%
%  Beyond the Standard Model III  Writeup on CDF Results
%   June 1992
%
\documentstyle[12pt,worldsci]{article}
%
\pagestyle{empty}
\renewcommand{\topfraction}{0.90}
\renewcommand{\floatpagefraction}{0.95}
\renewcommand{\textfraction}{0.10}
\hoffset 0.125in
\voffset 0.250in
%
\begin{document}
\title{THE SEARCH FOR PHYSICS \\
BEYOND THE STANDARD MODEL\\
WITH CDF}
\author{Pekka K. Sinervo\thanks{
Representing the CDF Collaboration$^1$ } \\
% \cite{ref: CDF institutions}} \\
{\em Department of Physics, University of Toronto, Toronto, \\
Ontario, M5S 1A7, Canada}\\
}
\maketitle
%
\setlength{\baselineskip}{2.6ex}
%
\input top.macros
\input latex.macros
\def\squark{${\tilde q}$}
\def\gluino{${\tilde g}$}
\def\photino{${\tilde \gamma}$}
\def\Msquark{$M_{\tilde q}$}
\def\Mgluino{$M_{\tilde g}$}
%
\begin{center}
\parbox{13.0cm}
{\begin{center} ABSTRACT \end{center}
{\small \hspace*{0.3cm} 
The results of searches for physics beyond the standard model 
undertaken by the CDF Collaboration are presented.
Studies of $\sim4$\ \invpb\ of \pbarp\ Tevatron Collider data place the most
stringent bounds on lepton and quark compositeness, the mass of the squark
and gluino in the minimal supersymmetric standard model, additional gauge
bosons and a first generation leptoquark.
The measurement of the rare decay $W^\pm\rightarrow\pi^\pm\gamma$\
and the study of events with unusual large depositions of energy in the
CDF detector are also described.
}}
\end{center}
%
%  Introduction
%
\section{Introduction}
The success of the standard model\cite{ref: SM description}\
as a description of the electroweak 
and strong forces is a compelling reason to believe that it is 
fundamentally a good approximation to physics at the subatomic scale.  
However, it has several well-known inadequacies:  the large number of 
parameters, that it does not predict the structure of 
the Higgs sector, 
and the lack of an explanation for the number of lepton and quark 
generations are only three of the shortcomings of the model.  Many 
extensions to the standard model
have been proposed that attempt to 
address these issues.  However, the only way to choose among these is to search 
for phenomena predicted by one or other of these new theories.

The study of high energy proton-antiproton (\pbarp) collisions provides a unique 
laboratory in which to search for much of this ``new physics.''  
Essentially anything that couples to quarks and gluons will be produced 
in such collisions, including both mediators of a new force and new 
particles.  The large centre-of-mass collision energies ($\sqrt{\hat{s}}$)  
and four-momentum transfer ($Q$) available in the parton-parton 
interactions gives access to mass scales of several hundred \GeVcc, and 
probes parton substructure at the multi-TeV energy scale.  Finally, the 
inherently high luminosity of a hadron collider makes it possible to 
perform searches that are quite sensitive to new phenomena.  

The 
Collider Detector at Fermilab (CDF) has been used to study \pbarp\
collisions at a centre-of-mass energy of 1.8 TeV using the Tevatron Collider.
In this article, I  review the recent results of searches for new
phenomena using a 4.2 \invpb\ data set acquired
during the 1988-89 Collider run.  
I will first briefly describe the CDF detector; further details can be found
in Ref. 3.  The following sections will then summarize the results on:
searches for compositeness, supersymmetric particles, additional gauge bosons,
leptoquarks, the rare decay $W^\pm \rightarrow \pi^\pm \gamma$, and events
with anomolously large amounts of transverse energy.

\section{The CDF Detector}
The CDF is a general-purpose, solenoidal detector designed to detect 
and record \pbarp\ collisions that produce one or more high 
transverse-momentum (\Pt) particles in the final state.\cite{ref: CDF Detector}
The detector, shown in Fig. 
\ref{fig: CDF Detector}, consists of charged particle tracking devices in 
the solenoidal magnetic field, surrounded by finely-segmented 
electromagnetic and hadronic calorimeters that measure the energy flow 
from the collision over the 
pseudorapidity\footnote{We define $\eta 
\equiv -\ln\tan(\theta/2)$, where $\theta$\ is the polar angle with respect 
to the incoming proton beam direction.}   
interval $|\eta| < 4.2$.
Charged particles are detected by
a vertex time projection chamber (VTPC) instrumenting the inner region out to a 
radius of 23 cm and a central tracking chamber (CTC) that tracks 
particles out to a radius of 1.2 m.  The momentum resolution 
of the tracking system is $\sigma_P/P \simeq 0.0011 P$.  The 
electromagnetic calorimeters surround the tracking volume and consist of 
plates of lead absorber interleaved with scintillator in the central 
pseudorapidity region $|\eta|<1.1$\ and lead plates interleaved with 
proportional gas counters over the remainder of the solid angle.  The 
hadronic calorimeters consist of plates of steel absorber interleaved with 
scintillator in the central region and interleaved with proportional gas 
counters in the pseudorapidity interval $|\eta|> 1.1$.  
\begin{figure}
\vspace{4in}
\caption{An elevation view of the CDF detector. }
\label{fig: CDF Detector}
\end{figure}

A proportional wire chamber located at a 
depth of six radiation lengths in the central EM calorimeter 
measures the position of electromagnetic showers to a few millimeters in 
both the azimuthal and axial directions.  This ``strip chamber'' is an 
important component of the CDF electron and photon identification 
system.  Muons are identified in the region $|\eta|\lessim0.6$\ using four 
layers of drift chambers located immediately outside the central hadronic 
calorimeter.  This system measures the position and trajectory of muon 
candidates and is used in conjunction with the CTC 
to identify high-\Pt\ muons.  An energetic  neutrino 
produced in a collision is detected by measuring the transverse momenta 
of the other charged and neutral particles in the event with the 
calorimeter system and inferring the neutrino transverse momentum 
magnitude and direction from the resulting missing transverse energy 
vector.  

The CDF identifies collisions with one or more high-\Pt\ particles
using a three-level trigger system.  The recorded events have to 
satisfy one of several trigger conditions, such as the 
presence of an electron candidate with $E_T>12$\ GeV, a muon 
candidate with $P_T > 9$\ \GeVc, a neutrino with $Et>25$\ GeV, or a jet 
with $Et>120$\ GeV.  These trigger conditions typically have efficiencies 
in excess of 95\%\ for correctly tagging candidate events.  
% 
%			Quark compositeness
%
\section{Quark and Lepton Compositeness}
The standard model assumes that the fundamental fermions (\ie\ the 
quarks and leptons) are point-like particles. 
It is important to test this ansatz as evidence of 
substructure would place strong constraints on any extension to the 
standard model.
Previous limits on quark and lepton substructure have been derived from studies 
of high transverse momentum lepton-lepton and quark-quark scattering 
\cite{ref: Previous Compositeness Limits}.  It is conventional to quote 
the limits set by these searches in terms of a generic scattering model 
\cite{ref: Compositeness Model}\ that adds an effective 4-fermion 
contact interaction to the Lagrangian.  The effective cross section is 
modified by a structure function of the form
\begin{eqnarray}
1 + \left( {{Q/\Lambda}}\right)^2,
\end{eqnarray}
where $Q$\ is the 4-momentum transfer in the interaction and 
$\Lambda$\ is a parameter that sets the compositeness scale, which 
depends on both the initial and final state fermions in the scattering 
process.  The experimental signal is an excess of events at high $Q^2$.  
%
\subsection{Quark Compositeness Searches}
CDF has searched for quark compositeness by measuring the inclusive 
jet \Et\ spectrum\cite{ref: CDF Inclusive Jet}\ 
and comparing these data with the next-to-leading order perturbative QCD 
predictions.\cite{ref: QCD Predictions}  
Events are selected that have at least one 
transverse energy cluster with $E_T>120$\ GeV in the central calorimeter.
The 
detector resolution is deconvoluted from the observed jet energy 
distribution to determine the produced jet \Et\ spectrum, which is shown in 
Fig.~\ref{fig: Inclusive Jet Data}(a) along with the result 
of the next-to-leading order QCD calculation.  The plots in 
Fig.~\ref{fig: Inclusive Jet Data}(b) show the difference between the data 
and the QCD predictions
normalized to the theory values, and illustrate the consistency of the QCD
calculation with the data.  
Although the very highest \Et\ points are 
somewhat above the QCD prediction, this effect is not statistically 
significant.

These data have been fit to the next-to-leading order QCD prediction 
including the 4-fermion interaction term, yielding a lower limit on the 
quark compositeness scale of
\begin{eqnarray}
\Lambda_{qq} > 1.4\ {\rm TeV\ at\ 90\%\ C.L.}
\end{eqnarray}
This result can be contrasted with the limits of $\Lambda_{qq} > 0.41$\ 
TeV from the UA1 collaboration.\cite{ref: Previous Compositeness Limits}
A recent CDF analysis of the dijet 
angular distribution sets a comparable limit of $\Lambda_{qq} > 1.0$\ 
TeV at 90\%\ C.L. 
\cite{ref: CDF Dijet Angular Analysis} 
\begin{figure}
\vspace{3.5in}
\caption{The inclusive jet energy spectrum is shown in (a), after 
corrections for detector resolution effects.  The curve is the prediction 
from the next-to-leading order QCD calculation.  The difference 
between the data and the QCD prediction scaled to the theoretical value 
is plotted in (b). }
\label{fig: Inclusive Jet Data}
\end{figure}
%
\subsection{Lepton-Quark Compositeness}
Lepton-quark compositeness in hadron-hadron collisions would first be 
observed as an excess of high-mass dilepton events above the expected 
Drell-Yan production rate.  CDF has searched for evidence of this 
substructure in both the 
dielectron\cite{ref: CDF Electron-Quark Compositeness}\
and dimuon\cite{ref: CDF Muon-Quark Compositeness}\
data sets.

The event selection requires two well-identified lepton candidates with 
$P_T>20$\ \GeVc.
Each lepton candidate is required to be isolated with respect to other
particles in the event as the signal
is expected to have lepton candidates that are uncorrelated with the 
energy flow in the collision whereas most of the background 
sources result in at least one non-isolated lepton 
candidate.  The 
isolation cut requires the additional calorimeter energy 
in a cone of radius $R \equiv\sqrt{(\Delta\eta)^2 + (\Delta\phi)^2} = 
0.4$\ surrounding each lepton candidate be less than 10\%\ of the lepton 
candidate \Et.  The lepton ID cuts are 
sufficient to reduce all expected backgrounds to of order one event. 

The invariant mass distribution for the dielectron data is shown in 
Fig.~\ref{fig: Dielectron Mass}\ (the dimuon data is similar).  
The expected contribution from Drell-Yan
production (excluding the $Z$\ pole) is also illustrated.  The data is 
dominated by the $Z$\ resonance but the tail of events at larger masses is 
consistent with the expected Drell-Yan contribution.  The absence of an 
excess of events at large invariant mass is used to set limits on the left and 
right-handed electron-quark 4-fermion contact interaction, \ie\ on the 
compositeness scales $\Lambda_{-}^{LL}$\ and $\Lambda_{+}^{LL}$, 
respectively:
\begin{eqnarray}
	\Lambda_{-}^{LL} &>& 2.2\  {\rm TeV\ at\ 95\%\ C.L.} \\
	\Lambda_{+}^{LL} &>& 1.7\  {\rm TeV\ at\ 95\%\ C.L.}
\end{eqnarray}
The dimuon data has the same absence of events at large invariant mass, 
which sets muon-quark compositeness 
limits of
\begin{eqnarray}
	\Lambda_{-}^{LL} &>& 1.6\  {\rm TeV\ at\ 95\%\ C.L.} \\
	\Lambda_{+}^{LL} &>& 1.4\  {\rm TeV\ at\ 95\%\ C.L.}
\end{eqnarray}
\begin{figure}
\vspace{4in}
\caption{The dielectron invariant mass distribution for the CDF
data set.  The prediction from Drell-Yan production is also shown. }
\label{fig: Dielectron Mass}
\end{figure}
%
%			SUSY  searches
%
\section{Supersymmetry Searches}
Supersymmetry\cite{ref: SUSY Reviews}\  remains an attractive 
extension to the standard model for 
several reasons:  it naturally explains the ``heirarchy'' problem where 
interactions at the grand unification (GUT) energy 
scale of $10^{16}$\ GeV lead to large 
cancellations that bring the Higgs mass down to the electroweak scale of 
order 100 \GeVcc\ to 1 \TeVcc; it provides a framework for 
string theory in which the four fundamental interactions stem from one
force, and 
predicts the unification of the electroweak and strong forces at the GUT 
scale.  The theory requires the existence of a new set of 
matter fields that are in 1-to-1 
correspondence with the quarks, leptons and vector bosons of the 
standard model.  However, there has been no direct experimental 
evidence for these supersymmetric partners, making their discovery an 
important test of the model.  

The supersymmetric partners to the quark and gluon, the squark (\squark) 
and gluino (\gluino), are predicted to couple strongly to ordinary 
quarks and gluons, so that they should be copiously pair-produced in 
hadron-hadron collisions.  The interactions of the supersymmetric 
particles are predicted to conserve a new quantum number, $R$, so that 
the produced squarks and gluinos will eventually decay to the lightest 
supersymmetric particle (LSP), which is usually assumed to be the 
photino (\photino).  The LSP does not interact with ordinary matter and  
therefore generates a missing transverse energy (\MEt) signature in SUSY pair 
production.      

Searches at $e^+e^-$\ colliders have set limits of \Msquark\ $> 45$\ 
\cite{ref: LEP SUSY limits}, but the most stringent limits have come 
from searches at hadron colliders.  The UA1 collaboration has published 
limits\cite{ref: UA1 SUSY}\ 
of \Msquark\ $> 45$\ and \Mgluino\ $> 53$\ at 90\%\ C.L. 
while the CDF collaboration has previously set 
limits\cite{ref: CDF SUSY}\   
of \Msquark\ $> 74$\ and \Mgluino\ $> 73$\ at 90\%\ C.L. 

The CDF collaboration has recently reported the results of a new
SUSY search that considerably extends the previous limits.
The recent CDF search focuses on the SUSY 
decay modes
\begin{eqnarray}
	& & \tilde{g} \rightarrow q \bar{q} \tilde{\gamma} \nonumber \\
	& & \tilde{q} \rightarrow q \tilde{g}\ 
		\quad {\rm for\ M_{\tilde{q}}> M_{\tilde{g}}} \\
	& & \tilde{q} \rightarrow q \tilde{\gamma}\ 
		\quad {\rm for\ M_{\tilde{g}}> M_{\tilde{q}}}, \nonumber
\end{eqnarray}
which results in events with significant amounts of missing transverse 
energy and up to six jets.  Events are selected by requiring $\MEt>40$\ 
GeV and at least two energy clusters in the calorimeter with observed 
$E_T>15$\ GeV and with $|\eta|< 3.5$.  The \MEt\ distribution for the 93 
events that survive this selection is shown in Fig. \ref{fig: SUSY Met}.
\begin{figure}
\vspace{4.75in}
\caption{The missing transverse energy distribution for the events in the 
SUSY candidate sample.  The events are required to have \MEt$>40$\ 
GeV and at least two jets. 
The dashed line shows the distribution expected from the standard model
sources described in the text. 
The inset figures show the \MEt\ distribution expected for two specific
scenarios: (a) \Msquark\ $= 125$\ \GeVcc\ and \Mgluino\ $=5000$\ \GeVcc,
and (b) \Msquark\ $= 225$\ \GeVcc\ and \Mgluino\ $=225$\ \GeVcc.}
\label{fig: SUSY Met}
\end{figure}

There are several potential standard model sources of events with large 
\MEt, with the largest being the production and leptonic decay of 
$W$\ bosons and the production of $Z$\ bosons following by the decay 
into neutrino pairs.  These background rates have been estimated using 
the measured boson cross sections and the 
ISAJET Monte Carlo programme\cite{ref: ISAJET}\ 
to model the kinematics of the $W$\ and $Z$\ boson daughters.  The 
other significant potential source of large \MEt\ events are from pair 
production of top or bottom quarks.  These rates have been estimated 
assuming a top quark with a mass of 91 \GeVcc, which gives the most 
conservative estimate for this background.  The estimated background 
event rates are listed in Table \ref{tab: SUSY backgrounds}.  The total 
background estimate is $91\pm17$\ events, which agrees well 
with the observed rate.
\begin{table}
\caption{The estimated rate of \MEt $+ \ge 2$\ jet events from the largest 
standard model sources. }
\begin{center}
\begin{tabular}{lc}
\hline
Background Source &	Number of Events \\
\hline
$Z\rightarrow \nu\bar{\nu}$ & 	$23\pm 8$ \\
$W\rightarrow \tau\bar{\nu}$ & 	$41\pm15$\\
$W\rightarrow \mu\bar{\nu}$ & 	$18\pm 6$\\
$W\rightarrow e \bar{\nu}$ & 	 $9\pm 3$\\
Heavy Quarks         	&	 $4\pm 4$ \\
\hline
\end{tabular}
\end{center}
\label{tab: SUSY backgrounds}
\end{table}

A limit on the pair production of \squark's and \gluino's is derived by 
fitting the observed \MEt\ distribution to contributions from the 
background sources and from SUSY production for various choices of 
\Msquark\ and \Mgluino.  Both the fraction of SUSY and 
background events are allowed to vary in the fit.  The likelihood 
distribution for the number of SUSY events in the data is then used to set 
an upper limit on the SUSY pair production cross section as a function of 
the squark and gluino mass.  The region in the \Msquark-\Mgluino\ 
plane where this upper limit is below the predicted cross section is 
shown in Fig. \ref{fig: SUSY limit}.  
The mass limits obtained when either
the \squark\ or \gluino\ is not present (or very massive) are
\begin{eqnarray}
	& &	M_{\tilde{g}} > 141\ \GeVccm\ {\rm at\ 90\%\ C.L.} \\
	& &	M_{\tilde{q}} > 126\ \GeVccm\ {\rm at\ 90\%\ C.L.}
\end{eqnarray}
\begin{figure}
\vspace{3in}
\caption{The region of squark and gluino masses excluded at 90\%\ C.L. 
by the CDF search for large \MEt\ and multijet events assuming the 
naive decay scenario is shown.
The dashed line reflects the previous CDF limits.
The excluded region when 
assuming a specific example of cascade decays is shown in (b).  The 
cascade scenario  assumes $\mu=-250$, $M_{H^+} = 500$\ \GeVcc\ 
and $\tan\beta = 2$.}
\label{fig: SUSY limit}
\end{figure}

It has been pointed out that for such large \squark\ and \gluino\ 
masses, the simple decay scenario assumed in establishing these limits is 
unlikely.\cite{ref: SUSY cascades}\  More complex 
``cascade'' decays of squarks and gluinos are expected involving 
additional supersymmetric particles that change the expected signature 
by increasing the number of daughter particles and 
softening their \Pt\ spectra.  This would tend to reduce the efficiency of 
the event selection and accordingly lower the mass bounds shown in Fig. 
\ref{fig: SUSY limit}(a).  The size of this effect depends on several 
parameters of the model making it difficult to summarize the mass 
limits; however, the mass limits are typically reduced by 20-30 \GeVcc\ 
for most parameter choices.  The excluded region of squark and gluino 
masses for a specific set of parameters ($\mu=-250$, $M_{H^+}=500$\ 
\GeVcc\ and $\tan\beta=2$) is shown in Fig. \ref{fig: SUSY limit}(b).

\section{$W^\prime$\ and $Z^\prime$\ Searches}
Numerous extensions to the standard model predict the existence of 
additional gauge symmetries beyond the 
$SU(3)\times SU(2)\times U(1)$\ symmetry of the standard model
\cite{ref: WZ prime theory}.  These symmetries would require 
additional gauge bosons that in general would be 
produced in quark-antiquark collisions, although the masses of 
these bosons and the strength 
of their couplings to the quark and lepton generations are generally 
model-dependent.  The CDF collaboration has searched for such bosons 
decaying leptonically into either a charged lepton and neutrino 
($W^\prime$) or into a lepton-antilepton pair ($Z^\prime$) 
\cite{ref: CDF WZ prime}.

The CDF search identified candidate events by requiring at least one 
high-\Pt\ charged lepton candidate and a large \MEt\ signature or by 
requiring two oppositely charged, high-\Pt\  lepton candidates.  
A signal for a heavy $W^\prime$\ would be an excess of 
events at large transverse mass, while a signal for a heavy $Z^\prime$\ 
would be an excess of events at large invariant dilepton mass.
These searches are insensitive to a $W^\prime$\ or $Z^\prime$\ degenerate 
with the standard model $W$\ or $Z$\ unless the coupling to the extra 
additional gauge boson is unusually large.  

The transverse mass distribution for the events with one charged lepton
and a large \MEt\ is shown in Fig. \ref{fig: Wprime Mt}, along with the
predicted contribution from the standard model $W$.
There is no excess of high 
mass events in the data;  the events above the $W$\ signal are 
consistent with the tail of the $W$\ resulting from the \MEt\ 
resolution of the CDF detector. 
A lack of high mass events is also apparent in the dilepton data
(see, for example, Fig. \ref{fig: Dielectron Mass}); the events above the $Z$\ 
resonance are consistent with the expected background from Drell-Yan 
production.  An upper limit on the number of such events in the data is 
determined by fitting the shape of each mass distributions to a standard 
model contribution and a contribution from a heavier gauge boson.
\begin{figure}
\vspace{3.8in}
\caption{The transverse mass distribution for the data requiring a charged
lepton with $P_T>30$\ \GeVc\ and \MEt\ $>30$\ GeV (points).  
The histogram shows the prediction from standard model $W$\ production and
decay. }
\label{fig: Wprime Mt}
\end{figure}

The searches place an upper limit on the product of the production cross 
section for a heavy gauge boson, its coupling to the initial state quarks 
and its coupling to the final state lepton pair as a function of
the mass of the gauge 
boson.  The 95\%\ C.L. upper limits for $W^\prime$\ and $Z^\prime$\ 
production are shown in Fig.~\ref{fig: WZ prime}(a) and (b).  These 
figures also illustrate the expected rate for new gauge bosons that have 
the same couplings to quarks and leptons as the standard model $W$\ 
and $Z$,  allowing for a $M^3$\ scaling as predicted in the standard 
model.  These data require that 
\begin{eqnarray}
	M_{W^\prime} &>& 520\ \GeVccm {\rm \quad at\ 95\%\ C.L.}\\
	M_{Z^\prime} &>& 412\ \GeVccm {\rm \quad at\ 95\%\ C.L.}
\end{eqnarray}
assuming that the new gauge bosons have such standard model 
couplings.
\begin{figure}
\vspace{3in}
\caption{The 95\%\ C.L. upper limit on the $W^\prime$\ production 
cross section as a
function of the $W^\prime$\ mass is shown in (a).  
The dot-dashed line represents the 
prediction assuming standard model couplings. 
The corresponding limit for $Z^\prime$\ production cross section is 
shown in (b).  The dashed line represents the standard model prediction.
}
\label{fig: WZ prime}
\end{figure}
%
%		Massive Stable Particle Search
%
\section{Massive Stable Particle Search}
Several theories predict extended multiplets of fermions containing 
massive particles that can be 
pair-produced in \pbarp\ collisions.\cite{ref: Stable Particle Theory}\
These particles are typically produced with velocities much less than the 
speed of light, and therefore do not interact hadronically because the 
available kinetic energy in the particle-nucleon center-of-mass frame 
falls below the threshold for $\pi$\ production.  The particles are therefore 
muon-like with the exception that they have velocities $\beta$\ much 
less than the speed of light.  A recent CDF analysis places the most 
stringent limits on the pair-production cross section 
of such particles.\cite{ref: CDF Stable Particle Search}

The collaboration searches for events with at least 
one charged particle with observed transverse momentum $P_T>25$\ 
\GeVc.  The CDF detector can measure the transit time of particles that 
penetrate through the central hadron calorimeter ($|\eta|<1.1$), as this 
subdetector is instrumented with a time-to-digital readout system on each 
calorimeter tower.  The candidate particle's energy deposition in the 
calorimeter is required  to be that expected of a minimum-ionizing track 
and its measured velocity is required to be inconsistent with a particle
with $\beta=1$.
The requirement that the particle not decay during its 
passage through the detector implicitly requires its lifetime to be 
$\gessim 10^{-8}$\ s. Only two events pass all these requirements, while 
the background is estimated to be of order one to 
two events and come
primarily from QCD jet production.  
Assuming that all of the candidate 
events come from the production of a heavy, stable particle, the 
collaboration sets the limits on the pair-production cross section as a 
function of the particle's mass shown in Fig.~\ref{fig: Heavy Stable 
search}.  
\begin{figure}
\vspace{3.4in}
\caption{The 95\%\ C.L. upper limits on the pair-production cross section 
of a heavy, stable particle as a function of the particle's mass.  The 
dashed curve is the prediction from a specific model. }
\label{fig: Heavy Stable search}
\end{figure}

These data can be used to constrain specific models.  For example,
a unit-charged fermionic colour triplet\cite{ref: Colour Triplet Model}\
with mass between 50 and 139 \GeVcc\ is ruled out at the 95\%\ C.L.,
while charge $2/3$\ and $4/3$\ objects are ruled out between the masses
of 50 \GeVcc\ and 116 and 140 \GeVcc, respectively.  Similar mass
constraints can be applied to other exotic colour multiplets.
%
%			Leptoquarks
%
\section{Search for a First Generation Leptoquark}
Leptoquarks are particles that couple to both the leptons and quarks of a 
given flavour generation.  Because of its quark couplings, a leptoquark 
should be pair-produced in \pbarp\ collisions with a rate that falls as a 
function of its mass, and it should decay preferentially into the quarks and 
leptons of the given generation.  Leptoquarks with masses greater than 
$\sim30$\ \GeVcc\ would therefore give rise to events with several 
energetic leptons and quark jets.  The CDF Collaboration has searched 
for the events that would arise from a first generation scalar leptoquark. 
Previous searches at $e^+e^-$\ colliders have set limits of $M_{LQ} > 
44.6$\ at 95\%\ C.L.\cite{ref: LEP LQ Searches}, while the most stringent
limit from a \pbarp\ collider\cite{ref: UA2 LQ Search}\ 
requires $M_{LQ} > 74$\ \GeVcc\ at 95\%\ C.L.

The analysis searches for events with at least one electron and one 
positron candidate with \Pt $>20$\ \GeVc\ in the pseudorapidity interval 
$|\eta|<1.0$\ and two jet clusters with $E_T>20$\ GeV. 
The primary background to a leptoquark signal arises
from Drell-Yan production of an electron pair in association with two 
or more jets, and is 
dominated by $Z +$\ multijet final states.  The $Z$\ decays were removed 
by rejecting all events with invariant electron pair mass between 75 and 
105 \GeVcc.  No candidate events are observed.

The collaboration sets a 95\%\ confidence level upper limit on the  
leptoquark pair production cross section by convoluting a Poisson 
distribution for the number of observed events with a Gaussian 
probability distribution to take into account the systematic uncertainties in 
the estimate of the integrated luminosity and the lepton and jet selection 
efficiencies.  This upper limit, shown in Fig. \ref{fig: leptoquark limit}, 
falls with increasing leptoquark mass due to the variation in kinematic 
acceptance for leptoquark pair production with $M_{LQ}$.  This upper 
limit can be used to set a lower limit on $M_{LQ}$\ for a specific model 
of leptoquark pair production.  The curve in Fig. \ref{fig: leptoquark 
limit}\ results from the lowest order ISAJET prediction for this process, 
and sets a limit of
\begin{eqnarray}
	M_{LQ} > 113\ \GeVccm\ {\rm at\ 95\%\ C.L.}
\end{eqnarray}
\begin{figure}
\vspace{4.5in}
\caption{The CDF 95\%\ C.L. upper limit on the first generation
leptoquark production 
cross section.  The curve is the ISAJET prediction for leptoquark 
production, asuming a K-factor of 1.0.  }
\label{fig: leptoquark limit}
\end{figure}

This mass limit is sufficiently high that only experiments at the HERA
$ep$\ collider will have the sensitivity to extend this search in
the near future.

\section{The Rare Decay $W^\pm\rightarrow \pi^\pm \gamma$}
The radiative decay $W^\pm \rightarrow \pi^\pm\gamma$\ is predicted 
to be strongly suppressed.  
A standard model calculation\cite{ref: SM W to PiGamma}\ predicts a partial 
width of
\begin{eqnarray}
\Gamma(W\rightarrow\pi\gamma)/\Gamma(W\rightarrow e\nu_e)\sim 
3\times 10^{-8}.
\end{eqnarray}
However, this partial width is sensitive to both the $W-
\gamma$\ coupling and to the QCD effects involved in the hadronization 
of the final state partons.  There has also been speculation that it is a 
sensitive probe of physics outside the standard model.  

Hadron collider 
experiments have now collected enough data on $W$\ decays that constraints
on this partial width can be placed.
Experiments at the CERN \pbarp\ Collider
established an upper limit\cite{ref: CERN W->PiGamma}\ of 
\begin{eqnarray}
\Gamma(W\rightarrow\pi\gamma)/\Gamma(W\rightarrow e\nu_e) < 
  5.4\times 10^{-4} \quad
{\rm at\ 90\%\ C.L.}
\end{eqnarray}
The CDF collaboration has recorded a data set in which $\sim24,000$\ 
$W+X$\ events were produced, and has searched for events consistent
with the radiative decay $W\rightarrow\pi\gamma$.
Events collected using the inclusive photon trigger were required to have
a well-identified photon candidate in the central detector. 
In addition, the events were required to
have a jet with $E_T>25$\ GeV associated with a single charged particle.
This selection results in 11 candidate events.

Events from $W$\ decay are expected to have large $\pi\gamma$\ invariant
mass.  The signal region defined by $71 < M(\pi\gamma) < 89$\ 
\GeVcc\ contains three events.  However, background from QCD production
of high \Pt\ jets is estimated to contribute at least 1.4 events to this signal
region.   A 95\%\ C.L. upper limit on the $W\rightarrow\pi\gamma$\ 
branching ratio is determined by assuming that the three observed
events come from a combination of this background and the 
$W\rightarrow\pi\gamma$\ signal.
This limit is
\begin{eqnarray*}
{{\Gamma(W^\pm\rightarrow\pi^\pm\gamma)}\over{
   \Gamma(W^\pm\rightarrow e^\pm\nu_e)}} < 7.5\times 10^{-3}\quad 
{\rm at\ 95\%\ C.L.}
\end{eqnarray*}
If the standard model value of 
$BR(W^\pm\rightarrow e^\pm\nu_e)=0.109$\ 
is assumed (this implies that $M_{top}>M_W$), then  we infer
\begin{eqnarray}
BR(W^\pm\rightarrow\pi^\pm\gamma) < 8.2\times 10^{-4}\quad 
{\rm at\ 95\%\ C.L.}
\end{eqnarray}
is inferred.

This is still many orders of magnitude greater than the expected 
standard model
rate, but does rule out a large partial width for this decay mode.
    
%
%	High Sum Et events
%
\section{High \Et\ Events}

The CDF collaboration has studied the events with the 
largest $\sum$ \Et\ depositions in the detector in order to search for
the production of massive particles that may be produced in
\pbarp\ collisions \cite{ref: SumEt paper}.
Such events are characterized by unusually large energy 
depositions, high-\Pt\ charged or neutral leptons or an unusual
number of high-\Et\ jets.   The standard model predicts that 
QCD production of two and three-jet final states should be the
predominate source of such large \Et\ events.

The analysis selects those events with at least 400 GeV of 
observed transverse energy in the detector.
There are 1189 events that satisfy this requirement.  
After removal of events coming from beam halo and cosmic ray
interactions, 279 events remain in the event sample.
The $\sum$ \Et\ distribution for these events is shown
in Fig. \ref{fig: sumEt}.
The QCD prediction, as calculated using the HERWIG Monte Carlo
programme \cite{ref: HERWIG}, is also shown for comparison.
\begin{figure}
\vspace{4.7in}
\caption{The $\sum$ \Et\ distribution for the the highest
transverse energy events recorded by CDF.
The histogram represents the prediction from QCD production,
while the dashed lines represent the systematic uncertainty in
this prediction resulting from the uncertainty on the calorimeter
energy scale. }
\label{fig: sumEt}
\end{figure}

The QCD prediction is in good agreement with the data distribution 
and rules out any obvious discrepancy with the standard model.
The collaboration has also searched for unusual events with high-\Pt\ 
electrons, muons or neutrinos,  and has concluded that there is
no evidence for anomolous production of such events.
The characteristics of these large $Q^2$\ interactions are in good
agreement with the standard model predictions for these final states.
%
%		Future plans
%			Run Ia, Ib = 100 pb-1
%
\section{Summary}

The search for new phenomena using CDF has yielded no evidence
for physics beyond the standard model.  The collaboration has
searched for:
	supersymmetric particles (\squark\ or \gluino);
	$W^\prime$\ and $Z^\prime$\ gauge bosons;
	quark or lepton compositeness;
	leptoquarks;
	anomolously large $BR(W^\pm\rightarrow \pi^\pm\gamma)$; and
	unusual (\eg\ high $\sum E_T$) events.
The data is in good agreement with the standard model.

The CDF collaboration expects to
increase its data set by a factor of $\sim25$\  over the next year.
This will increase the sensitivity
of all of these searches, and will allow the collaboration to study
even rarer processes (such as $W^\pm W^\mp$\ production).
Perhaps the most important goals of this coming run are the
discovery of the long sought-after top quark and a measurement
of the $W$\ boson mass to an accuracy of $\lessim 0.2$\%.
However, an even more exciting prospect would be the discovery of new
physics that would show us the way to a theory of elementary particles 
more fundamental than the standard model.
%
%  References
%
\bibliographystyle{unsrt}
\begin{thebibliography}{99.}
%
\bibitem{ref: CDF institutions} 
The CDF Collaboration consists of groups from:
Argonne National Laboratory, 
Brandeis University,
University of California at Los Angeles,
University of Chicago,
Duke University,
Fermi National Accelerator Laboratory,
Laboratori Nazionali di Frascati, Istituto Nazionale di Fiscia Nucleare,
Harvard University,
University of Illinois,
The Johns Hopkins University,
KEK,
LBL,
MIT,
University of Michigan,
Universita di Padova,
University of Pennsylvania,
Istituto Nazionale di Fiscia Nucleare, University and Scuola Superiore of
Pisa,
Purdue University,
University of Rochester,
Rockefeller University,
Rutgers University,
Texas A\&M University,
University of Tsukuba,
Tufts University and
University of Wisconson.
%
\bibitem{ref: SM description}
W.~Marciano, these proceedings.
%
\bibitem{ref: CDF Detector}
F.~Abe et al. (CDF Collaboration), Nucl.~Instr.~Meth.~{\bf A271}, 387 
(1988).
%
\bibitem{ref: Previous Compositeness Limits}
P.~Bagnaia et al. (UA2 Collaboration), Phys.~Lett.~{\bf 144B}, 283 
(1984); \\
G.~Arnison et al. (UA1 Collaboration), Phys.~Lett.~{\bf 158B}, 494 
(1985); \\
G.~Arnison et al. (UA1 Collaboration), Phys.~Lett.~{\bf 177B}, 244 
(1986); \\
F.~Abe et al. (CDF Collaboration), Phys.~Rev.~Lett.~{\bf 62}, 3020 
(1989).
%
\bibitem{ref: Compositeness Model}
E.~Eichten, K.~Lane, and M.~Peskin, Phys.~Rev.~Lett.~{\bf 50}, 811 
(1983).
%
\bibitem{ref: CDF Inclusive Jet}
F.~Abe et al. (CDF Collaboration), Phys.~Rev.~Lett.~{\bf 68}, 1104 
(1992).
%
\bibitem{ref: QCD Predictions}
S.~Ellis, Z.~Kunszt and D.~Soper, Phys.~Rev.~{\bf D40}, 2188 (1989);  
Phys.~Rev.~Lett.~{\bf 64}, 2121 (1990).
%
\bibitem{ref: CDF Dijet Angular Analysis} 
F.~Abe et al. (CDF Collaboration), 
FERMILAB-PUB-92-182-E, July 1992, submitted to Phys.~Rev.~Lett.
%
%
\bibitem{ref: CDF Electron-Quark Compositeness}
F.~Abe et al. (CDF Collaboration), 
Phys.~Rev.~Lett. {\bf 67}, 2418 (1991).
%
\bibitem{ref: CDF Muon-Quark Compositeness}
F.~Abe et al. (CDF Collaboration), 
Phys.~Rev.~Lett. {\bf 68}, 1463 (1992).
%
\bibitem{ref: LEP SUSY limits}
P.~Abreu et al. (DELPHI Collaboration), Phys.~Lett. {\bf 247B}, 148 (1990).
%
\bibitem{ref: UA1 SUSY}
C.~Albajar et al. (UA1 Collaboration),
Phys.~Lett. {\bf 198B}, 261 (1987).
%
\bibitem{ref: SUSY Reviews}
Recent reviews of supersymmetry include: \newline
H.~P.~Nilles, Phys.~Rep.~{\bf 110}, 1 (1984); \newline
H.~E.~Haber and G.~L.~Kane, Phys.~Rep. {\bf 117}, 75 (1985).
%
\bibitem{ref: CDF SUSY}
F.~Abe et al. (CDF Collaboration), 
Phys.~Rev.~Lett. {\bf 62}, 1825 (1989).
%
\bibitem{ref: ISAJET}
F.~Paige and S.~D.~Protopopescu, Brookhaven report BNL-38034 (1986).
%
\bibitem{ref: SUSY cascades}
See, for example, \newline
H.~Baer, J.~Ellis, G.~B.~Gelmini, D.~V.~Nanopoulos and
X.~Tata, Phys.~Lett.~{\bf 161B}, 175 (1985).
%
\bibitem{ref: WZ prime theory}
J.~Pati and A.~Salam, Phys.~Rev. {\bf D10}, 275 (1974); \newline
R.~E.~Marshak and R.~N.~Mohapatra, Phys.~Lett. {\bf 91B}, 222 (1980).
%
\bibitem{ref: CDF WZ prime}
F.~Abe et al. (CDF Collaboration), 
Phys.~Rev.~Lett. {\bf 67}, 2418 (1991); \newline
F.~Abe et al. (CDF Collaboration), 
Phys.~Rev.~Lett. {\bf 67}, 2609 (1991).
%
\bibitem{ref: Stable Particle Theory}
See, for example, \newline
E.~Eichten et al., Rev.~Mod.~Phys. {\bf 56}, 579 (1984),
and references quoted therein.
%
\bibitem{ref: CDF Stable Particle Search}
F.~Abe et al. (CDF Collaboration), 
submitted to Phys.~Rev.~Lett. 
%
\bibitem{ref: Colour Triplet Model}
R.~K.~Ellis, FERMILAB-PUB-91-30-T, 1991 and private communication.
%
\bibitem{ref: LEP LQ Searches}
B.~Adeva et al.(L3 Collaboration), Phys.~Lett. {\bf 261B}, 169 (1991); \\
G.~Alexander et al.(OPAL Collaboration), Phys.~Lett. {\bf 263B}, 123 (1991); \\
P.~Abreu et al. (DELPHI Collaboration), Phys.~Lett. {\bf 275B}, 222 (1992).
%
\bibitem{ref: UA2 LQ Search}
J.~Alitti et al. (UA2 Collaboration), Phys.~Lett. {\bf 274B}, 507 (1992).
%
\bibitem{ref: SM W to PiGamma}
L.~Arnell, M.~Marciano and Z.~Parsa, Nucl.~Phys. {\bf B196}, 378 (1982); \\
G.~Lepage and S.~Brodsky, Phys.~Lett. {\bf 87B}, 359 (1979); \\
G.~Kane, private communication.
%
\bibitem{ref: CERN W->PiGamma}
C.~Albajar et al. (UA1 Collaboration), Phys.~Lett. {\bf 241B}, 283 (1990); \\
J.Alitti et al. (UA2 Collaboration), Phys.~Lett. {\bf 277B}, 194 (1992).
%
\bibitem{ref: SumEt paper}
F.~Abe et al. (CDF Collaboration), Phys. Rev. {\bf D45}, 2249 (1992).
%
\bibitem{ref: HERWIG}
G.~Marchesini and B.~R.~Webber, Nucl. Phys. {\bf B310}, 461 (1988).
%
\end{thebibliography}
%
\end{document}
