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%\begin{document}
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\title*{Hard Diffraction at the TEVATRON}
%
%
\toctitle{Hard Diffraction at the TEVATRON}
%
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\titlerunning{Hard Diffraction at the TEVATRON}
% allows abbreviation of title, if the full title is too long
% to fit in the running head
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\author{Kristal Mauritz}
%\and Roger Temam\inst{2}
%\and Jeffrey Dean\inst{2}
%\and David Grove\inst{1}
%\and Craig Chambers\inst{2}
%\and Kim~B.~Bruce\inst{2}
%\and Elsa Bertino\inst{1}}
%
\authorrunning{Kristal Mauritz} 
% if there are more than two authors,
% please abbreviate author list for running head
%
%
\institute{Iowa State University, Ames IA 50011, USA}

\maketitle              % typesets the title of the contribution

\begin{center}
 (On behalf of the D\O\ and CDF Collaborations)
\end{center}


\begin{abstract}
Experimental results\index{abstract} on hard diffraction with the CDF and D\O\
detectors at the Fermilab TEVATRON are reviewed and compared with theoretical 
expectations. 
\end{abstract}


\section{Introduction}
%
Diffractive and elastic events have been studied for over 30 years and are 
responsible for about $40$\% of the $p\overline{p}$ cross-section, but still 
much is unknown 
about the nature of the process.  In addition to the diffractively scattered
proton or antiproton, they are characterized by the
complete, or nearly complete, absence of hadronic particle activity 
over a large rapidity or pseudorapidity region~\cite{ZLRG,HLRG}.  This region 
is called a `rapidity gap' and in elastic $p\overline{p}$ scattering, the 
`rapidity gap' is complete and extends over the whole kinematically allowed 
rapidity range.  Single diffraction is the break-up of the $p$ or 
$\overline{p}$ into a typically low-mass `diffractive system' at low momentum 
transfer generally assumed to be a spin-1/2 nucleon resonance with the 
quantum numbers of the proton.   The concept of a ``Pomeron'' was invented by 
Pomeranchuk to explain this diffractive process in the context of Regge 
theory~\cite{regge2}.  The pomeron, which is a color-singlet with quantum 
numbers of the vacuum, is the exchanged object presumed to produce a 
diffractive event.

Hard single diffraction (HSD) was introduced by Ingelman and 
Schlein\cite{IS} in 1985 as a model to probe the pomeron.  
The event is treated in a factorizable way, i.e. the pomeron is ``emitted'' 
by the anti-proton (or proton) with a certain probability or flux and then 
struck by the 
other proton (or antiproton) with a high $p_T$.  `Hard' diffraction 
constitutes a larger tranverse momentum process in addition to the 
diffractive scattering.   The events studied here have a hard scattered 
system of at least two jets with an $E_T \ge 7$\,GeV (usually higher) as well 
as a rapidity gap. The first experimental results on the subject were 
published by the UA8 Collaboration, which showed the existence of jets in 
single diffractive events and that these jets had rapidity and longitudinal 
momentum distributions consistent with a hard pomeron structure~\cite{UA8}.
The field of study has expanded dramatically since then.  
Recent results from HERA and the TEVATRON include studies of large rapidity 
gap events in deep inelastic scattering~\cite{ZLRG,HLRG,heradis}, diffractive 
jet production~\cite{d0old,CDFJ,H1,Zeus} and diffractive 
$W$-boson production~\cite{CDFW2}. Measurements at both HERA and the 
TEVATRON are consistent with a predominantly gluonic pomeron,
but measured rates at the TEVATRON are several times lower
than predictions based on HERA data\cite{fact}.  The 
combination of these results gives new insight into the exchanged object.

This paper will provide an introduction and brief review on the recent 
results at the TEVATRON of hard single diffraction and hard double pomeron 
exchange.  Studies of hard diffraction can be used to increase our knowledge 
of the structure of the pomeron,  especially when combined with complementary 
hard diffractive measurements at HERA.  They can also test such basic 
assumptions as to the very nature of the pomeron as a particle-like object.


\subsection{Hard Diffraction at the TEVATRON}

At the TEVATRON, there are three types of hard diffractive processes 
accessible to experimentation:  hard single diffraction, double diffraction 
or hard color singlet exchange (HCS), and hard double pomeron exchange (HDPE). 
Hard single diffractive jet production is a subset of single diffraction with 
a hard scatter in the final state.  Figure~\ref{SDDPPIC}(a) shows a two-jets 
final 
state in the  process $p + \overline{p} \rightarrow j + j + X$. 
Because the pomeron is a color-singlet, particle 
production is typically suppressed between the outgoing hadron and the jets 
and a forward rapidity gap results in these events.  Hard color singlet 
exchange (Fig.~\ref{SDDPPIC}b) is a double diffractive process, but at large 
$t$, which produces a final state of a rapidity gap between jets.  To produce
a rapidity gap, the exchanged particle must again be a color-singlet, but the 
event rates are too large to be explained by electroweak boson exchange and 
indicate a strong interaction process~\cite{d0gap2}.


\begin{figure}[b]
\begin{center}
\includegraphics[width=1.0\textwidth]{mauritz.1}
\end{center}
\caption[]{Event topology of dijet production in (a) single diffraction, (b) hard color singlet, and (c) hard double pomeron exchange.}
\label{SDDPPIC}
\end{figure}

Another type of diffractive event is double pomeron exchange,
characterized by particle production
only in the central rapidity region (Fig.~\ref{SDDPPIC}c).  Each incoming
hadron `emits' a (or interacts via an internal) pomeron 
(state) leading to large forward
and backward rapidity gaps, and the interaction
of the two pomerons results in central particle production.
This class of events was first observed at the ISR in
%
\begin{equation}
\rm{pp} \rightarrow \rm{pp } \pi^{+} \pi^{-}
\end{equation}
%
interactions~\cite{kerret}. At the ISR there was insufficient energy
to produce hard scattering in DPE events.
UA1 previously has made attempts to find ``hard double
pomeron exchange'' using central particle production and forward
rapidity gaps~\cite{joyce} (gaps close to the beam-pipe on either side).  
Although they did find a class of
events consistent with double pomeron exchange, they were unable to
show that these events did not arise from multiplicity fluctuations
in color exchange jet events.

All three classes of events can be tagged by the rapidity gap signature.  HSD 
and DPE can also be tagged by detecting the leading particle(s) on the gap 
side. Using rapidity gap tagging, the CDF and D\O\  collaborations have 
studied dijet production (two or more jets) in all three processes at 
$\sqrt{\rm{s}}=1800$\,GeV.  In addition, CDF has studied (single) diffractive 
$W$-boson, $b$-quark, and $J/\psi$ production using rapidity gaps, and dijet 
production in HSD and DPE using a ``roman pot'' magnetic spectrometer to 
detect leading antiprotons~\cite{Kerstin}.  D\O\  has also studied all three 
processes at $\sqrt{\rm{s}}=630$\,GeV and has made measurements of the 
dependence of HSD on jet pseudorapidity~\cite{Kristal}.   



\section{Hard Single Diffraction}
%
CDF~\cite{CDFdet} and D\O~\cite{NIM} measure the rate of single diffraction
in different processes as the fraction of events with forward rapidity gaps, 
called the gap fraction.  Forward rapidity gaps are identified by measuring the 
multiplicity in the forward detectors, or those closest to the beam pipe with 
the greatest pseudorapidity.  In both experiments, this is the forward 
calorimeter ($2.4<|\eta|<4.2$ at CDF and $3.0<|\eta|<5.2$ at D\O) and the 
forward scintillator arrays, called the beam-beam counter (BBC) at CDF
($3.2<|\eta|<5.9$) and the Level\O\ (L\O) detector at D\O\  ($2.3<|\eta|<4.3$). 
A particle is tagged by a hit in the scintillation 
counters or by the deposition of energy in a calorimeter tower greater than a 
certain threshold energy, set to just above the noise 
to maximize the sensitivity to particles.  At CDF, this threshold is 
$1500$\,MeV per calorimeter tower, and at D\O\ it 
is $150$\,MeV in an electromagnetic calorimeter tower or $500$\,MeV in a 
hadronic calorimeter tower.

%%%%%%%%%%%%%%%%%%
\begin{figure}
  \hspace{-5mm}
  \vspace{30mm}
  \begin{minipage}[t]{55mm}
    \vspace{-12mm}
    \includegraphics[width=.75\textwidth]{mauritz.2}
    \vspace{-15mm}
    \caption[]{D\O\ multiplicity distribution for $1800$\,GeV forward jet 
        events.}
    \label{raw_mult1}
  \end{minipage}
  \hspace{9mm}\vspace{-90mm}\begin{minipage}[t]{55mm}
    \includegraphics[width=1.05\textwidth]{mauritz.3}
    \vspace{1mm}
    \caption[]{CDF multiplicity distribution for $1800$\,GeV forward jet 
        events.}
\label{raw_mult2}
  \end{minipage}
  \hspace{9mm}
  \vspace{60mm}
\end{figure}
%%%%%%%%%%%%%%%%%%

Figures~\ref{raw_mult1} and~\ref{raw_mult2}, respectively, show sample 
multiplicity distributions at D\O\ and CDF.
The number of calorimeter towers ($\rm{n_{CAL}}$ or towers) above the energy 
threshold and the number of scintillator hits ($\rm{n_{L0}}$ or BBC) are 
measured opposite the leading two jets for the forward jet trigger 
(at least two jets with $E_T > 12$\,GeV and $|\eta | > 1.6$ for D\O\ or 
$E_T > 20$\,GeV and $1.8<|\eta|<3.5$ for CDF).  The distributions show the 
characteristic peak at zero multiplicity in qualitative
agreement with expectations for a diffractive signal component and a higher
multiplicity distribution associated with non-diffractive, background events. 
The diffractive and non-diffractive peaks at D\O\ are more separated because 
of the lower threshold and finer calorimeter segmentation.
Both experiments fit the distributions to extract the gap fraction, the number
of diffractive events divided by the total number of events in the sample.
CDF fits the two-dimensional multiplicity distribution to a line along the 
diagonal and D\O\ simultaneously fits the diffractive signal to a falling 
exponential and the background to a four-parameter fit.



\begin{table} [htbp]
\vspace{-0.3cm}
\caption{Diffractive to total production ratios at the TEVATRON}
\begin{center}
\renewcommand{\arraystretch}{1.4}
\setlength\tabcolsep{2pt}
\begin{tabular}{lcccc}
\hline\noalign{\smallskip}
SD hard process & $\sqrt{s}$ (GeV) & $R = \frac{\rm DIFF}{\rm TOTAL}$ (\%) & Comments & Exp't             \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}

$W (\rightarrow e\nu)$              & 1800 & (1.15 $\pm$ 0.55)${\cal A}^\dag$      & $E_T^e, {E\!\!\!\!/\,}_T >$ 20 GeV                 & CDF~\cite{CDFW2}     \\
Forward Jets                        & 1800 & (0.75 $\pm$ 0.10)${\cal A}^\dag$      & $E_T^{jet} >$ 20 GeV, $|\eta^{jet}| >$ 1.8           & CDF~\cite{CDFJ}      \\
Forward Jets                        & 1800 & 0.65 $\pm$ 0.04                        & $E_T^{jet} >$ 12 GeV, $|\eta^{jet}| >$ 1.6           & D$\emptyset^{\ast}$  \\
Forward Jets                        &  630 & 1.19 $\pm$ 0.08                        & $E_T^{jet} >$ 12 GeV, $|\eta^{jet}| >$ 1.6           & D$\emptyset^{\ast}$  \\
Central Jets                        & 1800 & 0.22 $\pm$ 0.05                    & $E_T^{jet} >$ 15 GeV$^\ast$ $^\ast$, $|\eta^{jet}| <$ 1.0           & D$\emptyset^{\ast}$  \\
Central Jets                        &  630 & 0.90 $\pm$ 0.06                        & $E_T^{jet} >$ 12 GeV, $|\eta^{jet}| <$ 1.0           & D$\emptyset^{\ast}$  \\
$b (\rightarrow e + X)$             & 1800 & (0.62 $\pm$ 0.25)${\cal A}^\dag$      & $\mid \eta^e \mid <$ 1.1, 9.5 $< p_T^e <$ 20 GeV   & CDF~\cite{CDFB}      \\
$J/\psi (\rightarrow \mu\mu)$       & 1800 & 0.64 $\pm$ 0.12                        & $\mid \eta^\mu \mid <$ 0.6, $p_T^\mu >$ 2 GeV      & CDF$^{\ast}$    \\ 

\noalign{\smallskip}
\hline
\noalign{\smallskip}
\end{tabular}
\end{center}
$^\ast$ Preliminary \\ 
${\cal A}^\dag$ Includes rapidity gap acceptance based on a hard gluon 
structure function \\
$^\ast$ $^\ast$ The diffractive jet gap fractions show no $E_T$ dependence (shown 
later), so the central jet gap fractions at $1800$ and $630$\,GeV can be 
directly compared. \\
\vspace{-0.5cm}
\label{results}
\end{table}


Table~\ref{results} shows the measured gap fractions at both experiments
for final state forward jet, central jet, $W$-boson, $J/\psi$, and $b$-quark
production.  There are several notable observations:

\begin{itemize}
\item
All gap fractions for hard single diffraction are $\sim\it{O}$($1$\%).
\item
Forward jet gap fractions $>$ central jet gap fractions.
\item
Gap fractions at $\sqrt{\rm{s}}=630$\,GeV are at least twice as large as
the gap fractions at $\sqrt{\rm{s}}=1800$\,GeV.  
\end{itemize}

As can be seen by the ${\cal A}^\dag$ in the gap fraction measurements in
Table~\ref{results}, the two experiments treat the measurement of the 
rate for hard diffraction slightly differently.  To understand this, it
is important to look at the phenomenology.

\subsection{Phenomenology}

The theory of diffraction relies on phenomenological models.  The 
Ingelman-Schlein model (IS) supposed that the pomeron is
a composite pseudoparticle, composed of quarks and gluons.  They proposed
several simple structure functions and calculated the cross-section for
hard diffraction as the probability of a pomeron being `emitted' (called the 
flux factor) with the QCD hard matrix element. The diffractive Monte Carlo
POMPYT~2.6~\cite{pompyt} is based on the IS model and assumes a pomeron is 
emitted from the proton.   The standard Donnachie-Landshoff
flux factor is used at the TEVATRON, and the results can be easily 
rescaled for different flux factors.  It allows
for several possible choices of a presumed pomeron structure function, $s(x)$. 
The four main structure choices are a: (i) `hard gluon', a pomeron consisting 
of two light gluons, $s(x)\propto x(1-x)$; (ii) `flat gluon', 
$s(x)\propto \rm{constant}$; (iii) `quark', a pomeron consisting of two light 
quarks, $s(x)\propto x(1-x)$; and (iv) `soft gluon', with a gluon distribution 
similar to that in the proton, $s(x)\propto(1-x)^5$.  The pomeron takes a 
small fraction of the proton's momentum called 
$\xi$, and a parton in the pomeron with a momentum fraction $\beta$ to 
interact in the hard scattering. 

The corresponding diffractive Monte Carlo multiplicity distributions with
POMPYT show the same characteristic peak at low multiplicities as observed in 
the diffractive data with a tail extending to larger multiplicities that is 
dependent on the structure function choice.  The expected fraction of 
diffractive events that are produced with a rapidity gap, called the rapidity
gap acceptance, can be calculated for each structure function. 
The rapidity gap acceptance is treated differently between 
the two experiments.  CDF assumes a hard gluon structure function (which has
its basis in HERA data) and folds the acceptance into the data gap fraction
to provide a ``true'' diffractive rate. 
D\O\ chooses to measure the rapidity gap fraction with no model dependence
and folds the gap acceptance into the Monte Carlo predictions.
For comparison, the D\O\ $1800$\,GeV forward jets gap fraction 
with a hard gluon gap efficiency increases the preliminary ``measured'' gap 
fraction to $(0.88 \pm 0.05)$\%. 

\subsection{D\O\ Analysis}

The gap fraction can be calculated from Monte Carlo as the 
ratio of the number of rapidity gap events using POMPYT to 
the number of non-diffractive events with PYTHIA~5.7~\cite{PYTHIA}
divided by the gap acceptance.  The Monte Carlo gap fractions are shown in
Table~\ref{fitgapfrac}, and the trend is for the harder gluon rates to be much
higher than the data, although the different data sets do not favor a 
particular $\sqrt{\rm{s}}$-dependent scale factor as suggested by 
Ref.~\cite{renorm}.   

In the gap fraction ratios also shown in Table~\ref{fitgapfrac},
the flux factor cancels for the same $\sqrt{\rm{s}}$, while for different 
$\sqrt{\rm{s}}$, any dependence on the flux factor is reduced.
The Monte Carlo $630/1800$ ratios are in much better agreement with the
data than the numerator and denominator separately.  However, the 
hard and flat gluon structures, which have been favored
by previous measurements, 
are inconsistent with the forward/central jet ratio, despite the
full cancellation of the flux factor. For a gluon dominated pomeron to
describe the data, the addition of a significant
soft gluon component, which rarely produces central jet events with rapidity
gaps, would be required.

%%%%%%%%%%%%%%%%%%
\begin{table}[htbp]
\vspace{-0.5cm}
\caption{The D\O\ preliminary measured and predicted gap fractions and ratios.}
\label{fitgapfrac} \begin{center} 
\begin{footnotesize}
\begin{tabular}{cccccc} 
\hline
\multicolumn{6}{c}{~Gap Fraction (in \%)} \\ 
Sample & Data & Hard Gluon & Flat Gluon & Soft Gluon & Quark \\
\hline
 $1800$\,GeV  $|\eta|>1.6$ & $0.65 \pm 0.04$  &
     $2.2 \pm 0.3$ & $2.2 \pm 0.3$ & 
     $1.4 \pm 0.2$ & $0.79 \pm 0.12$ \\
 $1800$\,GeV  $|\eta|<1.0$ & $0.22 \pm 0.05$   &
     $2.5 \pm 0.4$ & $3.5 \pm 0.5$ &
     $0.05 \pm 0.02$ & $0.49 \pm 0.06$ \\
 $630$\,GeV  $|\eta|>1.6$  & $1.19 \pm 0.08$   &
     $3.9 \pm 0.9$ & $3.1 \pm 0.8$ &
     $1.9 \pm 0.4$ & $2.2 \pm 0.5$ \\ 
 $630$\,GeV  $|\eta|<1.0$  & $0.90 \pm 0.06$   &
     $5.2 \pm 0.7$ & $6.3 \pm 0.9$ &
     $0.13 \pm 0.11$ & $1.6 \pm 0.2$ \\ \hline
\multicolumn{6}{c}{~Gap Fraction Ratio} \\ \hline
 $630/1800$ FWD JET & $1.8 \pm 0.2$  &
     $1.7 \pm 0.4$ & $1.4 \pm 0.3$ & 
     $1.4 \pm 0.3$ & $2.7 \pm 0.6$ \\
 $630/1800$ CEN JET & $4.1 \pm 1.0$   &
     $2.1 \pm 0.4$ & $1.8 \pm 0.3$ &
     $2.7 \pm 2.4$ & $3.2 \pm 0.5$ \\
 $1800$ FWD/CEN JET & $3.0 \pm 0.7$   &
     $0.88 \pm 0.18$ & $0.64 \pm 0.12$ &
     $29. \pm 11.$ & $1.6 \pm 0.3$ \\ 
 $630$ FWD/CEN JET & $1.3 \pm 0.1$   &
     $0.75 \pm 0.16$ & $0.48 \pm 0.12$ &
     $15. \pm 12.$ & $1.4 \pm 0.3$ \\   \hline    
  \end{tabular}
\end{footnotesize}
 \end{center}
\vspace{-0.8cm}
\end{table}

\normalsize
%%%%%%%%%%%%%%%%%%

D\O\ also uses an inclusive jet trigger in coincidence with a rapidity gap in  
the L\O\ detector to obtain a large number of low background single 
diffractive candidate events with which to study the event characteristics.
After reinforcing the rapidity gap in the calorimeter, 
the number of jets, jet width, $\delta \phi$, 
and $E_T$ of the leading two jets are shown
in figure~\ref{char} for $1800$\,GeV diffractive (solid) and non-diffractive 
(dashed) central 
jet events.  The diffractive events are consistent with less overall radiation
than the non-diffractive events, and the $E_T$ distributions are similar. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
%\vspace{-5mm}
\includegraphics[width=.5\textwidth]{mauritz.4}
\end{center}
\vspace{-0.3cm}
\caption[]{The number of jets, 
 jet width, $\delta \phi$ between jets, and the
 $E_T$ distribution for the two central leading jets at $1800$\,GeV for the  
  diffractive ({\it solid line}) and non-diffractive ({\it dashed line}) 
 events (D\O\ preliminary)}
\label{char}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\clearpage

The $\xi$  distribution, or the momentum loss of the diffracted proton, can 
also be calculated using~\cite{collins1} 

\begin{equation}
\xi \approx \Sigma \frac{E_{T_i}e^{\eta_i}}{\sqrt{s}}, 
\end{equation}

\noindent summing over the particles with the highest $\eta$ and 
largest $E_T$.  
The outgoing diffracted proton (or the rapidity gap) is defined to be 
at positive $\eta$.  This formula measures $\xi$ using only the calorimeter,
emphasizing the well-measured central region close to the gap.  It contains no
model-dependence, and it can be defined even for non-diffractive events.  After
correcting for energy scale differences between Monte Carlo and data, the 
$\xi$ distribution (solid) for $1800$\,GeV and $630$\,GeV forward 
and central jets are shown in Figure~\ref{svxi}.  The dotted and dashed
curves reflect the high and low error.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[htbp]
\begin{center}
%\vspace{-5mm}
\includegraphics[width=.5\textwidth]{mauritz.5}
\end{center}
%\vspace{-5mm}
\caption[]{The $\xi$ distribution ({\it solid line}) and one sigma uncertainty
for a)-b) $\sqrt{\rm{s}}=1800$\,GeV and c)-d) $\sqrt{\rm{s}}=630$\,GeV 
forward and central jets (D\O\ preliminary)}
\label{svxi}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The forward jet $\xi$ distribution at both $1800$ and $630$\,GeV is peaked
toward lower values of $\xi$ although separated from zero because the
pomeron requires a certain amount of momentum to create two
$12$\,GeV jets.  The central jet $\xi$ distribution is spread over
higher values, consistent with the pomeron requiring more momentum to balance
the parton in the non-diffracted (anti)proton.  The $\xi$ distribution at
$630$\,GeV is higher overall than at $1800$\,GeV, as expected because more 
momentum is needed from the pomeron at lower $\sqrt{s}$ with the same jet
requirements. Although the trends of
the $\xi$ distribution are consistent with expectations, pomeron exchange is
typically thought to dominate for very low values of $\xi < 0.05$.  The large
values of $\xi$ observed, however, can be reproduced well with Monte Carlo.



\subsection{CDF Analysis}

The gluon content of the diffractive structure function is measured at CDF by 
comparing the hard single diffractive rates for final states with different 
sensitivity to quarks and gluons.  This is similar to what is done by ZEUS, 
which compares the diffractive deep inelastic scattering (D-DIS) to dijet 
photoproduction rates, and by H1, through a QCD analysis of the $Q^2$ 
evolution of the diffractive structure function measured in D-DIS. Both 
experiments measure a high gluon content.  CDF measured, with the $W$ and 
dijet production rates, a gluon fraction of $f_g = 0.7 \pm 0.2$~\cite{CDFW2}, 
and has a new measurement including the $b$-quark production rate of 
$f_g = 0.54^{+0.16}_{-0.14}$~\cite{CDFB} (see Fig.~\ref{glufr}).
 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.5\textwidth]{mauritz.6}
\end{center}
\caption[]{The ratio, D, of measured to predicted diffractive rates as a
function of the gluon content of the Pomeron.  The predictions are from POMPYT
using the standard Pomeron flux and a hard Pomeron structure.}
\label{glufr}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

In 1996 CDF installed three forward proton detectors to be able to tag the 
diffractively scattered proton.  Data were taken at both 
$\sqrt{\rm{s}}=1800$\,GeV and $\sqrt{\rm{s}}=630$\,GeV, requiring a good
reconstructed track.  The forward proton detectors have acceptance for 
$0.4<\xi<0.1$ and $|t|<1\rm{GeV}^2$ at $\sqrt{\rm{s}}=1800$\,GeV and
$|t|<0.2\rm{GeV}^2$ at $\sqrt{\rm{s}}=630$\,GeV.
From these data, events are selected with two jets of $E_T \ge 7$\,GeV, and 
the momentum fraction of the parton in the pomeron can be measured from

\begin{equation}
\beta = \frac{E_{T}^{jet1}e^{\eta_1} + E_{T}^{jet2}e^{\eta_2}}{\sqrt{s}\xi}. 
\end{equation}

After a correction from pile-up background and detector acceptance, 
the ratio of the data $\beta$-distribution in comparison to a Monte Carlo 
flat gluon structure is shown in Fig.~\ref{cdfbeta}.  Although well-described
at large $\beta$ by a flat structure, there is an excess of events at 
low-$\beta$, implying a softer structure component.  This is consistent with 
MC comparisons to data at D\O.


\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.7\textwidth]{mauritz.7}
\end{center}
\caption[]{The ratio of background subtracted data to Monte Carlo simulation
using a flat gluon Pomeron structure and standard flux.}
\label{cdfbeta}
\end{figure}



\section{Hard Double Pomeron Exchange}

Hard double pomeron exchange is another process to enable better 
understanding of diffraction.  In the Ingelman-Schlein model, both the 
incoming proton and anti-proton can be said to ``emit'' a pomeron and the two 
pomerons interact to produce a massive system.

The data analysis for HDPE is analagous to hard single diffraction, except 
that a rapidity gap or forward proton track is required on one side and the
multiplicity on the opposite side is measured.  
D\O\ triggers at $1800$\,GeV ($630$\,GeV) on two $15$ ($12$) GeV jets and a 
rapidity gap in the L\O\ detector.  Figure~\ref{dpom} shows the opposite 
multiplicity distributions at $1800$\,GeV.  The distributions at $630$\,GeV 
are similar.  A clear peak at low multiplicity is observed in both 
distributions above a flat background in qualitative agreement with 
expectations for an HDPE signal.  Figure~\ref{dpom} also shows the jet $E_T$ 
distribution for events with two gaps, one gap, and an inclusive distribution. 
The jet $E_T$ spectra for jets in both kinds of gap events are observed to be 
similar to the inclusive $p\overline{p}$ scattering.  CDF finds similar 
preliminary results
at $\sqrt{\rm{s}}=1800$\,GeV and measures the rates for hard double pomeron 
exchange to be $\sim 10^{-3}/{\cal A_{HDPE}}$\% where the gap acceptance 
${\cal A_{HDPE}}\sim0.1$ for two jets with $E_T>7$\,GeV and 
$0.04<\xi_{\overline{p}}<0.1$~\cite{Kerstin}.  The kinematic properties of 
HDPE candidates are in agreement with expectations events with very little
radiation.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.5\textwidth]{mauritz.8}
\end{center}
\caption[]{The multiplicity at $1800$\,GeV after requiring a rapidity gap on 
the opposite side.  The peak in the low multiplicity bins shows a clear 
double gap 
signal.  The bottom figure is the corresponding jet $E_T$ distribution for the
double gap ({\it circles}), one gap ({\it dotted}), and an inclusive jet 
({\it solid})
samples.}
\label{dpom}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Hard Color Singlet Exchange}

Both experiments have also studied events with a central rapidity gap between 
jets~\cite{d0gap2,d0gap1,cdfgap1,d0gap3,cdfgap2}.  This topology could be due 
to very large momentum transfer pomeron exchange (a class 
of double diffractive events), with $|t|>>100$\,GeV$^2$ compared to the 
previously mentioned processes which typically have $|t|\simeq0$\,$\rm{GeV}^2$.  
The fraction of dijet events with a central rapidity gap is typically on the order 
of $1$\%.  D\O\ observes an increase in the gap fraction with 
transverse energy and pseudorapidity.  Comparisions to Monte Carlo show 
that the data favor a soft color model~\cite{LishG,LishE}, where
the hard interaction is a standard QCD exchange and the rapidity gap is 
generated by a cancellation of the color by soft radiation.  The two gluon 
models for the pomeron do not describe the data well.  Although CDF does not 
observe an increase in the gap fraction with energy and pseudorapidity, the 
measurements are consistent with D\O.

\section{Conclusion}

Hard diffraction has been studied and observed at the TEVATRON in three 
types of processes: single diffraction, double diffraction, and double 
pomeron exchange at both $\sqrt{\rm{s}}=630$ and $1800$\,GeV.  The analyses 
at D\O\ and CDF present consistent and complimentary results. The diffractive 
events are quieter in general than ordinary QCD events and the pomeron 
structure in single diffraction contains a significant soft component.  The 
hard single diffractive and double diffractive gap fractions are 
$\sim\it{O}$($1$\%), which when compared to the HERA results 
$\sim\it{O}$($10$\%), represent a breakdown in the factorization of the
Ingelman-Schlein model. Moreover, there does not appear to be a single scale, 
dependent on $\sqrt{\rm{s}}$, between the $p\overline{p}$ and $ep$ experiments.  



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