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\title{Exclusive Diffraction at CDF}

\author{A. Hamilton\footnote{University of Geneva} (for the CDF Collaboration)}

\maketitle


Diffractive $pp$ collisions are mediated by the exchange of a
colorless object with the quantum numbers of the vacuum, the Pomeron,
which allows the protons to stay intact while still producing some
cental system $X$, $pp \to p + X + p$.  If $X$ is completely
determined, then the interaction is called an {\it exclusive
  diffractive} collision.  Exclusive diffractive processes heavily
favour final states with the quantum number of the vacuum,
\mbox{$J^{PC}=0^{++}$}.

Exclusive diffraction could play a significant role in the observation
(and precision measurement) of the Standard Model (SM) Higgs boson and
other beyond the SM processes at the LHC - if suitable proton tagging
detectors are installed~\cite{cox}.  The advantages of exclusive
processes rely on two things: 1) $M_X$ can be determined by the
momentum of the outgoing protons, 2) $X$ is heavily favoured to have
\mbox{$J^{PC}=0^{++}$}.  The detectors necessary for proton tagging at
ATLAS and CMS are being developed by the FP420
Collaboration~\cite{fp420}

One of the challenges in the development of the exclusive experimental
program at LHC, is the lack of confirmation of the theoretical models
for exclusive diffraction.  Two theoretical models have been proposed
and developed to the point where they can be experimentally tested;
the Durham model~\cite{durham} implemented in the {\sc ExHuME}
MC~\cite{exhume} and the Saclay model~\cite{saclay} implemented in the
{\sc DPEMC} MC~\cite{dpemc}.

The Collider Detector at Fermilab (CDF)~\cite{CDF} is attempting to distinguish
these models using $p\bar{p}$ collisions at
\mbox{$\sqrt{s}=1.96$~TeV}.  CDF has looked at three exclusive
diffractive production processes; $\gamma\gamma$ (through a quark
loop), dijet, and $\chi_c \to J\psi+\gamma$.

In the $\gamma\gamma$ channel three candidate events have been
observed, but the background estimates are not yet complete.  The {\sc
  ExHuME} MC predicts $1^{+3}_{-1}$ events expected in the data sample
examined in the $\gamma\gamma$ analysis.

Because the definition of an {\it exclusive jet} is experimentally
ambiguous, the dijet channel examines a variable called the {\it dijet
  mass fraction}, $R_{jj}\equiv\frac{M_{jj}}{M_{X}}$, where $M_{jj}$
is the mass of the dijet system and $M_{X}$ is the mass reconstructed
using all the observed particles in the detector.  The dijet channel
has extracted an exclusive dijet signal in the high $R_{jj}$ region of
an inclusive diffractive dijet sample.  The signal favors the {\sc
  ExHuME} MC predictions over the {\sc DPEMC} predictions.  By using
the fraction of heavy flavor jets in the inclusive diffractive dijet
sample, the \mbox{$J^{PC}=0^{++}$} selection of exclusive events has
also been observed.

In the $\chi_c$ channel, candidate events have been selected, but
detailed analysis of acceptance, efficiency, and backgrounds are not
yet complete.  Backgrounds from $\gamma$-Pomeron interactions to
$J\psi$ are expected.

In conclusion, the CDF Collaboration is actively searching for
exclusive diffractive processes to distinguish proposed theoretical
models.  The results in the dijet channel favour the Durham model of
exclusive production over the Saclay model.


\begin{thebibliography}{9}

\bibitem{cox}B.Cox, Proceedings of DIS2006 (and refs therin) Archive: hep-ph/0609209 

\bibitem{fp420}www.fp420.com

\bibitem{durham}V. Khoze, A. Martin, M. Ryskin, {\em Eur. Phys. J.} {\bf C 23} 311 (2002), {\bf C 26} 229 (2002), {\bf C 25} 391 (2002), {\bf C 34} 327 (2004). 

\bibitem{exhume}J. Monk and A. Pilkington, {\em Comput.Phys.Commun.} {\bf175} 232 (2006)

\bibitem{saclay}M. Boonekamp, R. Peschanski and C. Royon, Nucl. Phys. B669, 277 (2003).  Erratum-ibid. B676, 493 (2004). E-Print archive: hep-ph/0301244. 

\bibitem{dpemc}M. Boonekamp and T. Kucs, {\em Comput. Phys. commun.}{\bf 167}, 217 (2005).

\bibitem{CDF} D. Acosta {\it et al.}, Phys. Rev. D~{\bf71}, 032001 (2005).



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