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%  B Physics at P-Pbar Colliders        La Thuille, 1991 
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\begin{document}
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\input top.macros 
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\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,\, min}}
\def\Ptbmin{$\mPtbmin$} 
\def\sigmab{$\sigma_b$} 
\def \rightdownarrow
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\def \mrightdownarrow
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                                                \longrightarrow}}}
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\date{}
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\title{
{Bottom Physics at Hadron Colliders} } 
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\author{
Pekka~K.~Sinervo \\[0.05in]
{\it Department of Physics} \\
{\it University of Toronto} \\
{\it Toronto, CANADA} \\
{\it  M5S 1A7} 
}
\begin{abstract}
Results from recent studies of bottom 
quarks produced in hadron collisions
at the CERN \SppbarS\ and Fermilab Tevatron 
collider are reviewed. 
The measurements of the bottom quark production cross section are
compared with the theoretical calculations of Nason, Dawson and
Ellis.  
A new measurement of mixing in the neutral $B$\ meson system 
and the observation of the decays $B^\circ_d \rightarrow \mJPsi K^{\ast\circ}$\
and $B^\pm_d \rightarrow \mJPsi K^\pm$\
from the CDF experiment are reported.
The limits on
$B$\ meson flavour-changing neutral currents are summarized.
\end{abstract}
\maketitle 
\newpage
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% Intro 
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\section{Introduction}

The study of bottom quarks provides us with a unique window into the
heavy flavour sector of the standard model.  The  lifetimes and partial
widths of bottom hadrons can be directly related to  the 
Cabibbo-Kobayashi-Maskawa matrix elements
and the mass of the hypothesized top quark while the production properties of
bottom quarks (\b-quarks) in high-energy collisions reflect their couplings
to the other fermions \cite{ref: b quark reference}. 

Much of our current knowledge of bottom hadrons has come from the CESR and
DORIS  $e^+e^-$\ colliders, where the production and decay of the
$\Upsilon(4S)$\ resonance into $B\bar{B}$\ meson pairs provides us with a
copious source of $B$\ mesons.  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}.  
The large \b-quark production cross section at a hadron collider is
tempered by the  difficulty 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.
  
The UA1  collaboration at the
CERN \SppbarS\ collider and the CDF collaboration  at the Fermilab Tevatron
Collider have  been studying bottom quark
systems produced in hadron-hadron collisions and have
made several recent 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 their most recent \b-physics
results focusing on (i) the measurement  of the \b-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{The UA1 and CDF Detectors}

The muon detection
capabilities of the UA1 detector are used throughout their bottom quark
studies.
The UA1 detector \cite{ref: 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 $9-10$\  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.  The detector triggers on inclusive muon candidates with 
muon \Pt $>6$\ \GeVc, while the inclusive dimuon trigger accepts events
with two muon candidates each with \Pt $>3$\ \GeVc.  

The CDF detector \cite{ref: CDF detector}\ combines high-resolution charged
particle detection in a solenoidal magnetic field with both electromagnetic
(EM) and hadronic (HAD) calorimeter coverage out to pseudorapidities
($\eta$) of $\pm4.2$. Electrons are identified by using the
finely-segmented EM calorimeter to identify electron showers and by requiring a
charged track in the central tracking chamber (CTC) matching the position
and energy of the EM shower.  Muons are identified by requiring the presence
of a charged track stub in a set of drift chambers located outside the HAD
calorimeter  well matched to a CTC track.   
The CDF collaboration uses events tagged either by requiring
an energetic electron candidate with \Et $>12$\ GeV, two muon candidates
with \Pt $>3$\ \GeVc, or a muon candidate with \Pt $>3$\ \GeVc\ and an
electron candidate with \Et $>5$\ GeV in their \b-quark studies. 

\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 approximations 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 top quark searches provides
 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.

Bottom quark production in hadron-hadron collisions is expected to have
large  contributions from the leading order processes dominated by  the
gluon fusion 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 
an important test of the theory is provided by the measurement of the
differential cross section as a function of such variables as the
\b-quark transverse momentum (\Pt).  Both the UA1 and CDF collaborations have
done this by measuring the rate of 
events with leptons arising from \b-quark production and subsequent
semileptonic decay, and inferring from these data
the \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{itemize} 
\item high-\Pt\ muons accompanied by a jet
\cite{ref: UA1 bottom cross section},
\item dimuon events with large dimuon
effective mass \cite{ref: UA1 bottom cross section},
\item low-mass, non-resonant dimuon 
events \cite{ref: UA1 bottom cross section}, and
\item \JPsi$\rightarrow \mu^+\mu^-$\ decays \cite{ref: UA1 JPsis}. 
\end{itemize} 
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
rapidity ($y$) interval.  A model-dependent
extrapolation is made to determine the total \b-quark cross section.

 \subsubsection{Inclusive Muon Sample}

The semileptonic decay of a \b-quark typically results in a lepton 
associated with several charged and neutral hadrons.  The UA1
collaboration uses this 
``non-isolated'' lepton signature to select muons
from \b-quark decay and reject muons arising from $W$\ and $Z$\ boson decay
and Drell-Yan production, which typically are well-isolated from other
particles in the event.  The detailed isolation characteristics of
the surviving muon candidates are used to determine the
\b-quark signal rate relative to the background processes consisting of muons
from charm quark (\c-quark) semileptonic decays, muon candidates from 
decays-in-flight of $K$\  and $\pi$\ mesons, and fake muon candidates
resulting from hadron  punch-through and leakage through the absorber.  

The muon candidates are selected
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 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\  and well separated from the muon 
candidate is  required
to further reduce these backgrounds while retaining
from 65 to 80\%\ of the 
\b-quark events (this efficiency depends on the \b-quark \Pt). 
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\ further reduces contributions from $W^\pm$\
decay ($P_T^\mu$\ is the transverse momentum of the muon candidate,
$P_T^\nu$\ is the missing transverse momentum and $\phi^{\mu\nu}$\ is the
azimuthal angle between these two momentum vectors). 
   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 larger values of \Ptrel\ compared
to \c-quark decay, while decays-in-flight tend to have relatively smaller
\Ptrel\ values, as shown in
Fig.~\ref{fig: isolation}. The fraction of 
\b-quark decay events in the UA1 event sample 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{6in} 
\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, and the overall normalization of this
background is taken 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. 
The fitted fraction of events resulting from \b-quark decay is 
 $0.33\pm0.03\pm0.03$, where the second uncertainty comes from the
normalization of the decay-in-flight background. 

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
semileptonic decay for several muon \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 \Pt\ bin 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  the model for  \b\ quark
fragmentation ($\pm6$\%);  the integrated luminosity ($\pm8$\%); 
the detector acceptance ($\pm10$\%); the branching ratio for
$b\rightarrow \mu$, assumed to be  equal to $10.2\pm1.0$\%; and 
the  \b-quark  \Pt\ spectrum ($\pm20$\%). 
\begin{table}
\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 $|y|<1.5$. }
\label{tab: inclusive mu rates}
\vspace{.25in}
\begin{center}
\begin{tabular}{lccc}
\hline \hline
\vspace{.1in}
 Channel  		&  \Ptbmin	&  Muon Cross Section	& \b-Quark Cross Section \\
 			& (\GeVc)		& (nb)		& (nb) \\
   \hline
\JPsi\ Events		& 6	&		&  $2360\pm1215$ \\
High-Mass Dimuons	& 6	&		&  $2660\pm1330$ \\
Low-Mass Dimuons	&10	&		&  $ 390\pm170 $ \\
$\mu+$\ jet (10-15 \GeVc) & 15	&  $1283\pm269$	&  $ 120\pm38  $ \\
$\mu+$\ jet (15-20 \GeVc) & 23  &  $180\pm40$	&  $ 24\pm8  $ \\
$\mu+$\ jet (20-25 \GeVc) & 30  &  $24.3\pm6.5$	&  $ 4.1\pm1.4 $ \\
$\mu+$\ jet (25-30 \GeVc) & 39  &  $3.2\pm1.4$	&  $ 0.55\pm0.30 $ \\
$\mu+$\ jet (30-35 \GeVc) & 46  &  $1.1\pm0.6$	&  $ 0.32\pm0.20 $ \\
$\mu+$\ jet (35-40 \GeVc) & 54  & $0.14\pm0.09$	&  $ 0.04\pm0.03 $ \\
\hline \hline
\end{tabular}
\end{center}
\end{table}

\subsubsection{Bottom Cross Section from Dimuon Events}

The non-resonant component of the inclusive dimuon event sample has a
contribution from \b-quark production and therefore provides an independent
measure of \sigmab.  
However, the background and signal characteristics change as
the dimuon effective mass $m_{\mu\mu}$\ 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 similar to the one employed in the inclusive muon analysis is made
requiring that one or both muons be non-isolated.  There are 731 and 525
events in the low and high dimuon mass samples, respectively. 

A  fit of the $m_{\mu\mu}$\ distribution for the low-mass dimuon sample is
performed  to extract the contribution from semileptonic \b-quark decays,
where the  resulting charm system also decays semileptonically (``same-side 
sequentials'').  This fit  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.
The result of this fit as a function of dimuon effective mass is shown in Fig.~\ref{fig: low mass muu}.
This gives an estimated \b-quark cross section, integrated above a \Pt\ of
10 \GeVc, corresponding to $390\pm170$\ nb.
\begin{figure}
\vspace{4.5in}
\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. } 
\label{fig: low mass muu}
\end{figure}

The  \Ptrel\ distribution for the high mass 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 
 of $55\pm4\pm1$\%.  
A fit  of the same-sign \Ptrel\ distribution subtracting
the expected contribution  from decays-in-flight yields a distribution that
is consistent with coming only from \b-quark decays.  This is
confirmation that the  decay-in-flight background rate is correctly
calculated, as the like-sign sample is not expected to have a contribution
from \c-quark decay. 
This analysis results in a \b-quark cross section estimate of 
$2660\pm1330$\ nb for \b-quark $|y|<1.5$\ and \Pt$>6$\ \GeVc.
       
\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 decay $B\rightarrow\mJPsi X$.    A  measure of the
\JPsi\ cross section along with a correction for the fraction  due to the
former process provides a measure of  $\sigma_b$. 

The UA1 collaboration selects \JPsi\ candidates by requiring 
two opposite-sign muon candidates in each event, each with \Pt $>3$\ \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 gives 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 $|y|<2.0$\ and 
\Pt $>5$\ \GeVc.  This corresponds to an integrated \b-quark cross section 
for \b-quark \Pt $>6$ \GeVc\ and 
$|y|<1.5$\ 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{6.2in}  
\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{Summary of UA1 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 rates and
the parent \b-quark cross sections as a function of \b-quark  \Pt, as
described 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{7.5in}
\caption{The cross section for
$p\bar{p}\rightarrow b X$\ integrated above \b-quark \Ptbmin\
plotted as a function of \Ptbmin
(this does not include the cross section for \bbar\ production). 
The theoretical calculation of P.~Nason
\etal\ is also shown.}
\label{fig: UA1 bcross sections}
\end{figure}

The theoretical estimate for \b-quark production to next-to-leading order 
is also shown in Fig.~\ref{fig: UA1 bcross 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 
$\left|y\right|<1.5$\ of $12.8^{+7.0}_{-5.4}$\ $\mu$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
uncertainty in the 
background substraction is relatively small.   However, the
isolation characteristics of the lepton  employed in  the UA1
analysis to measure the charm quark contribution are not used in
the CDF analysis as the correlation between the electron identification 
efficiency and the isolation of the electron 
reduce the effectiveness of this technique.  

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 those 
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, with electron
\Et\ above 7 GeV (the sample with \Et\ between 7 and 12 GeV is 
prescaled).

Energetic photons 
converting into electron-positron pairs near the interaction region and
$\pi^\circ\rightarrow\gamma e^+e^-$\ decays form a significant
background.  These are reduced by rejecting  events that have a second
charged track, opposite in sign to the  candidate, that along with the
electron  forms a photon conversion candidate.  The
remnant  conversion background is estimated to be $20\pm5$\%\ of the
sample.   The  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{7.2in} 
\caption{The \Et\ spectrum of the CDF inclusive
electron sample after  the selection decribed in the text. } 
\label{fig: electron Et spectrum} 
\end{figure}

$W^\pm$\ 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  $W^\pm$\  production is removed by requiring that the transverse mass in
the  event (\MEt) 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 effective 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 \Et\ spectrum, the resulting 
electron \Et\ spectrum would only have contributions from charm and  bottom
production.  
The relative contribution of \c-quark decays is 
expected to be small because of the isolation requirements made by the 
electron identification cuts, and is difficult to measure 
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 assumption
introduces a systematic uncertainty in the resulting \b-quark cross section 
of $+5$\%\ and $-12$\%\ if one assumes a factor of two uncertainty in the
 ISAJET ratio of charm to bottom quark production cross sections.  

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, \Ptbmin.  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.
An uncertainty in the calculation is introduced by the \b-quark production \Pt\ 
distribution used in the Monte Carlo calculation.  The ISAJET \Pt\ 
distribution for the lowest-order \b-quark production process  is
used as that matches the \Pt\ distribution obtained from the higher-order
QCD calculation \cite{ref: NDE}.   
The uncertainty introduced by this assumption  when
calculating the \b-quark production cross section above a specific \Ptbmin\  is 
neglible compared with the other uncertainties.
\begin{table}
\vspace{2in}
\caption{The systematic uncertainties in the CDF \b-quark production cross
section from the inclusive electron analysis. }
\label{tab: sys uncertainties CDF xsect}
\vspace{.25in}
\begin{center}
\begin{tabular}{lc}
\hline\hline
\hfil Source of Uncertainty	&  Uncertainty in Cross Section \\
\hline
Conversion background		&  5\%  \\
Hadron contamination		& 15\%	\\
Charm production 		& 10\%	\\
Electron identification efficiency	& 10\% \\
Uncertainty from underlying event model	& 8\%	\\
Trigger efficiency		& 10\%	\\
\b-quark fragmentation		& 16\%	\\
$B$\ semileptonic decay fraction	& 10\% \\
Integrated luminosity		& 7\%	\\
\hline
Total				& 32\% \\
\hline\hline
\end{tabular}
\end{center}
\end{table}

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 \Et\ 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 
discrepancy is only a  few standard deviations because of the relatively
large   uncertainties, it is rather striking given the good
agreement between the measured and  predicted values at $\sqrt{s}=630$\
GeV.
\begin{table}
\caption{The CDF \b-quark production cross section from the inclusive
electron analysis. 
The corresponds to the cross section for \b-quark production 
in the \b-quark rapidity interval $|y|<1.0$\ and 
\Pt\ greater than \Ptbmin.
}
\label{tab: CDF xsect}
\vspace{.25in}
\begin{center}
\begin{tabular}{ccc}
\hline\hline
Electron \Et	&	\Ptbmin 	&	\b-Quark Cross Section \\
(GeV)		&	 (\GeVc)	&	   (nb) \\
\hline
10-15		&	  15		&	   $1220\pm390$ \\
15-20		&	  23		&	   $220\pm70$ \\
20-25		&	  32		&	   $ 56\pm18$ \\
\hline\hline
\end{tabular}
\end{center}
\end{table}
\begin{figure}
\vspace{7in}
\caption{The CDF \b-quark production cross section integrated above
\Ptbmin\ versus \Ptbmin.  The prediction from Nason \etal\ is shown. }
\label{fig: CDF xsect}
\end{figure}  

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

The observed 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.  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-Kobayashi-Maskawa matrix.  A measurement of  this mixing,
which is expected to differ for $\Bzero_s$\ and $\Bzero_d$\ mesons, is  an
important test of the standard model and can  be used to set limits on
these parameters \cite{ref: SM mixing}. 

The CLEO and ARGUS experiments  directly
measure the mixing parameter $\chi_d$\ defined as 
\begin{eqnarray}
\chi_d = {{{\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
$\Bzero_d$\ mesons are 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 relative fractions of produced $\Bzero_d$\
and  $\Bzero_s$\ mesons.   A prediction or 
measurement of these fractions then allows one to determine both  $\chi_s$\
and $\chi_d$\ .

The UA1 collaboration reported the first observation of $\BzBzbar$\  mixing
in 1987 using the ratio of like-sign to unlike-sign dimuon events  to
obtain $\chibar= 0.121\pm0.047$\ \cite{ref: UA1 Old mixing}.  This was
followed  by observations at ARGUS and CLEO of mixing in the 
$\Bzero_d$\ system \cite{ref: CLEO ARGUS mixing}.  Recently, the ALEPH and
L3 experiments at LEP  have reported measurements of $\bar{\chi}$\ 
\cite{ref: ALEPH/L3 mixing}.  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 consistent with their
earlier result has been  reported after this conference  
\cite{ref: UA1 New mixing}.} 

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 semileptonic 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 dilepton events relative to the number  of opposite
sign dileptons, so that the ratio 
\begin{eqnarray}  
R = {{N(l^+l^+) +
N(l^-l^-)}\over{N(l+l-)}} 
\end{eqnarray}  
can be related to the mixing
parameter $\chibar$.
The CDF  collaboration has measured $R$\
in an event sample selected by 
requiring an   electron and muon candidate.  This
sample has  a factor of two more sensitivity than the comparable dielectron or
dimuon  data, and does not suffer from backgrounds in the
opposite-sign  sample arising from Drell-Yan production and 
\JPsi\ and $\Upsilon$\ decay.

\subsection{Event Selection} 
The $e\mu$\ event sample is defined by
requiring events that have  passed the CDF  dilepton 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 charged 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
 energy deposition in the
calorimeter associated with the charged track is required to be consistent 
with a minimum-ionizing particle. This selection results in 1340 events.

There are several background contributions 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 $m_{ee}< 0.5$\ \GeVcc\  or that do not have a
charged track candidate in the inner-most tracking  chamber.  There
are no backgrounds from Drell-Yan, $Z$, \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 other sources of dilepton events are
\begin{eqnarray*}
&&p\bar{p} \rightarrow b\bar{b} X \\
          &&\qquad\,\mrightdownarrow e^- c X^\prime \\
          &&\qquad\quad\quad\quad\mrightdownarrow \mu^+ X^{\prime\prime} 
\end{eqnarray*} 
where both leptons arise from the sequential decay of the same \b-quark,
and 
\begin{eqnarray*}
&&p\bar{p} \rightarrow b\bar{b}X \rightarrow b(e^+X^\prime) X\\
&&\qquad\,\mrightdownarrow  c X^{\prime\prime} \\
&&\qquad\,\,\,\quad\mrightdownarrow \mu^+ X^{\prime\prime\prime} 
\end{eqnarray*} 
where the $\bar{b}$\ decays semileptonically to $e^+ X^\prime$.
The former decay mode produces
dileptons with invariant masses less  than the $B$\ meson mass.  
These are rejected by requiring  $m(e\mu)> 5.0$\ \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} 

The remaining sources of background
events are i) fake electron and muon candidates, ii) charm
production and semileptonic decay, and iii) sequential bottom
quark decay.
 
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 
passing the CDF minimum-bias trigger, and is $(2.7\pm0.9)\times10^{-3}$.  This
is a sum of the probability that a real muon track is identified
as  a  $\mu$\  candidate and the probability that a charged
hadron  is misidentified as a muon.  The product $f_d N_t$\ represents 
the number of  events expected 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.  This background
calculation has been checked by  verifying that it reproduces the background
rates observed in the \JPsi\  data sample.    

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 heavy quark decays in the $e\mu$\ sample  of $20\pm10\%$. 
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 dilepton 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 direct dilepton production, and to  estimate the relative
rate of charm events to bottom quark events in the opposite-sign sample.   
The latter contribution
is small so that the estimated uncertainty of $\pm100$\%\ on
the predicted  charm quark production
cross section introduces a small uncertainty in  the mixing parameter.  
The estimated contributions 
are listed in 
Table~\ref{eqn: ISAJET  sequentials}.
These  estimates predict that
$R=0.233\pm0.051$\ in the absence of \b-quark  mixing, in clear conflict
with the measured value, and imply a value of 
\begin{eqnarray} 
\chibar = 0.176 \pm
0.028 ({\rm stat}) \pm 0.025 ({\rm syst}) \pm
      0.032 ({\rm MC}). 
\end{eqnarray}
\begin{table}
\caption{The fraction of observed events from \b-quark and \c-quark 
decay in the
$e\mu$\ sample 
predicted by the ISAJET Monte Carlo calculation
(normalized to the total number of observed
$e\mu$\ events). }
\label{eqn: ISAJET  sequentials}
\begin{center}
\begin{tabular}{lc}
\hline\hline
Process		&	Fraction of Observed Events \\
\hline
\b-quark direct decays 		& 0.76 \\
\b-quark sequential decays	& $0.19\pm0.07$ \\
\c-quark decays			& $0.05\pm0.05$ \\
\hline\hline
\end{tabular}
\end{center}
\end{table}

The systematic uncertainty in $\chibar$\ is dominated by the uncertainty in the
background  subtraction.  The CDF collaboration has investigated the 
Monte Carlo dependence of this result,
including uncertainties in heavy-quark  fragmentation and the relative
fraction of lowest-order to higher-order \b-quark production. A separate
systematic uncertainty has been  assigned to these model-dependent
uncertainties.  The collaboration is  currently considering ways of
reducing this model-dependent  uncertainty.

This value for $\chibar$\ can be combined with 
the measurements of $\chi_d$\ from CLEO and  ARGUS to
indirectly place bounds on value for $\chi_s$.  
This requires the unmeasured fraction of $\Bzero_s$\ and
$\Bzero_d$\ mesons in the data sample.
If one assumes that contributions to the event sample from bottom baryon
production is negligible, a $B_u: B_d: B_s$\ production ratio of 
$0.4: 0.4: 0.2$, and common semileptonic branching ratios for all $B$\ mesons,
one predicts $f_d=0.4$\ and $f_s=0.2$.
The data for $\chi_d$\ and $\chibar$\ can be then shown plotted
together, as is shown 
in Fig.~\ref{fig: chid vs chis}.
The mixing measurements are
consistent with  standard model predictions for $\chi_s$\ and 
$\chi_d$\ \cite{ref: SM mixing}, also shown in the figure.
\begin{figure} 
\vspace{5.8 in} 
\caption{The regions of $\chi_d$\ and $\chi_s$\ preferred by the CDF
mixing measurements,  
along with the combined CLEO/ARGUS  measurements for
$\chi_d$.  
The standard model prediction is shown
as the shaded region. }
\label{fig: chid vs chis} 
\end{figure}

%  
%  Describe direct decays search 
% 
\section{Inclusive and Exclusive {\it B}\ Meson Decays} 
The observation of
$B$\ mesons through exclusive decay modes provides a direct
confirmation of the preceding results, but faces severe combinatorial
backgrounds in a hadron collider experiments.  These 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 clean \JPsi\ signal is
readily  obtained and there are relatively few other sources of \JPsi\
mesons.   These features have been exploited in the UA1
\b-quark  cross section measurement described earlier.  

The CDF collaboration has analyzed a sample of $\sim2500$\ \JPsi\ decays 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$K^\pm$\
candidate events were selected by requiring  a \JPsi\  candidate with 
\JPsi\ \Pt$>8$\ \GeVc\ as \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 $K^\pm$\ candidates.  The invariant  $\mJPsi K^\pm$\ invariant
mass is shown plotted in Fig.~\ref{fig:  JPsiK_mass}(a)\ and shows a signal
of approximately 12 events above a  comparable background.
\begin{figure}
\vspace{7.0in}
\caption{The effective $\mJPsi K^\pm$\ mass distribution is shown in (a),
the effective $\mJPsi K^\ast$\ mass distribution is shown in (b), and the
combined mass distribution is shown in (c). }
\label{fig:  JPsiK_mass}
\end{figure}  

The \JPsi$K^\ast$\ candidates are selected using the the same 
\JPsi\ sample and 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}(b).  A small signal
at the mass of the $B$\ meson is evident. 

The invariant mass distribution for both channels is shown in 
Fig.~\ref{fig:  JPsiK_mass}(c), and a fit 
to this signal employing a Gaussian lineshape for the signal 
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 $B\rightarrow \mJPsi
X_s$\ 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} 
to occur at a branching ratio of
$10^{-9}- 10^{-8}$\ ($X_s$\ is a strange meson)
\cite{ref: sm B->mumu}, whereas 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 UA1 analysis \cite{ref: UA1 exclusive decays}\
of 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, 
shown in Fig.~\ref{fig: UA1 dimuon mass}.   There is no apparent signal,
allowing the 
 UA1 collaboration to place the 90\%\ confidence level 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}
\begin{figure}
\vspace{4.5in}
\caption{The UA1 dimuon effective mass distribution in the direct search
for $B\rightarrow \mu^+\mu^-$. }
\label{fig: UA1 dimuon mass}
\end{figure}

The UA1 study also places an upper limit on dimuon decay  mode
involving strange mesons by requiring in addition to the two muons two
charged tracks consistent with a $K^\ast(890)$.   There is again no  evidence
for a signal, which allows the collaboration to set a limit 
\begin{eqnarray}
BR(B^\circ \rightarrow\mu^+\mu^-K^\ast) < 2.3\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.  

Both the CDF and D0 collaborations expect to obtain 
run data samples  an
order of magnitude larger than the existing data sets in the 1991  Tevatron.  
In addition, these detectors will have 
excellent \b-quark tagging capabilities, provided by the 
new CDF silicon vertex detector and the good D0 muon
identification.   It is reasonable to expect 
significant new \b-physics results from these collaborations in the next 
several years.   

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\end{document}
