$D^+\rightarrow h^-\mu ^+\mu^+$.
\end{itemize}

The first decays (FCNC) are rare, namely they are processes that can proceed
via an internal quark loop in the Standard Model. The other two categories
are
strictly forbidden within the Standard Model. However they are are allowed
in some of its extensions, such as extended technicolor \cite{joanne96}. The
expected rates for class (1) decays
 are several orders of magnitude below
the experimental sensitivity. However this may represent a window of
opportunity to discover new physics.

\begin{table*}[hbt]
\begin{center}
\caption{\label{rared}Measured experimental limits for various rare $D$
meson decays together with the  Standard Model predictions for the branching
fractions due to short (${\cal B}_{SD}$) and long distance
 contributions ((${\cal B}_{LD}$).}
\begin{tabular}{llll}
\br
Decay Mode & Experimental limit (90 \% C.L.) &
${\cal B}_{SD}$) & (${\cal B}_{LD}$) \\
\hline
$D^o\rightarrow \mu^+\mu^-$ & $4.1\times 10^{-6}$ \cite{pdg98}
 & $(1-20)\times 10^{-19}$ &$<3\times 10^{-15}$\\
$D^o\rightarrow e^+e^-$ & $6.2\times 10^{-6}$ \cite{e791r}
$(2.3-4.7)\times 10^{-24}$ & -- \\
$D^o\rightarrow \mu^{\pm}e^{\mp}$ & $8.1\times 10^{-6}$ \cite{e791r}& $0$ &$0$\\
\hline
$D^o\rightarrow \gamma\gamma $& -- & $10^{-16}$ & $<10^{-9}$ \\
\hline
$D\rightarrow X_u\gamma$ & ~~& $1.4 \times 10^{-7}$ & -- \\
$D^o\rightarrow \rho ^o\gamma$ & $2.4\times 10^{-4}$ \cite{pdg98}
& -- & $<2\times 10^{-5}$\\
$D^o\rightarrow \phi \gamma$ & $1.9\times 10^{-4}$  \cite{pdg98}
& -- & $<10^{-4}$ \\
$D^+\rightarrow\rho ^+\gamma$ & ~~ & ~~ & $2\times 10^{-4}$ \\
\hline
$D^o\rightarrow X_u\ell ^+ \ell ^-$ & ~~ & $4\times 10 ^{-9}$ & ~~ \\
$D^o\rightarrow \pi ^o ee/\mu\mu$ &$(4.5/2.6)\times 10^{-5}$  \cite{pdg98}
& ~~ & ~~ \\
$D^o\rightarrow \overline{K}^o ee/\mu\mu$ &$( 1.1/2.6)\times 10^{-4}$  \cite{pdg98}
& ~~ & $<2\times 10^{-15}$ \\
$D^o\rightarrow \rho ^o ee/\mu\mu$ & $1.0/2.3\times 10^{-4}$  \cite{pdg98}
&~~ & ~~ \\
$D^+\rightarrow \pi^+ ee/\mu\mu $ & $(5.2/1.5)\times 10^{-5}$ \cite{e791r} &
few$\times 10^{-10}$ & $<10^{-8}$ \\
$D^+\rightarrow K^+ ee/\mu\mu $ & $(20/4.4)\times 10^{-5}$ \cite{e791r}&
few$\times 10^{-10}$ & $<10^{-8}$ \\
\br
\end{tabular}
\end{center}
\end{table*}

\subsection{CP Violation and $D^o\overline{D}^o$ Mixing}

Another window of opportunity towards new physics discoveries is provided
by the study of CP violation and flavour oscillations in charm decays. Both
effects are expected to be highly suppressed. CP violation asymmetries are
expected to be around $10^{-3}$ \cite{bucella} in Cabibbo suppressed decay
such as $D^+\rightarrow K^-K^+\pi ^+$ and $D^o\rightarrow K^-K^+$. Recent preliminary
results from Focus \cite{daniele} based on 59\% of their data have given
${\cal A}_{CP} = -0.004\pm 0.017$ for the decay mode $D^+\rightarrow K^-K^+\pi ^+$
and ${\cal A}_{CP}=0.003\pm 0.039$ for $D^o\rightarrow K^-K^+$.

In the case of the $D^o$ the asymmetry may be a combination of direct
CP asymmetry and indirect CP asymmetry mediated by mixing. The
$D^o\overline{D}^o$ mixing parameter $\Delta M_D$ is affected by small
distance contributions described by box diagrams via internal $d,\ s,\ b$
quarks and long distance contributions that are more difficult to evaluate.
At any rate, the Standard Model expectations for $\Delta M_D$ are between
$10^{-18}$ and $10^{-16}$ \cite{joanne96}.

The probability that a $D^o$ oscillates into a $\overline{D}^o$ is generally
expressed as:
\begin{equation}
I(t) \propto \left|\frac{q}{p}\right|^2 e^{-\Gamma _1 t}\left[1+e^{\Delta \Gamma t}+2 e^{0.5\Delta \Gamma t} \cos{\Delta mt}\right]
\end{equation}
where $\Delta m\equiv m_1 -m_2$, $\Delta \Gamma = \Gamma _1 -\Gamma _2$ and
the
subscripts 1 and 2 identify the two neutral $D$ meson mass eigenstates
and the complex parameters $p$ and $q$ account for CP violation  effects.

The parameter $r_{WS}$ for the decay $D^o\rightarrow K^+\pi ^-$ can be expressed as:

\begin{equation}
r_{ws}\approx e^{-\Gamma t} \begin{array}{l}[ r_{D} +r_{mix}
\times \frac{\Gamma ^2 t^2}{2} + \\
 \sqrt{2r_{mix}r_{D}}\cos{\Phi}\times \Gamma t]
 \end{array}
\end{equation}
where the first term is the $DCSD$ contribution parameterized by the quantity
$r_D$, the second is the one due to mixing and the last one is an
interference term between mixing and $DCSD$. The latter term
is set to zero for simplicity in some of the experimental estimates of
$r_{mix}$, but this is not a legitimate assumption. Alternatively, we can parameterize $r_{ws}$ as:
\begin{equation}
r_{ws}= e^{-t}\begin{array}{l}[R_D+\sqrt{R_D}y^{\prime }t+ \\
+ \frac{1}{4}({x^{\prime}}^2 + {y^{\prime}}^2)t^2]
\end{array}
\label{dmix2}
\end{equation}
where $R_D$ is the rate of the direct doubly-Cabibbo-suppressed decay
$\overline{D}^o\rightarrow K^+\pi ^-$, $x^{\prime}=x\cos{\delta} +y \sin{\delta}$
 and $y^{\prime} = y\cos{\delta} - x\sin{\delta}$ and $x =\Delta
M/\overline{\Gamma}$, $y=\Delta \Gamma/\overline{ \Gamma}$. $\overline
{\Gamma}$ represents the average lifetime and $\delta$
represents
a strong phase between the doubly-Cabibbo-suppressed decay and the Cabibbo
favored one.
CLEO \cite{cleodmix} has recently used the formulation in Eq. \ref{dmix2} to obtain a very
precise measurement of the parameter $R_D=0.50^{+0.11}_{-0.12}\pm 0.08$. Their
limit at 95 \% C.L. are $(1/2) {x^{\prime}}^2<0.05\%$ and $-5.9\%<y^{\prime}
<0.3\%$.  E791 has extracted the
mixing parameter $r_{mix}$ \cite{rmixsl} also from the semileptonic decay
$D^o\rightarrow K\ell \nu$. This leads to a more straightforward determination
because the $DCSD$ contribution is absent, obtaining $r_{mix}<0.50\%$
at 90\% C.L. Thus the amplitudes that describe $D^o\overline{D}^o$ are still
consistent with 0. Soon CLEO and FOCUS results based on
semileptonic data will be available \cite{daniele}.

\section{Outlook}
The selected sample of flavour physics topics that I have discussed shows
that
there are several predictions of the Standard Model that we have yet to test
thoroughly. In particular we must explore the phenomenology of CP
violation in $b$ and $c$ decays, flavour oscillations in the $B_s$ system and
study rare decays of beauty and charm. Our ability to challenge the Standard
Model and to discover new physics will rely on two different areas where
progress is needed. On one hand, we need to reach a new level of
sophistication in our experimental study of these decays. On the other hand,
we need to refine the theoretical inputs, to develop less model dependent
predictions for a larger class of branching fractions and CP asymmetries.

\begin{table*}[hbt]
\begin{center}
\caption{Required Measurements for $b$'s}
\label{cp}
\vspace*{2mm}
\begin{tabular}{llcccc} \hline\hline
Physics & Decay Mode & Hadron & $K\pi$ & $\gamma$ & Decay \\
Quantity&            & Trigger & sep   & det & time $\sigma$ \\
\hline
$\sin(2\alpha)$ & $B^o\to\rho\pi\to\pi^+\pi^-\pi^o$ & $\surd$ & $\surd$& $\surd$
&\\
$\cos(2\alpha)$ & $B^o\to\rho\pi\to\pi^+\pi^-\pi^o$ & $\surd$ & $\surd$&
$\surd$ &\\
sign$(\sin(2\alpha))$ & $B^o\to\rho\pi$ \& $B^o\to\pi^+\pi^-$ &
$\surd$ & $\surd$ & $\surd$ & \\
$\sin(\gamma)$ & $B_s\to D_s^{\pm}K^{\mp}$ & $\surd$ & $\surd$ & & $\surd$\\
$\sin(\gamma)$ & $B^-\to \overline{D}^{0}K^{-}$ & $\surd$ & $\surd$ & & \\
$\sin(\gamma)$ & $B^o\to\pi^+\pi^-$ \& $B_s\to K^+K^-$ & $\surd$ & $\surd$& &
$\surd$ \\
$\sin(2\chi)$ & $B_s\to J/\psi\eta',$ $J/\psi\eta$ & & &$\surd$ &$\surd$\\
$\sin(2\beta)$ & $B^o\to J/\psi K_s$ & & & & \\
$\cos(2\beta)$ &  $B^o\to J/\psi K^o$, $K^o\to \pi\ell\nu$  & & & & \\
$\cos(2\beta)$ &  $B^o\to J/\psi K^{*o}$ \& $B_s\to J/\psi\phi$  & & &
&$\surd$ \\
$x_s$  & $B_s\to D_s^+\pi^-$ & $\surd$ & & &$\surd$\\
$\Delta\Gamma$ for $B_s$ & $B_s\to  J/\psi\eta'$, $ D_s^+\pi^-$, $K^+K^-$ &
$\surd$ & $\surd$ & $\surd$ & $\surd$ \\
\hline
\end{tabular}
\end{center}
\end{table*}

I will focus my discussion on the experimental techniques most suitable for
a thorough investigation of beauty and charm decays.
Table \ref{cp} summarizes the measurements that need to be done in beauty
physics in
order to overconstrain the CKM matrix. The first measurements of some of
these
quantities will be performed by the several new or upgraded experiments
pursuing $b$ physics in the next few years. In particular the $e^+e^-$\
experiments, CLEO, BaBar and Belle should see CP violation in 2000. CLEO
is sensitive to direct CP violation in rare decays. BaBar and Belle should also
see CP violation in $B\rightarrow \psi K_s$, where CDF has already
seen a hint \cite{cdfbeta} . CDF and D0 are scheduled to turn on in 2001 and
are
both planning to pursue some of these measurements. HERA-B should also turn
on
in this time scale. Moreover ATLAS and CMS are planning to study CP violation
in $B\rightarrow \psi K_s$ when LHC turns on.

None of these experiments  is capable of completing the physics program
summarized in Table~\ref{cp}. The $e^+e^-$\ facilities are limited in
statistical
accuracy for several measurements due to the low cross section for $B\overline{B}$\
production. Furthermore, they cannot address $B_s$ physics. On the other
hand, the current, upgraded high $p_t$\ hadron collider experiments
have a rudimentary particle identification system and do not have
calorimeters suitable for the study of final states involving
$\gamma$'s and $\pi ^o$'s with high resolution and efficiency.
Furthermore they have limited triggers. Thus the need to design dedicated
experiments to address beauty and
charm at hadronic machines has emerged as a crucial need to complete this
physics program.

It is often customary to characterize heavy quark production in hadron
collisions with the two variables $p_t$ and $\eta$. The latter variable is
defined as:
\begin{equation}
\eta = -ln\left(\tan\left({\theta/2}\right)\right),
\end{equation}
where $\theta$ is the angle of the particle with respect to the beam
direction.
According to QCD based calculations of $b$ quark production, the $b$'s are
produced ``uniformly" in $\eta$ and have a truncated transverse momentum,
$p_t$, spectrum, characterized by a mean value approximately equal to the $B$
mass \cite{artuso}.

\begin{figure}[htb]
\vspace{-.9cm}
\epsfig{figure=bg_vs_eta.ps,width=2.6in}
\caption{\label{n_vs_eta}  The  $\beta\gamma$ of the  $B$
 versus $\eta$  for the Tevatron.}
\end{figure}

There is a strong correlation between the $B$ momentum and $\eta$. Shown in
Fig.~\ref{n_vs_eta} is the $\beta\gamma$ of the $B$ hadron versus $\eta$.
It can clearly be seen that near $\eta=0$, $\beta\gamma\approx 1$, while
at larger values of $|\eta |$, $\beta\gamma$ can easily reach values of ~6.
This is important because the higher boost in the forward direction makes it
easier to use vertices displaced from the primary interaction points as $b$
decay selection criteria.

Fig.~\ref{bbar} shows another key feature of the $b\overline{b}$ production
at hadron colliders that favors the forward geometry: the production
angles of the hadron containing the $b$ quark is plotted versus the
production
angle of the hadron containing the $\bar{b}$ quark according to the Pythia
generator (for the Tevatron). There is a very strong
correlation in the forward (and backward) direction: when the $B$ is forward
the $\overline{B}$ is also forward. This correlation is not present in the
central region (near zero degrees). By instrumenting a relative small region
of angular phase space, a large number of $b\bar{b}$ pairs can be detected.
Furthermore the $B$'s populating the forward and backward regions have large
values of $\beta\gamma$.

\begin{figure}[htb]
\centerline{\epsfig{figure=bbar.ps,height=3.in}}
\caption{\label{bbar}The production angle (in degrees) for the hadron
containing a $b$ quark plotted versus the production angle for a hadron
containing $\bar{b}$ quark. (For the Tevatron.)}
\end{figure}

\begin{figure}[hbt]
\begin{center}
\epsfig{figure=lhcb.eps,width=3in}
\epsfig{figure=btev_det.eps,width=3in}
\caption{ Schematic view of the LHCb (a) and BTeV (b) detectors}
\label{btev-fig}
\end{center}
\end{figure}

The conclusions that we can draw from these data is that dedicated $B$
experiments at hadron colliders are
specially suited to pursue this physics with the highest prospects of
success.
 Two such experiments have been proposed, LHCb at the LHC and BTeV at
Fermilab. These detectors are shown in Fig.~\ref{btev-fig} a) and b)
respectively. LHCb has been approved, while BTeV is an approved R\&D project;
they have been invited to submit a proposal
in the summer of 2000. Both these experiments
exploit the high cross section for beauty production at hadronic machines and
the advantages of the forward
geometry to achieve optimal performance. LHCb exploits the $\approx$ 5
times higher cross
section at LHC compared to the Tevatron, due to the higher CM energy.

Both experiments feature excellent hadron identification. However, they
differ in their implementation of some key detector components. BTeV is
planning to build a state of the art vertex detector based on high
granularity pixel sensors that are used in the first level trigger.  LHCb is
considering microstrip silicon trackers whose information is used only at a
higher trigger level. Furthermore BTeV has proposed an excellent crystal
calorimeter based on PbWO$_4$, whereas LHCb will use a much more modest
Shaslik calorimeter. The difference in the quality of the electromagnetic
calorimeter is reflected by the difference in the projected sensitivities
 for the decay $B^o\rightarrow \rho^{\pm}\pi^{\mp}$,
where LHCb claims an efficiency of $1.7\times 10^{-4}$ \cite{lhcb-tdr},
whereas BTeV projects and efficiency of $(1.0\pm 0.2)$\% \cite{btev-ptdr}.
Taking into account the difference in production cross section, the ratio
between the projected yields per year in the
two experiments favor BTeV with a ratio 12:1 with respect to
LHCb \cite{btev-ptdr}.

\begin{table}[hbt]
\begin{center}
\caption{\label{phyreach} Sensitivies for BTeV running for one year and
${\cal L}=2\times 10^{32}\ cm^{-2}s^{-1}$ and LHCb. The LHCb sensitivity
numbers have been taken from their Technical Design Report \cite{lhcb-tdr}
and the BTeV numbers from their Preliminary Technical Design
Report \cite{btev-ptdr}. }
\begin{tabular}{lll}
\br
Measurement & BTeV  & LHCb \\
\hline
$x_s$ & $>80$ & $>74$ \\
CP asy ($B^o\rightarrow\pi^+\pi^-$) & $\pm 0.032$ & $\pm 0.034$\\
$\gamma (D_sK)\dagger$ & $\pm 11^{\circ}$ & $\pm 6.1^{\circ } -
\pm 13^{\circ }$\\
$\gamma (D^o K)$ & $\pm 13^{\circ}$ & ~~  \\
$\gamma (D^o K^{\star })$ & ~~ & $\pm 10^{\circ}$  \\
\br
\end{tabular}
\end{center}
$\dagger$ Both simulations assume $x_s=20$. The range of LHCb sensitivity
corresponds to different
assumptions on the strong and weak phases between
the amplitudes $<f|\overline{B}>$ and $<f|B>$.
\end{table}

Table~\ref{phyreach} summarizes the expected physics reach of BTeV and LHCb
for
some key measurements in a year of running.  Their competitive effort will
insure a detailed and precise exploration of $b$ and $c$ decays and one of
the most thorough tests of the Standard Model in a sector where there is a
stronger motivation for new physics.

\section{Conclusions}
The examples discussed in this paper show that much progress
has been made in the field of flavour physics. However, we have not
 accomplished our main goals. The new
experiments being planned to do high precision studies of beauty and charm,
BTeV and LHCb, have the opportunity of providing crucial information to
address
the puzzle of flavour and CP violation. In parallel, the study of rare $K$
decays can uncover
complementary information on CP violation and  ATLAS and CMS
will explore the mechanism of electroweak symmetry breaking and maybe
find some evidence for supersymmetry. In parallel, the experimental progress
will be undoubtely matched by a refinement of theoretical tools.
Thus the mystery of flavour may be finally uncovered.

\section{Acknowledgements}
I would like to thank the organizers of this conference for
a very enjoyable and interesting conference. While preparing this manuscript,
I have benefited from several interesting discussions with Sheldon
 Stone, Tomasz Skwarnicki, Zoltan Ligeti, Ikaros Bigi, Matthias Neubert
and Amarjit Soni.

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text:
Welcome to Hi-Ex
Sadly there will be no weekend convention Hi-Ex event in 2013.
The first comics event of its kind in the Highlands was held February 2008, at Eden Court, Inverness. It all started with a chance conversation and snowballed from there into a great first-year success – despite having no budget, no time and snow blocking the main roads on the actual weekend! Hi-Ex went on to hold successful weekend events in 2009, 2010 and 2012.
The aims of Hi-Ex are to:
When possible have an annual weekend comic expo event in Inverness.
host smaller talks and events throughout the year.
have outreach projects to involve schools and young people throughout the highlands in comics, books, sci-fi, film & related genres.
give opportunities for highland families to participate in new activities, promoting literacy and inclusion, furthering an understanding of comics.
provide a focus in Scotland and the north of the UK for comics professionals and amateurs to network.
promote Scottish comic talent.
promote a wider understanding and forward-thinking attitude to comics as an important storytelling medium and evolving art and literary form.
Address inclusion and equality issues within the comics industry.
Raise money for charity.
provide opportunities for self publishing creators, emerging talent and publishers.
create links internationally between comic creators, publishers and their audience.
The History of Hi-Ex!
Hi-Ex 2008 was held at Eden Court early February 2008. A sudden snowfall blocked the major roads and prevented some of the main guests from reaching Inverness, but this did nothing to deter the determined public, who came in un expected numbers. The event was still hailed as a great success and received rave reviews. A second Hi-Ex was inevitable!
Hi-Ex 2009 was booked slightly later, on 14th & 15th February 2009, in an attempt to avoid a repeat of any snow related drama – no such luck, as 2009 was the spring where the whole of the UK was snowed in! However, despite slightly reduced numbers the event was still enjoyed by all who attended. Thanks to incredibly generous donations from comics publishers and professionals and the public – Every Hi-Ex raises an incredible amount for Children 1st in an Auction and raffle.
The long term future of Hi-Ex is vulnerable: while there is a strong demand for an event of this kind in Scotland and in the North, funding is a problem. For Hi-Ex 2010 the Highland Council kindly stepped in with a grant to assist with outreach and other additional activities.
Hi-Ex took a break in 2011 due to the organisers workloads and a lack of funding, but people just missed it too much and Hi-Ex 2012 was inevitable.
Hi-Ex organisers are currently artist Vicky Stonebridge and Futurequake editor & writer Richmond Clements.
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Stephanie is a professional educator and artist. She earned a Bachelor of Arts in Studio Art and English with a concentration in creative writing as well as a Master of Fine Arts in Creative Writing from Hollins University. She grew up in Houston, Texas, where she attended Beyonce's alma mater, the High School for the Performing and Visual Arts, as a visual arts major. Stephanie has taught art, art history, art criticism, painting and creative writing in Houston, Baltimore, and Roanoke. She also is the recipient of numerous poetry awards and grants including an artist grant from the Baltimore Office for the Promotion of the Arts and the Gertrude Claytor Poetry Prize from the Academy of American Poets. She publishes as S.H. Lohmann, and you can read her work in Rattle, The Indiana Review, Third Coast, and elsewhere.
Mariam is a professional artist and Museum staff member in the Education Department. Her business, Fostered Design, specializes in fine art using a variety of media, including watercolor, acrylic paint, charcoal, ceramics, and pen and ink, as well as personalized stationery with hand lettering and modern calligraphy. She is a Roanoke College graduate, and is excited to share her passion for the arts with the community.
Alison earned a Bachelor of Arts in Studio Art from the University of Mary Washington. She has taught elementary through adult-aged classes, workshops, outreach programs and summer camps at the Taubman Museum of Art since 2015. She also teaches gifted art after-school classes to elementary-aged students in Roanoke County Public Schools. Alison has a dance background, and is also a working artist who enjoys participating in community shows, fundraisers and collaborative projects, creating primarily with mixed-media materials.
Ana is a Roanoke-based artist who works primarily as a painter. She earned a Bachelor of Fine Arts in Studio Art from James Madison University and a Master of Fine Arts in Studio Art from the School of the Art Institute of Chicago. She has exhibited her work nationally and locally, and in 2015 was awarded second place at the Roanoke College Biennial. Ana is on staff in the Education Department at the Taubman Museum of Art.
Katrina earned a Bachelor of Art in Art History from Roanoke College and has been with the Taubman Museum of Art since 2015 as a professional educator. She enjoys experimenting with different media and has extensive experience with acrylic paint techniques. Katrina also practices dance and is co-president of the American Association of Dance.