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{\Large\bf Colour-Singlet Exchange and Tests of Models of Diffractive DIS\\}
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{\large 
Jennifer C. Williams\\
Wadham College\\
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Department of Physics $\cdot$
Theoretical Physics\\
University of Oxford}
%$\cdot$ Wadham College $\cdot$\\
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%$\cdot$ Department of Physics $\cdot$ 
%Theoretical Physics $\cdot$\\ 
%$\cdot$ University of Oxford $\cdot$}
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{\large Thesis submitted in partial fulfillment of the requirements
for\\ the Degree of Doctor of Philosophy at the\\ University of
Oxford\\
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$\cdot$ March 2000 $\cdot$}
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\begin{abstract}
Diffractive deep-inelastic scattering events observed at the HERA
electron--proton collider are interpreted as an interaction involving
a virtual photon scattering off a colour-singlet state within the
proton. Models which attempt to describe the colour-singlet exchanged
in diffractive interactions range from the purely
phen\-omeno\-lo\-gi\-cal Don\-na\-chie-Land\-shoff form factor
approach to the QCD-moti\-vated gluon-ex\-change models and the
scalar-pom\-eron model. It is important to find ways to test these
models.

In this thesis colour-singlet exchange models of diffractive DIS are
compared with cross section and structure function data from the H1
detector. H1 select diffractive data by requiring there to be a large
angle between the forward proton direction and any other significant
detector activity. This {\em pseudo-rapidity gap} cut extracts
colour-singlet exchange events from the standard DIS data sample. For
a wide range of the parameter space covered by the HERA experiments,
however, the pseudo-rapidity gap cuts restrict the final-state phase
space available for diffractive scattering. One consequence is that
pseudo-rapidity gap cuts can be used to select diffractive events in
which the colour-singlet only couples to off-shell partons. To leading
order in the strong coupling constant, the diffractive final state
consists of a quark--antiquark pair. Higher-order events include
diffractive production of quark--antiquark--gluon states. In the
region where pseudo-rapidity gap cuts restrict the accessible phase
space, the cuts reject low transverse momentum quark--antiquark
diffractive events. Pseudo-rapidity gap data selection cuts also allow
selection of an enhanced 3-jet data sample.

The structure function and transverse momentum distribution data can
be described by either a two-gluon model or by the Donnachie-Landshoff
model, both models requiring a significant contribution from
quark--anti\-quark--gluon diffractive final states to fit the full
kinematic range of the diffractive data.

Further experiments and analyses are suggested to refine the studies
of diffractive DIS and colour-singlet exchange models.

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\it 
I am an idealist. I don't know where I'm going but I'm on the way.
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\hfill{\small Carl Sandburg}

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\it 
\hspace*{6cm}To Mum,

\hspace*{5cm}thanks for everything
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%% ******** Acknowledgments  ******** 
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\chapter*{Acknowledgments} 
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		 {\protect\numberline{Acknowledgments\hspace{-96pt}}} 

Many thanks to Graham Ross for his guidance and supervision and for
many enlightening conversations. Thanks also to John Ellis and to many
people from H1, ZEUS, DESY Theory and the Oxford University
Theoretical Physics and Particle and Nuclear Physics subdepartments
for useful conversations and patient explanations.

I am grateful for financial support from a Commonwealth Scholarship
(ref.NZD5500011), the New Zealand Vice Chancellors Committee for a Sir
William Hartley Scholarship and also for additional support from the
New Zealand Federation of University Women through an NZFUW Post
Graduate Fellowship and a Sadie Balkind Scholarship. Additional travel
assistance supported in part by The British Council DAAD Academic
Research Collaboration Programme grant 757 is also gratefully
acknowledged.

The work in this thesis benefited from visits to various conferences,
workshops and institutes which I visited, all of which extended
excellent hospitality.

Finally, many thanks all my friends and family for their support and
encouragement.  Special thanks to Peter Richardson and Paul Coe for
reading this manuscript, and to Todd Huffman and Is Ridge without whom
I might never have finished this work.

\subsection*{Publications and Original Work}

The large pseudo-rapidity gap structure function analysis of
Chap.\,\ref{chap:sfn} was done in collaboration with Graham Ross and
John Ellis, and is published in\,\cite{Ellis:1998qt}. The extension of
the original Ellis-Ross calculations of phase space
constraints\,\cite{Ellis:1996cg} appears in full detail in
App.\,\ref{app:a}. The full analysis of the implications of
pseudo-rapidity gap cuts and phase space restrictions was presented at
workshops in Hamburg\,\cite{Williams:1998jw} (exchanged-quark
virtuality constraints) and Berlin\,\cite{Williams:1999ze}
(diffractive final-state transverse momentum constraints) and appears
in Sects.\,\ref{sect:psrconstraints} and~\,\ref{sect:azi}.  Cross
section calculations in Chaps.\,\ref{chap:models}
and~\ref{app:csnappendix} are original work except where indicated in
the text. Finally, Chap.\,\ref{chap:tvd} consists of original work
which was published in\,\cite{Williams:1999pe}.


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