%
%  B Physics at CDF
%
\documentstyle{report}
%
\def\Et{$E_T$}
\def\Pt{$P_T$}
\def\W{{\it W}}
\def\Zzero{$Z^\circ$}
\def\Ptbmin{$P_T^{b,{\rm min}}$}
\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\Ptrel{P_T^{rel}}
\def\b{{\it b}}
\def\bbar{$\bar{b}$}
\def\bbbar{$\bar{b}b$}
\def\GeVc  {$\rm GeV\!/c$}
\def\GeVcm {\rm GeV\!/c}
\def\TeVcc {$\rm TeV\!/c^2$}
\def\GeVcc {$\rm GeV\!/c^2$}
\def\MeVcc {$\rm MeV\!/c^2$}
\def\MeVc  {$\rm MeV\!/c$}
\def\mMEt{\not\kern-.35em {E_T}}
\def\MEt{\hbox{$\mMEt$}}
\def\Kzero{$K^\circ$}
%
\begin{center}
{\bf Bottom Physics at CDF} \\
\end{center}

%
%  Discuss theory 
%	1) Production Mechanisms
%	2) Decay Processes
\begin{document}
The bottom quark provides us with a unique laboratory to study and 
probe the electroweak sector of the standard model by measuring the 
decay proporties of hadrons containing one or more \b-quarks.  The 
lifetime and partial widths of bottom hadrons can be directly related to 
the CKM matrix elements and the mass of the unknown top quark.  This 
has prompted an intensive study of bottom hadrons over the last ten 
years.

The $B$\ meson  production cross section at a hadron collider is of order 
10 $\mu$b, which at the Fermilab Tevatron corresponds to $10^9$\ events 
in an 100 pb$^{-1}$\ exposure.
This enormous production rate is tempered by the 
difficulties encountered separating the bottom hadron  events from the 
much larger rate of events arising from the production of lighter quark 
final states.  This separation is typically achieved by requiring a 
distinctive signature or ``tag'' such as the presence of an energetic lepton 
accompanied by the hadron activity that results from the semi-leptonic \b\ 
quark decay.  The efficiency of such tagging schemes can be quite low 
and they restrict the \b\ quark final states that are experimentally 
available.  

Despite these problems, the CDF collaborations have 
made several measurements of \b\ quark production and decay 
properties using data acquired in 1988 and 1989.  
We briefly summarize the 
most recent results of these studies, focusing on (i) the measurement 
of the bottom quark production cross section,
(ii) a measurement of $\BzBzbar$\ 
mixing from a study of 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, Ellis and Diemov.  The results 
of this  calculation are sensitive to several assumptions made to take into 
account the higher-order corrections and the light quark and gluon 
structure functions.  Thus, the measurement of the total and differential 
cross section provides a strong consistency check of this calculation.  The 
cross section itself is an important ``engineering number,'' as it  provides 
us with the ability 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\ factory facilities.

The production of\b-quarks in hadron-hadron collisions has large 
contributions from both the leading order processes, which are 
dominated by the reaction $gg\rightarrow b\mbbar$, and higher order 
diagrams such as ``gluon splitting,'' where a two gluon final state is 
produced and one of the final state gluons fragments into a \bbbar\ 
system.  The kinematics of the resulting \b-quark final states can be used 
to estimate the relative contributions from the leading-order and higher-
order diagrams.  However, this requires measurement of not only the 
total cross section but the differential cross section as a function of the 
such variables as the \Pt\ of the \b-quark. 

CDF has measured the 
total \b\ quark cross section and its dependence on the \Pt\ distribution of 
the \b\ quark using a sample of inclusive electron events.  
These measurements have been made in a semi-inclusive 
sense by first measuring the rate of events with leptons arising from \b\ 
quark production and subsequent semi-leptonic decay, and then 
correcting this to a \b\ quark cross section taking into account other 
sources of leptons and the fragmentation and decay properties of the \b\ 
quark.

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 and charged track momentum is 
required to satisfy $0.75 < E/p < 1.4$.  There are ??? candidate events.

A significant background in this sample comes from energetic photons 
converting into a electron-positron pair near the interaction region and 
from $\pi^\circ$\ Dalitz decays.  This background 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 event sample consists of ??? events.
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}

Sources of prompt electrons at the Fermilab collider are \W\ and \Zzero\ 
boson production, and charm and bottom decay.  The contribution from 
\W\  production is removed by requiring that the transverse mass in the 
event $\mMEt < 8\sqrt{E_T}$, which effectively requires that the 
transverse mass be consistent with that expected from heavy flavour 
decay.  The \Zzero\ contribution is removed by rejecting events that 
have a second electron cluster satisfying much looser electron 
identification cuts that forms a di-electron invariant mass greater than 80 
\GeVcc.  The cuts result in an event sample of ?? events.

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.

One of the cleanest signatures for $\Bzero-\Bzerobar$\ production
is the requirement of two leptons in the event, one
coming from the semi-leptonic decay of each $\Bzero$\ meson.  This 
signature has relatively small backgrounds, and yet  provides a 
reasonable event rate.  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.

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.

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 $m_{ee}< 0.5$\ \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.

A source of di-lepton events is the semi-leptonic decay of a \b-quark
followed by the semi-leptonic decay of the resulting charm hadron.
This  decay mode produces di-leptons with invariant masses less 
than the mass of the $B$\ meson, and are rejected 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.

The remaining sources of di-lepton events have to be accounted for
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 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 (i.e. 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 results in an estimated background rate of 
$20\pm10\%$, which 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}

Taking into account the estimated number of opposite-sign events from
charm production and decay, we find that this value for $R$\ 
implies
\begin{eqnarray}
\chibar = 
= 0.176 \pm 0.028 ({\rm stat}) \pm 0.025 ({\rm MC}) \pm
      0.032 ({\rm MC}),
\end{eqnarray}
where we have included a systematic uncertainty on this estimate due
to the Monte Carlo calculation for the fraction of lowest-order to higher
order production, and other uncertainties related to te ISAJET 
prediction.

\section{Inclusive and Exclusive $B$\ Decays}  

\subsection{Exclusive \JPsi $K$\ Decays}
The \JPsi\ sample in the CDF data set is expected to  be
a large source of $B$\ meson decays as one expects \JPsi\ mesons
to be produced only indirectly via $\chi_c$\ and $B$\ meson 
production and decay.   The measures of the fraction of $B$\ 
decays in the \JPsi\ sample consistently indicate that approximately
two-thirds of our \JPsi\ candidates are from $B$\ decays.
The most direct measure of this is to reconstruct the decay mode
\begin{eqnarray}
\chi_c \rightarrow J/\Psi \gamma
\end{eqnarray}
by finding the low-energy photon as a shower in the Electromagnetic 
calorimeter.  
The mass difference between the $J/\Psi \gamma$\ system and the
\JPsi\ candidate shows a clear $\chi_c$\ peak.  Folding in our 
estimated reconstruction efficiency and relevant branching ratios, 
we find that ??? \%\ of the \JPsi\ events are attributable to $\chi_c$\
decay.

This has motivated us to attempt to reconstruct specific exclusive
$B$\ meson decay modes involving a \JPsi\ final state.
We selected \JPsi$K$\ candidate events by requiring a 
\JPsi\ with \Pt$>8$\ \GeVc\ along with a charged track with \Pt$>3$\
\GeVc\ in proximity to the \JPsi\ candidate.  
We also searched for the exclusive decay mode 
$\mJPsi K^\pm \pi^\mp$\ using a similar event selection, but now
requiring charged tracks that form an invariant $K\pi$\ mass
that is within 50 \MeVcc\ of the nominal $K^\ast(890)$\ mass.
The combined \JPsi$K$\ and \JPsi$K^\ast$\ invariant mass distribution
is shown in Fig.  ??? and shows a clear signal of $35\pm9$\
events.  

\subsection{Rare $B$\ Meson Decay Modes}
CDF also has searched for the rare decay mode
\begin{eqnarray}
B^\circ \rightarrow \mu^+\mu^-
\end{eqnarray}
by selecting a sample of clean di-muon events using a selection 
similar to the one employed for the \JPsi\ study.  
The invariant mass distribution in the vicinity of the $\Bzero$\
mass shows no structure and is consistent with a flat background.
If we assume that the \JPsi$^\prime$\ events come entirely from \b-quark
production, then we can place an upper limit on the \b-quark di-muon
branching fraction of $1.1\times 10^{-5}$. % Rohaly's number here...
We are currently repeating this analysis using the \b-quark
cross section as measured from the exclusive decay mode channels
described above.
\end{document}
