% 
%  B Physics at P-Pbar Colliders        La Thuille, 1991 
%
\documentstyle{article} 
% 
%  Macros... 
% 
\input top.macros 
\input latex.macros 
% 
\def\bbbar{$b\bar{b}$} 
\def\mbbar{\overline{b}}
\def\mpbarp{\overline{p}p} 
\def\mJPsi{J/\Psi} \def\JPsi{$\mJPsi$}
\def\Z{{\it Z}}  
\def\Bzero{B^\circ} 
\def\Bzerobar{{\bar{B}}^\circ}
\def\BzBzbar{B^\circ\!-\!\bar{B}^\circ} 
\def\bfBzBzbar{{\bf B^{\bf\circ}\!-\!\bar{\bf B}^{\bf \circ}}}
\def\chibar{\bar{\chi}} 
\def\mPtrel{P_T^{rel}} 
\def\Ptrel{$\mPtrel$}
\def\SppbarS{$S\bar{p}pS$} 
\def\mPtbmin{P_T^{b,\, min}}
\def\Ptbmin{$\mPtbmin$} 
\def\sigmab{$\sigma_b$} 
% 
\begin{document} 
\title{
{Bottom Physics at Hadron Colliders} } 
% 
\author{ Pekka~K.~Sinervo \cr
{\it University of Toronto} \cr 
{\it Toronto, ON} \cr 
{\it Canada} } 
\maketitle 
%
% Intro 
% 
\section{Introduction}

The bottom quark provides us with a unique laboratory to study the heavy
flavour sector of the standard model.  The  lifetimes and partial widths of
bottom hadrons can be directly related to  the CKM matrix elements and the
mass of the unknown top quark while the production properties of \b-quarks
in high-energy collisions reflect their couplings to the other fermions. 

Much of our current knowledge of bottom hadrons has come from the CESR and
DORIS  $e^+e^-$\ colliders, where the  lowest lying \bbbar\ states are
produced.  In particular, the decay of the $\Upsilon(4S)$\ resonance into
$B\bar{B}$\ meson pairs allows one to make in-depth studies of the $B$\
meson system.  However, the production rate of bottom hadrons at  \pbarp\
colliders is approximately three orders of magnitude higher than what can
be  currently achieved at $e^+e^-$\ colliders \cite{ref: Ellis and
Kernan}.   Two groups, the UA1  collaboration at the CERN \SppbarS\ collider
and the CDF collaboration  at the Fermilab Tevatron Collider, have taken
advantage of this and have  been studying bottom quark systems produced in
hadron-hadron collisions.

The advantage in the \b-quark production rate at a hadron collider is
tempered by the  difficulties encountered separating the bottom hadron 
events from the  much larger rate of events arising from the production of
light quark and gluon final states.  This separation is typically achieved
by requiring a  distinctive signature or ``tag'', such as the presence of an
energetic lepton and the associated hadrons that result when a  \b-quark 
decays semileptonically.  The efficiency of such tagging schemes can be quite
low and  they tend to restrict the \b-quark final states that are
experimentally accessible.  

Both the UA1 and CDF collaborations have overcome this difficulty and have
made several measurements of \b-quark production and decay  properties.  The 
UA1 collaboration has accumulated a data sample with an integrated
luminosity of  4.7 \invpb, while the CDF experiment has gathered a  4.4
\invpb\ data set.  I will summarize the most recent \b-physics results from
these collaborations focusing on (i) the measurement  of the bottom quark
production cross section \sigmab, (ii) a study of $\BzBzbar$\  mixing using
electron-muon final states,  (iii) reconstruction of  $B$\ meson exclusive
final states, and (iv) the search for the flavour-changing neutral current
decay $B\rightarrow \mu^+\mu^-$.

\section{Bottom Quark Production}

The production cross section for heavy quarks has been calculated to 
next-to-leading  order by Nason, Dawson, and Ellis \cite{ref: NDE}. The
results of this  calculation are sensitive to assumptions made to compute
the higher-order diagrams and the light quark and gluon structure 
functions, as illustrated by the work of G.~Altarelli \etal\ \cite{ref:
Alterelli etal}.  Thus, the measurement of the total and differential cross 
section is a consistency check of this calculation.  An understanding of
heavy quark production as a background to the top quark searches provides
even further motivation to directly measure \sigmab.  Finally, \sigmab\ is
an important ``engineering number'' allowing us to predict the  productivity
of future \b-quark studies at hadron colliders and compare  such experiments
with efforts at fixed target facilities and proposed \b\ factories
\cite{ref: b factories}.

Bottom quark production in hadron-hadron collisions is expected to have
large  contributions from the leading order processes dominated by  the
reaction $gg\rightarrow b\mbbar$, and higher order diagrams such as  ``gluon
splitting'' where a two-gluon final state is produced with one of  the
gluons fragmenting into a \bbbar\ system.  These processes result in
different kinematic configurations for the \b\ and \bbar-quark, so that it
is important not only to measure the total \b-quark cross section  but the
differential cross section as a function of variables such as the \b-quark
\Pt.  Both the UA1 and CDF collaborations have made these measurements in a
semi-inclusive manner by measuring the rate of  events with leptons arising
from \b-quark production and subsequent semileptonic decay, and correcting
this to a \b-quark cross section  taking into account the fragmentation
and  decay properties of the \b-quark.

\subsection{UA1 Cross Section Measurement}

UA1 has measured the \b-quark cross section by studying the rates of 
\begin{enumerate} 
\item high-\Pt\ muons accompanied by a jet 
\cite{ref: UA1 bottom cross section},
\item \JPsi$\rightarrow \mu^+\mu^-$\ decays \cite{ref: UA1 JPsis}, 
\item dimuon events with large dimuon 
effective mass \cite{ref: UA1 bottom cross section}, and
\item low-mass, non-resonant dimuon events. 
\end{enumerate} 
Each measurement is sensitive to a different range of \b-quark  transverse
momenta, and taken together provide both a measure of the total  cross
section as well as an estimate of the differential cross section as a 
function of \Pt.  They are presented as differential cross sections
integrated  above a specific \b-quark \Pt\ cut and within a specific
pseudorapidity interval, and are relatively insensitive to details of the
model used to make the correction from the observed lepton sample to
\sigmab.  A model-dependent extrapolation can then be made to determine the
total \b-quark cross section.

 \subsubsection{Inclusive Muon Sample}

The UA1 detector has excellent muon identification,  employing a
central drift chamber to measure the muon  candidate momenta in a dipole
magnetic field.  This is followed by $\sim10$\  interaction lengths of
absorber material and a set of chambers outside the aborber that measure the
trajectories of muon candidates penetrating through the absorber.  A
hadronic calorimeter measures the energy flow around the muon
candidate.  A more complete description of the UA1 detector can be found
elsewhere \cite{ref: UA1 detector}.

The semileptonic decay of a \b-quark typically results in a lepton 
associated with $\sim2-3$\ charged and neutral hadrons.  This 
``non-isolated'' lepton signature is used to statistically separate muons
from \b-quark decay from the  background processes consisting of i) muons
from charm quark semileptonic decays, ii) muon candidates from 
decays-in-flight of $K$\  and $\pi$\ mesons, and iii) fake muon candidates
resulting from hadron  punch-through and leakage through the absorber.  The
dominant  production mechanisms for \b-quarks typically result in
another  energetic parton within the acceptance of the
UA1 detector in addition to  the bottom hadron.  
The UA1 collaboration therefore selects muon candidates by
requiring a charged track with \Pt$>10$\  \GeVc\  associated with a 
track stub  detected in the outer muon chambers. 
The quantity 
\begin{eqnarray} 
I = \sqrt{ \left(\sum E_T/3\right)^2 +
\left(\sum p_T/2\right)^2} 
\end{eqnarray} 
is used to characterize the
isolation characteristics of the candidate,  where the sum is taken over all
calorimeter towers and tracks within a  cone of $R=\sqrt{\Delta\eta^2 +
\Delta\phi^2}=0.7$.  The requirement $I>2$\ GeV rejects most of the muons
from $W^\pm$\ and \Zzero\ decay and Drell-Yan production, as these are
typically well-isolated from other hadrons in the event.  A jet
with  \Pt$>10$\ \GeVc\  well separated from the muon candidate is  required
to further reduce backgrounds from these backgrounds.  The
additional requirement that the transverse mass 
$M_T\equiv\sqrt{2 p_T^\mu p_T^\nu\left(1-\cos\phi^{\mu\nu}\right)}$\ be
less than 25 \GeVcc even further reduces any contributions from $W^\pm$\
decay.   This results in  an event sample consisting of $\sim5000$\ events.  

The \Pt\ of the muon relative to the jet axis surrounding the lepton 
candidate, \Ptrel, is an effective way of discriminating
between  different sources of non-isolated muons.  The  decay of a
\b-quark results in events with typically larger values of \Ptrel\ compared
to \c-quark decay, while decays-in-flight tend to have even smaller
\Ptrel\ values, as shown in Fig.~\ref{fig: isolation}. The fraction of
events in this sample coming from \b-quark decay is  determined
statistically by fitting the \Ptrel\ distribution to the expected 
contributions from \b-quark decay, \c-quark decay and decays-in-flight.      
\begin{figure}  
\vspace{2in} 
\caption{The isolation distribution
of the muons in the UA1 inclusive  muon sample. } 
\label{fig: isolation}
\end{figure}

The ISAJET Monte Carlo program \cite{ref: ISAJET}\ is used to model  the
\Ptrel\ distributions for muons from charm and bottom quark decay.  The
shape of the \Ptrel\ distribution for decays-in-flight is determined using a
detector simulation of this process, but the overall normalization of this
background is determined from an estimate of the rate of  such
 events using the kinematics of  $K$\ and $\pi$\ meson decay and
the observed distribution of charged  hadrons at the \SppbarS\ collider. 
This background estimate is then used  to fix the size of the decay in
flight contribution to the total \Ptrel\  distribution.  These distributions
are  then fit to the  observed \Ptrel\ distribution. The  fraction of events
resulting from \b-quark decay is estimated to be  $0.33\pm0.03\pm0.03$,
where the second uncertainty comes from the normalization of the
decay-in-flight background.  This gives an 
inclusive muon cross section for muons from \b-quark decay as a function of
the $\mu$\ \Pt.  

The results of this study are listed in Tab.~\ref{tab: inclusive mu rates}, 
which shows the efficiency-corrected cross sections for muons from \b-quark
semi-leptonic decay for several $\mu$\ \Pt\ bins.  These are converted to
\b-quark cross sections above a given \b-quark \Pt\ threshold
(determined by requiring that 90\%\ of the muons in
the sample come from \b-quarks above this threshold).  This technique 
reduces the sensitivity of the measured cross section to uncertainties in 
the produced \b-quark \Pt\ distribution and provides a measure of the \Pt\ 
dependence of the cross section.  The  systematic uncertainties in this
analysis  come from uncertainties in  i) the model for  \b\ quark
fragmentation ($\pm6$\%),  ii) the integrated luminosity ($\pm8$\%),  iii)
the detector acceptance ($\pm10$\%)
 iv) the branching ratio for $b\rightarrow \mu$, which is assumed to be 
equal to $10.2\pm1$\%, and v) the  \b-quark  \Pt\ spectrum ($\pm20$\%).
\begin{table}
\vspace{2in}
\label{tab: inclusive mu rates}
\caption{The rate of muons from \b-quark decay as a function of the $\mu$\
\Pt\ for different muon samples.  The corresponding \b-quark
cross sections are also listed and correspond to integrated rates above the
indicated \Pt\ threshold and for $|\eta|<1.5$. }
\end{table}

\subsubsection{Bottom Cross Section From \JPsi\ Decays}

The \JPsi\ meson is produced in hadron-hadron collisions by both direct
charmonium production $p\bar{p}\rightarrow\chi_c X$\ followed by the decay
$\chi_c \rightarrow \mJPsi X^\prime$\ and by $B$\ meson production
followed by the $B\rightarrow\mJPsi X$\ decay.    A  measure of the \JPsi\
cross section along with a correction for the fraction  due to this other
process provides a measure of  $\sigma_b$.  Since the UA1 di-lepton trigger
is sensitive to \JPsi\ \Pt's of order 5 \GeVc,  this provides an 
estimate of  $\sigma_b$\ integrated above a comparable \b-quark \Pt\
threshold.

The UA1 collaboration selected \JPsi\ candidates by requiring the events to
have two opposite-sign muon candidates, one with \Pt $>3$\ \GeVc and the
other with \Pt $>2$\ \GeVc.  The resulting dimuon effective mass
distribution shows a clear \JPsi\ signal of $\sim1250$\ events on a
background of order $\sim250$\ events.

The  decay $\chi_c \rightarrow\mJPsi
X$\  can be distinguished from the decay $B\rightarrow\mJPsi X$\ by  using
the isolation properties of the \JPsi, which in this case is  determined from
the charged track density as a function of $R$\ from the  \JPsi\ meson
direction.  This distribution, shown in Fig.~\ref{fig: track  density}, is
fit to contributions from both $\chi$\ and $B$\ decays,  resulting in 
\begin{eqnarray} 
{{N(B\rightarrow \mJPsi)}\over{N(\mJPsi)}} = 
    0.31 \pm 0.02 ({\rm stat}) \pm 0.12 ({\rm syst}) . 
\end{eqnarray}
This results in a cross section for \JPsi\ mesons from \b-quark decays of 
$1.92\pm0.15\pm0.79$\ nb for \JPsi's in the rapidity interval $|y|<2$\ and 
\Pt $>5$\ \GeVc.  This corresponds to an \b-quark cross section  integrated
above \b-quark \Pt above 6 \GeVc\ of $2360\pm1215$\ nb, after correcting
for the fraction of \JPsi's estimated to come from the cascade decay
$b\rightarrow \Psi^\prime X \rightarrow \mJPsi\gamma X$\ (25\%\ of the
\JPsi\ decays are estimated to come from this source).
\begin{figure}   
\vspace{3in}  
\caption{The charged
track density around the \JPsi\ candidates as a function of the separation
$R$\ from the \JPsi.}  
\label{fig: track density} 
\end{figure} 

\subsubsection{Bottom Cross Section from Dimuon Events}

The non-resonant component of the inclusive di-muon event sample has a
contribution from \b-quark production and therefore provides another
measure of \sigmab.  
However, the background and signal characteristics change as
the dimuon invariant mass increases, so UA1 chose to perform two separate 
analyses on the unlike-sign dimuon samples, one using the event sample with
  $2<m_{\mu\mu} < 6$\ \GeVcc\ and the other using
the events  with  $6<m_{\mu\mu} <35$\ \GeVcc.  In both cases, an isolation
cut is made, similar to the one performed in the inclusive muon analysis,
requiring that one or both muons be non-isolated.  There are 731 and 525
events in the low and high dimuon effective mass samples, respectively. 

A multi-dimensional fit of the low-mass dimuon sample is performed  to
extract the contribution from semi-leptonic \b-quark decays where the 
resulting charm system also decays semi-leptonically (``same-side 
sequentials'').  This fit takes into account the isolation characterisitcs
of  the muons in the sample and the dimuon effective mass,  and allows for
contributions from same-side sequential \b-quark decays, Drell-Yan dimuon
production,  leptonic decays of light mesons and resonant \JPsi\ and
$\Psi^\prime$\ decays. The fit estimates the \b-quark contribution as 
$100\pm27$\ events out of a total of 731 unlike-sign events in this sample.

The results of the fit as a function of dimuon effective mass for the
non-isolated sample is shown in Fig.~\ref{fig: low mass muu}.
This gives an estimated \b-quark cross section, integrated above a \Pt\ of
10 \GeVc, of $390\pm170$\ nb.
\begin{figure}
\vspace{2.5in}
\label{fig: low mass muu}
\caption{The dimuon effective mass distribution for the non-isolated
low-mass dimuon events.  The shaded region shows the estimated
contribution from \b-quark same-side sequential decays. } 
\end{figure}

There are 850 high-mass dimuon events of both like and opposite-sign
in the UA1 sample.  The  \Ptrel\ distribution for the unlike-sign dimuons is
used to separate the fraction of  \b-quark events in the sample from the
\c-quark and decay-in-flight  backgrounds.  The fit of this distribution to
the \b\ and \c-quark  contributions yields an overall \b-quark fraction in
the opposite-sign  sample of $55\pm4\pm1$\%.  The like-sign event sample
provides a  check of the background calculation, since one expects this
sample to  have contributions only from \b-quark decay and
decays-in-flight.  A fit  of the same-sign \Ptrel\ distribution subracting
the expected contribution  from decays-in-flight yields a distribution that
is consistent with coming only from \b-quark decays, as expected since
we do not expect a \c-quark contribution to the like-sign sample.  This is
confirmation that the  decay-in-flight background rate is correctly
calculated.        

\subsubsection{Bottom Cross Section Results}

These four methods give estimates of the cross section for inclusive  muon
and dimuon events from \b-quark decay.  These muon-level cross sections are
converted into \b-quark cross sections using the ISAJET Monte Carlo  program
to determine the relationship between the observed muon cross  sections and
the parent \b-quark cross sections as a function of \b-quark  \Pt, as
described earlier in the inclusive muon analysis.  

The  \b-quark cross sections from the different analyses are listed in 
Table~\ref{tab: inclusive mu rates}\ and plotted in 
Fig.~\ref{fig: UA1  bcross sections}.  The systematic uncertainties
introduced in translating  the muon level cross sections to \b-quark cross
sections comes from the  uncertainty in the \b-quark fragmentation, the
produced \b-quark \Pt\  spectrum and the branching fraction
$BR(b\rightarrow\mu X)$. 
\begin{figure}
\vspace{3in}
\label{ fig: UA1  bcross sections}
\caption{The \b-quark cross section integrated above \Ptbmin\ plotted as a
function of \Ptbmin.  The theoretical calculation of P.~Nason \etal.\ is also shown. }
\end{figure}

The theoretical estimate for \b\-quark production to next-to-leading order 
is also shown in Fig,~\ref{fig: UA1 b cross sections}, and is in good
agreement  with the measured values.  Extrapolation of the integral \b-quark
cross  section to \Ptbmin$=0$\ gives a total \b-quark cross section for 
$\left|\eta\right|<1.5$\ of $12.8^{+7}_{-5.4}$\ $\mu$b.  

\subsection{Bottom Quark Production at the Tevatron}

The CDF collaboration has measured the \b-quark cross section at 
$\sqrt{s}=1.8$\ TeV using a sample of inclusive electron events.  This 
measurement differs from the UA1 inclusive muon measurement in  several
respects:  The CDF electron sample is substantially cleaner and  so the
background substraction is not as large as in the UA1 case.   However, the
isolation characteristics of the lepton  used in  the UA1
analysis to measure the charm quark contribution are less useful in
the CDF analysis because the efficiency of the electron identification 
requirements are anti-correlated with the isolation of the electron.  

The event sample is selected by requiring an electron candidate in the 
central pseudorapidity region $|\eta|<1.0$.  The shower in the EM 
calorimeter is required to have transverse profiles consistent with that 
expected of an electron.  The shower leakage into the hadronic  calorimeter
must be $<4$\% of the EM shower energy, and candidates  with more than one
charged track pointing to the calorimeter shower are  removed.  This latter
cut is used to reduce the backgrounds from fake  electrons resulting from
hadronic shower fluctuations.   In order to further  reduce backgrounds from
charged hadrons overlapping with $\pi^\circ$\  showers, the ratio of
calorimeter energy to charged track momentum is  required to satisfy $0.75
< E/p < 1.4$.  There are $\sim20~000$\ candidate events.

Energetic photons 
converting into a electron-positron pairs near the interaction region or 
from $\pi^\circ$\ Dalitz decays are a significant background.  This is
reduced by rejecting  events that have a second charged track, opposite in
sign to the  candidate, that is consistent with a photon conversion.  The
remnant  conversion background is estimated to be $20\pm5$\%\ of the
sample.   The remnant background from charged hadrons  is estimated to be 
$15\pm15$\%.  The \Et\ spectrum of
the electron candidates is shown in Fig.~\ref{fig:  electron Et spectrum}.
\begin{figure} 
\vspace{3in} 
\caption{The \Et\ spectrum of the CDF inclusive
electron sample after  the selection decribed in the text. } 
\label{fig: electron Et spectrum} 
\end{figure}

\W\ and \Zzero\ 
boson production, and charm and bottom decay are expected to be the principle
sources of prompt electrons at the Tevatron collider.  The contribution
from  \W\  production is removed by requiring that the transverse mass in
the  event $\mMEt$\ be less than $8\sqrt{\sum E_T}$, where the sum is over
all the calorimeter cells in the detector.  \Zzero\ decays are
removed by rejecting events  having a second electron cluster forming a
dielectron invariant mass greater than 80  \GeVcc.  

The \Pt\ distribution of the remaining conversion and charged hadron 
background in the event sample is assumed to be the same as that for the 
identified conversion electron sample.  After statistically subtracting this 
contribution from the oberved electron \Pt\ spectrum, the resulting 
electron \Pt\ spectrum will only have contributions from charm and  bottom
production.  The technique employed in the UA1 analysis to  relate the
observed lepton and parent quark transverse momentum is  used to infer the
cross section for \b-quark production above a minimum  \b-quark \Pt.  The
ISAJET Monte Carlo program is used to determine  this relationship, after 
tuning the program to reproduce the fragmentation  and decay properties of
\b-quarks as measured at CLEO and ARGUS.

The relative contribution of charm quark decays to the event sample is 
expected to be small because of the isolation requirements made by the 
electron identification cuts, and so it is difficult to measure this rate 
directly as is done in the UA1 analysis.  The CDF group therefore uses  the
ISAJET prediction for the relative rate of charm and bottom quark  decay
events passing the event selection.  This ratio, predicted to be ???, 
introduces a systematic uncertainty in the resulting \b-quark cross section 
of $+5$\%\ and $-12$\%\ if one assumes an uncertainty in the relative 
ISAJET charm to bottom quark production cross sections of a factor of  two.  

An uncertainty in the calculation is introduced by the \b-quark \Pt\ 
distribution used in the Monte Carlo calculation.  The \b-quark  \Pt\ 
distribution predicted by ISAJET for the lowest-order production process  is
used as that matches the \Pt\ distribution obtained from the higher- order
QCD calculation.   The uncertainty introduced by this assumption  when
calculating the \b-quark production cross section above a \Ptbmin\  is 
relatively small.

A summary of the statistical and systematic uncertainties of this analysis
is  shown in Table~\ref{tab: sys uncertainties CDF xsect}.  The resulting 
integrated cross sections are listed in Table~\ref{tab: CDF xsect}\ for 
three different choices of \Pt\ cuts on the candidate electrons, and are 
plotted in Fig.~\ref{fig: CDF xsect}\ along with the QCD prediction.   One
sees that the observed integrated cross sections are all higher than  the
predicted values by approximately a factor of two.  Although this 
descrepancy is only a  few standard deviations because of the relatively
large theoretical  uncertainties, it is rather striking given the good
agreement between the measured and  predicted values at $\sqrt{s}=630$\
GeV.  

\section{\bf $\bfBzBzbar$\ Mixing} 

The physical neutral bottom meson states are expected to be mixtures of  the
even and odd charge-parity eigenstates of the weak Lagrangian, in  analogy
with the \Kzero\ meson system.  This mixing is predicted by the  Standard
Model to arise from ``box diagrams,'' such as those shown in  Fig.~\ref{fig:
box diagrams}.  The size of the mixing depends on several  fundamental
parameters in the standard model, such as the mass of the  top quark, the
lifetime of the \b-quark, and the size of several  components of the
Cabibbo-Kobi-Maskawa matrix.  A measurement of  this mixing thus provides an
important test of the standard model, and can  be used to set limits on
these parameters.  

The mixing is also predicted to be different for $\Bzero_s$\ and 
$\Bzero_d$\ mesons\ mesons.  The CLEO and ARGUS experiments  directly
measure the mixing parameter $\chi_d$, which is defined as \begin{eqnarray}
\chi_s = {{{\rm Prob}(\Bzero_d\rightarrow \Bzerobar_d)}\over {{\rm
Prob}(\Bzero_d\rightarrow \Bzero_d) +  {\rm
Prob}(\Bzero_d\rightarrow\Bzerobar_d) }}, \end{eqnarray} since only the
$\Bzero_d$\ mesons are easily produced at their centre- of-mass energies. 
Experiments at hadron collider facilities and LEP can  measure a linear
combination \begin{eqnarray} \bar{\chi} \equiv f_d \chi_d + f_s \chi_s,
\end{eqnarray} where $f_d$\ and $f_s$\ are the fractions of $\Bzero_d$\ and 
$\Bzero_s$\ mesons produced at these facilities.   A prediction or 
measurement of these fractions then allows one to determine both  $\chi_s$\
and $\chi_d$\ by combining the mixing measurements made at  the different
facilities.

The UA1 collaboration reported the first observation of $\BzBzbar$\  mixing
in 1987 using the ratio of like-sign to unlike-sign di-muon events  to
determine $\chibar= 0.121\pm0.047$.  This was followed  subsequently by
observations at ARGUS and CLEO of mixing in the  $\Bzero_d$\ system. 
Recently, the ALEPH and L3 experiments at LEP  have reported measurements of
$\bar{\chi}$.  The newest result from  hadron colliders is from CDF, where a
measurement of $\bar\chi$\ has  been made using electron-muon events.  I
will therefore focus on this  latest measurement.\footnote{An updated UA1
measurement has been  reported after this conference.  This will be
mentioned in the summary of  this section.}

The cleanest topological tag for $\Bzero-\Bzerobar$\ production at a hadron 
collider is the requirement of two leptons in the final state, with a lepton 
coming from the semi-leptonic decay of each $\Bzero$\ meson.  This 
signature has relatively small backgrounds, and yet  provides a  reasonable
rate of events.  The mixing in the $\Bzero-\Bzerobar$\ system  produces an
excess of like-sign di-lepton events relative to the number  of opposite
sign di-leptons.  The ratio \begin{eqnarray}  R = {{N(l^+l^+) +
N(l^-l^-)}\over{N(l+l-)}} \end{eqnarray}  can be related to the mixing
parameter $\chibar$\ by taking into account  all sources of like and
unlike-sign di-lepton events.  The CDF  collaboration has used a di-lepton
event sample defined by requiring an   electron and muon candidate to make
this measurement.  This sample has  a factor of two more events than the
comparable di-electron or di-muon  final states, and does not suffer from
backgrounds in the opposite-sign  sample arising from Drell Yan production.

\subsection{Event Selection} The $e\mu$\ event sample is defined by
requiring events that have  passed the CDF  di-lepton trigger, which
requires an electromagnetic  shower in the CEM with \Et$>5$\ GeV and a muon
candidate with  \Pt$>3$\ \GeVc.  The electromagnetic shower is further
required to have  less than 4\%\ energy leakage into the hadronic
calorimeter,  transverse  shower profiles consistent with an electron
shower, and a charged track  reconstructed in the CTC that extrapolates to
the EM shower position.   The ratio of calorimeter energy to track momentum
is required to be less  than 1.5.  The muon candidate is required to have a
well-measured CTC  track consistent with coming from the primary vertex and
having a good  match between the CTC track extrapolated to the muon chambers
and  the muon track stub detected in the $\mu$\ chambers.  The charged track 
isalso required to have an energy deposition in the calorimeter consistent 
with a minimum-ionizing particle. This selection results in ??? events.

There are several background processes that contribute to this event 
sample.   $W$\ bosons are rejected by requiring \MEt$<15$\ GeV.    Electrons
from photon conversions in the inner part of the tracking  system or from
Dalitz decays are rejected by vetoing events that have  either  a second
track forming an invariant mass $m_{ee}< ??$\ \GeVcc,  or that do not have a
charged track candidate in the VTPC tracking  chamber.  However, there are
no backgrounds in the sample from Drell- Yan, $Z^\circ$, \JPsi\ or
$\Upsilon$\ production due to the requirement  that the two leptons come
from different generations. This results in 429 like-sign (LS) and 911 
opposite-sign (OS) events.

Two sources of di-lepton events are the processes \begin{eqnarray} ...put in
same-side sequential \end{eqnarray} and \begin{eqnarray} ...put in opposite
side sequentials \end{eqnarray} The former decay mode produces di-leptons
with invariant masses less  than the mass of the $B$\ meson.  Hence, we
reject these by requiring  that $m(e\mu)> 5.0$\ \GeVcc.  The remaining
sequential background is  calculated using the ISAJET Monte Carlo, as
described below.  This  results in 346 like-sign and 554 opposite-sign
events.

\subsection{Sources of Di-lepton Event Candidates} 

All  sources of di-lepton
events that have to be taken into account to be  able to interpret this
value of $R$\ in terms of $\chibar$.  The relevant  sources are i) charm
production and semi-leptonic decay, ii) backgrounds  from sequential bottom
quark decay, and iii) processes generating fake  electron and muon
candidates.
 
The ISAJET Monte Carlo program is used to predict the total rate of like-
sign and opposite-sign events from charm production that satisfy the  event
selection.   The number of events from sequential decays of the  form shown
in Eqn.~\ref{eqn: opp side sequentials}\ depends on the \b- quark production
process.  These have been evaluated using the ISAJET  Monte Carlo program
and are listed in Table~\ref{eqn: ISAJET  sequentials}.

The number of events due to fake electron, fake muon and fake electron  and
muon candidates has been determined by measuring the probability  $f_\mu$\
that a charged track passing the track selection requirements  also is
identified as a muon candidate, and weighting  the number of such  tracks in
the event sample, $N_t$, by this probability.  The probability  $f_\mu$\ is
defined as the ratio of the number of muon candidates  divided by the total
number of tracks passing the track selection in a  sample of events that
passed the CDF minimum-bias trigger.  This is  therefore the sum of the
probability that a real muon track is identified as  a  $\mu$\  candidate
together with the probability that a charged hadron  is misidentified as a
muon.  The product $f_d n_t$\ represents an  estimate of the number of
expected events coming from  sources of  muon candidates not associated with
heavy flavour decay (\ie\ decay-in- flight and punch-through).  This
estimate also includes events with fake  electrons (since $n_t$\ includes
the events that have hadrons and  conversions misidentified as prompt
electrons)  where the muon  candidate is from a source other than \c\ or
\b-quark decay.   

The probability $f_\mu$\ is estimated to be $0.0027\pm0.0009$, using a 
sample of minimum-bias events (the overall fraction of heavy-flavour 
ffevents is quite small  in this data set so that any muon candidates 
observed in this sample are either fakes or real muons from production of 
light quark jets and gluons).  The systematic uncertainties in $f_mu$\  come
from the uncertainty in the $K/\pi$\ ratio and \Pt\ spectrum  of the 
minimum-bias sample relative to  the $e-\mu$\ sample, and are estimated  as
$\pm15$\%\ and $\pm20$\%\ respectively.  This results in an  estimated
background to the heavy quark decays in the $e\mu$\ sample  of $20\pm10\%$. 
This background estimate has been checked by  verifying that it reproduces
the background rates observed in the \JPsi\  data sample.  This background
contributes equally to the like-sign  and opposite-sign   samples so that
the value of $R$\ corrected for background contributions  is 
\begin{eqnarray} R = {{346 - 90}\over{554-90}} 
      = 0.552 \pm 0.049 ({\rm stat})
                        ^{+0.039}_{-0.048} ({\rm bkg}). 
\end{eqnarray}

The mixing parameter $\chibar$\ can be determined from $R$\ by  accounting
for the like and opposite sign di-lepton events from sequential  \b-quark
decays and charm quark production.  The ISAJET Monte Carlo  program was used
to estimate the remaining contribution of sequential  \b-quark  decays
relative to the direct di-lepton production, and to  estimate the absolute
value of charm events to the opposite-sign sample.   The latter contribution
is small so that even a large error in the predicted  charm quark production
cross section introduces a small uncertainty in  the mixing parameter.  The
estimated contributions to the dilepton  sample are listed in Table
\ref{tab: contributions}\ are separated into the  contributions from
leading-order and higher-order processes.  These  estimates predict that
$R=0.233\pm0.051$\ in the absence of \b-quark  mixing, in clear conflict
with the measured value.

The measured value of $R$\ implies that 
\begin{eqnarray} 
\chibar = 0.176 \pm
0.028 ({\rm stat}) \pm 0.025 ({\rm syst}) \pm
      0.032 ({\rm MC}). 
\end{eqnarray} 
The systematic uncertainty arises
primarily from the background  subtraction.  The collaboration has
investigated various sources of  uncertainty due to assumptions in the
modeling of the \b-quark and \c- quark production and decay.  These include
uncertainties in heavy-quark  fragmentation, on the relative fraction of
lowest order to higher-order  production processes. A separate systematic
uncertainty has been  assigned to these model-dependent uncertainties.  The
collaboration is  currently investigating ways of further reducing this
model-dependent  uncertainty.

This value for $\chibar$\ can be combined with estimates for $f_s$\ and 
$f_d$\  and with the measurements of $\chi_d$\ from CLEO and  ARGUS to
indirectly place bounds on value for $chi_s$.  These data are  shown plotted
in Fig.~\ref{fig: chid vs chis}, and yield lower bounds of 
\begin{eqnarray}
chi_s > ??\ {\rm at }\ 90\%\ {\rm C.L.} \\ 
chi_s > ??\ {\rm at }\ 95\%\ {\rm C.L.}. 
\end{eqnarray} 
These data can be combined with similar measurements
of $\chibar$\  from the ALEPH and L3 collaborations 
\begin{eqnarray} \chibar = ??   \ {\rm (ALEPH)} \\ 
\chibar = ??  \  {\rm (L3)}  
\end{eqnarray} 
to
place more stringent lower bounds on $\chi_s$\ of 
\begin{eqnarray} chi_s >
??\ {\rm at }\ 90\%\ {\rm C.L.} \\ 
chi_s > ??\ {\rm at }\ 95\%\ {\rm C.L.}.
\end{eqnarray} 
These bounds, shown in Fig,~\ref{fig: chid vs chis}, are
consistent with  standard model predictions of $\chi_s\sim 0.5$.
\begin{figure} 
\vspace{3.0 in} 
\label{fig: chid vs chis} 
\caption{The regions of $\chi_d$\ and $\chi_s$\ preferred by the recent 
mixing measurements.  The CDF measurements and the $\pm1$\  $\sigma$\
contours are shown, along with the combined CLEO/ARGUS  measurements for
$\chi_d$.  The region of $\chi_s$\ and $\chi_d$\  excluded by these
measurements at 90\%\ CL is shown as the dashed  line .  The 90\%\
confidence level limit obtained from combining the  recent measurement from
UA1, ALEPH, L3 and CDF is shown as the  dot-dashed contour.} 
\end{figure}

%  
%  Describe direct decays search 
% 
\section{Inclusive and Exclusive {\it B}\ Meson Decays} 
The observation of
$B$\ meson decays in hadron collider experiments  faces severe backgrounds
from the higher cross section light-quark  production processes.  Tthese
backgrounds can be reduced by  considering final states with multiple lepton
candidates.  The $B$\ decay  modes resulting in a \JPsi\ meson that
subsequently decays to two  leptons is particularly promising as a very
clean \JPsi\ signal is easily  obtained and there are relatively few other
sources of \JPsi\ mesons.   These features have been exploited in the
previously described \b-quark  production cross section measuremnts.  

The CDF collaboration has analyzed the same \JPsi\ sample for evidence  of
the exclusive decays 
\begin{eqnarray} B^\pm \rightarrow \mJPsi K^\pm  \\
B^\circ \rightarrow \mJPsi {K^\ast}^\circ. 
\end{eqnarray} 
The \JPsi$K$\
candidate events were selected by requiring  a \JPsi\  candidate with 
\JPsi\ \Pt$>8$\ \GeVc\ as the \JPsi\ mesons from charm  production are
expected to have a softer \Pt\ spectrum.  All charged  tracks with
\Pt$>2.0$\ \GeVc\ in a $60^\circ$\ cone around the \JPsi\  candidate were
considered as $K^\pm$\ candidates.  The invariant  $\mJPsi K^\pm$\ invariant
mass is shown plotted in Fig.~\ref{fig:  JPsiK_mass}\ and shows a signal of
approximately ?? events above a  comparable background.  

The search for the \JPsi$K^\ast$\ decay mode starts by making the same 
\JPsi\ selection and then requiring two oppositely charged tracks that  have
an invariant $K\pi$\ mass within 50 \MeVcc\ of the nominal  $K^\ast(890)$\
mass.  Only the three highest \Pt\ tracks in the event are  considered in
order to reduce the combinatorial backgrounds.  A small  $K^\ast$\ signal is
evident on a large background, and the resulting  \JPsi$K^\ast$\ invariant
mass spectrum is plotted in Fig.~\ref{fig:  JPsiK_mass}.  A small signal at
the mass of the $B$\ meson is evident. 

The invariant mass distribution for both channels is also shown, and a fit 
to this signal employing a Gaussian lineshape for the signal fixed to the 
expected mass resolution of ?? \MeVcc\ and a smooth background  results in
an estimated rate of $35  \pm 9$\ events.  Although this is a modest signal,
it represents the world's largest sample  of observed $B\rightarrow \mJPsi
X$\ events.  An estimate of the \b- quark production cross section from this
signal is expected to yield a  measurement that is completitive with the
measurements described  earlier.

\subsection{Upper Limits on ${\bf B\rightarrow \mu^+\mu^-}$}

The standard model predicts the flavour-changing decays \begin{eqnarray}
B\rightarrow \mu^+\mu^- \ {\rm and}\ B\rightarrow\mu^+\mu^- X_s
\end{eqnarray} ($X_s$\ is a strange meson)  to occur at a branching ratio of
$10^9- 10^{10}$.   A branching ratio significantly larger than this would
require  an extension to the minimal standard model.  For this reason, both
UA1  and CDF have searched for these decay modes.

The search for the exclusive $\mu^+\mu^-$\ decay mode is made by  selecting
events with  two muon candidates and then searching for a  $B$\ meson signal
in the dimuon invariant mass spectrum. The resulting  dimuon mass spectrum
is shown in Fig.~\ref{fig: UA1 dimuon mass}.   There is no apparent signal
and from this the UA1 collaboration estimates  an upper limit on the
$B\rightarrow\mu^+\mu^-$\ branching ratio of 
\begin{eqnarray}
BR(B\rightarrow\mu^+\mu^-) < 8.3\times 10^{-6} \quad ({\rm UA1}).
\end{eqnarray} 
The CDF collaboration, using a similar analysis, sets a limit
\begin{eqnarray} 
BR(B\rightarrow\mu^+\mu^-) < 3.2\times 10^{-6} \quad ({\rm
CDF}). 
\end{eqnarray}

The UA1 analysis also attempts to place an upper limit on dimuon decay  mode
involving a strange meson by requiring in addition to the two  muons two
charged tracks consistent with a $K^\ast(890)$.   There is no  evidence for
a signal, which allows the collaboration to set a limit 
\begin{eqnarray}
BR(B\rightarrow\mu^+\mu^-K^\ast) < 1.1\times 10^{-5} \quad ({\rm  UA1}).
\end{eqnarray} 
These limits are substantially more restrictive than earlier
results obtained  at $e^+e^-$\ colliders.

\section{Future Bottom Physics at ${\bf p\bar{\bf p}}$\ Colliders} 

The $B$\ physics program at the CERN \SppbarS\ collider is now  drawing to a
close, but at the same time the bottom physics program at  the Fermilab
Tevatron is on the threshold of a potential ``golden era.''   The  results
discussed in this report illustrate the potential of $B$\ physics  at hadron
colliders and the Tevatron in particular.  

Both the CDF and D0 collaborations expect to obtain \JPsi\ data samples  an
order of magnitude larger than the existing data sets in the 1991  Tevatron
run.  In addition, these detectors will have augmented $B$\  physics
capabilities such as the CDF silicon vertex detectors that will  provide
further \b-quark tagging capabilities.   It is reasonable to expect 
significant new \b-physics results from these collaborations in the next 
several years.   

\begin{thebibliography}{} 
%
\bibitem{ref: Ellis and Kernan} 
N.~Ellis and A.~Kernan, Phys. Rep. {\bf 195}\ (1990), 23. 
% 
\bibitem{ref: NDE}
P.~Nason, S.~Dawson and R.~K.~Ellis, Nucl. Phys. {\bf B303}\ (1988), 607;
Nucl.~Phys. {\bf B327}\ (1989), 49;  and Nucl. Phys. {\bf B335}\ (1990), 260.
% 
\bibitem{ref: Alterelli etal} 
G.~Altarelli, M.~Diemoz, G.~Martinelli and
P.~Nason, Nucl. Phys. {\bf B308}\ (1988), 724. 
% 
\bibitem{ref: UA1 bottom cross section}
C.~Albajar \etal, (UA1 Collab.), CERN-PPE/90-155 (1990).
% 
\bibitem{ref: UA1 JPsis}
C.~Albajar \etal, (UA1 Collab.), CERN-PPE/90-154 (1990). 
%
\bibitem{ref: b factories}
B factory reference. 
%
\bibitem{ref: UA1 detector}
C.~Albajar \etal, (UA1 Collab.), Z. Phys. {\bf C38}\ (1990), 1.
% 
\bibitem{ref: ISAJET}
F.~Paige and S.~D.~Protopopescu, Brookhaven report BNL-38034 (1986).
\end{thebibliography} 
\end{document}
