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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
                & & & \\
\multicolumn{4}{l}{{\bf
                International Europhysics Conference 
                on High Energy Physics, EPS03},
                July~17-23,~2003,~Aachen} \\
                (Abstract {\bf 110} & Parallel Session & {\bf 5}) & \\
                & & & \\
\multicolumn{4}{l}{{\bf
                XXI International Symposium on  
                Lepton and Photon Interactions, LP03},
                August~11-16,~2003,~Fermilab} \\ 
                & & & \\
                \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf Diffractive photoproduction of high-{\boldmath$p_t$} photons at HERA}\\

  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}

\begin{abstract}
\noindent
The process $\gamma p \rightarrow \gamma Y$ in which the outgoing
photon has transverse momentum $p_{t(\gamma)} > 2$ GeV and there is a
large rapidity gap between the proton dissociative system $Y$ and the
outgoing photon is studied for the first time with the H1 detector at
HERA. Cross sections are measured differentially in the squared
4-momentum transfer at the proton vertex, $t$, and
$x_{_{I\!\!P}}=(E+p_z)_\gamma/2E_p$, where $E_p$ is the incoming
proton energy. All cross sections are consistent with a perturbative
QCD model calculated using the leading logarithmic approximation of
BFKL.

\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}
\begin{figure}
\centering
\begin{picture}(200,80)

\put(10,0){
\epsfig{file=./H1prelim-03-012.fig1.eps,width=.78\textwidth}
\label{PhotonDiag}
}

\end{picture}
\caption{Schematic illustration of the process $\gamma p \rightarrow \gamma Y$.}
\label{fig1}
\end{figure}
\noindent
\label{intro}
\noindent
The process $\gamma p \rightarrow \gamma Y$ (figure \ref{PhotonDiag})
where the final state photon carries a large transverse momentum and
is well seperated from the proton dissociative system $Y$ provides a
uniquely clean probe of the underlying dynamics of the diffractive
process
\cite{Ginzburg:1985tp,Ginzburg:1996vq,Ivanov:1998jw,Evanson:1999zb,Cox:1999kv}.
Requiring that the scattered photon has a large transverse momentum
$p_{t(\gamma)}^2 \simeq -t >> \Lambda^2_{\rm QCD}$ ensures the
applicability of perturbative QCD \cite{Forshaw:1998wn}. Because the
$X$ system consists of only a single photon, an experimental
measurement can be made in an extended pseudorapidity range compared
with high-$t$ diffractive vector meson production
\cite{Chekanov:2002rm,Aktas:2003zi}. This has the important effect of
giving access to the region of large centre of mass energy of the hard
subprocess $\hat s$ (the separation in rapidity between the struck
parton in the proton and the final state photon is $\Delta \eta \simeq
{\rm log} (\hat s / p_{t(\gamma)}^2)$), which is desirable from a
theoretical point of view because perturbative calculations within the
leading logarithmic approximation of BFKL \cite{BFKL1,BFKL2,BFKL3} are
strictly valid only in the asymptotically high $\hat s$ region. The
theoretical calculations are further simplified by the absence of a
vector meson wavefunction: the only non-perturbative part resides
within the proton structure function, which factorises in the usual
way.

\noindent
After a brief description of the H1 detector in section 2, the
selection of the events and the definitions of the measured cross
sections are discussed in section 3. The Monte Carlo models used to
correct the data and to compare to the BFKL predictions, are described
in 4. The results and model comparisons are presented and discussed in
section 5.

\section{The H1 Detector}
\label{detector}
A detailed description of the H1 apparatus can be found
elsewhere~\cite{h1nim}.  The following briefly describes the detector
components relevant to this analysis.

\noindent
A liquid argon (LAr) calorimeter covers the range in polar angle
$4^{\circ} < \theta < 153^{\circ}$ $(3.35 > \eta > -1.43)$ with full
azimuthal coverage \footnote{$\theta$ is measured relative to the
  outgoing proton beam direction, which defines the positive $z$ axis
  and the forward direction. Pseudorapidity is defined as $\eta = -{
    \rm ln (tan} \theta / 2)$.}  . The LAr calorimeter consists of an
electromagnetic section with lead absorbers and a hadronic section
with steel absorbers, with a combined depth between 4.5 and 8
interaction lengths. Both sections are highly segmented in the
transverse and longitudinal directions with about 44000 cells in
total.  The absolute hadronic energy scale is known to $4 \%$ for this
analysis. The polar region $153^{\circ} < \theta < 177.8^{\circ}$
$(-1.43 > \eta > -3.95)$ is covered by the SPACAL \cite{spac}, a
lead-scintillating fibre calorimeter with both electromagnetic and
hadronic sections, with a combined depth of 2 interaction lengths. The
scattered photon energy is measured in this detector to an accuracy of
$1 \%$. The scattered photon angle is measured to an accuracy of $\pm$
1 mrad.

\noindent
Charged particles are detected in the Central Tracking Detector (CTD)
$(1.74 > \eta > -1.74)$ and Backward Silicon Tracker (BST) $(-1.84 >
\eta > -3.35)$. The CTD comprises two large cylindrical jet drift
chambers and two $z$-chambers arranged concentrically around the
beam-line. The BST consists of eight planes of silicon detector discs
with 16 wedge shaped four-inch wafers per disc. The trackers lie
within a solenoidal magnetic field of 1.15T.

\noindent
The luminosity is measured from the reaction $ep \rightarrow ep\gamma
$ with two TlCl/TlBr crystal calorimeters \cite{h1nim}, the electron
and photon taggers, installed in the HERA tunnel. The electron tagger
is located at $z = -33 \ {\rm m}$ from the interaction point in the
direction of the outgoing lepton beam and the photon tagger is at $z =
-103 \ {\rm m}$.
           
\section{Event Selection and Kinematic Reconstruction}
\label{evselect}
\noindent
The data for this analysis were collected with the H1 detector during
the 1999-2000 running period, when HERA collided 27.6 {\rm GeV}
positrons with 920 {\rm GeV} protons. An integrated luminosity of 47.6
${\rm pb}^{-1}$ is used.  

\noindent
Photoproduction events were selected by
detecting the scattered positron in the electron tagger of the
luminosity system.  This restricts the virtuality of the photon to
$Q^{2} < 0.01 $ GeV$^{2}$. The photon-proton centre of mass energy was
restricted to the range $175 < W < 247 \ {\rm GeV}$ to avoid regions
of low electron tagger acceptance.

\noindent
Events were triggered by demanding energy in the electromagnetic
section of the SPACAL calorimeter. One of the triggers used
additionally required an energy deposit in the 33m electron tagger. No
tracking requirements were imposed at the trigger level.  The trigger
efficiency was calculated from data using a combination of independent
triggers and special data-taking runs, and found to be close to 100 \%
for all measured data points.

\noindent
Photons with an energy of at least 8 GeV were identified in the SPACAL
calorimeter by imposing cuts on the electromagnetic cluster radius and
hadronic energy behind the cluster, and demanding that there was no
track associated with the cluster. Additional fiducial cuts were
applied on the position of the cluster in SPACAL to remove regions of
low efficiency. No other energy deposits (above a noise threshold)
were allowed in the SPACAL.

\noindent
Hadronic final state objects were defined using a combination of
tracking and calorimetric information. An algorithm was used which
avoids the double counting of tracks and calorimeter clusters
\cite{fscomb}.

\noindent
Diffractive events were selected by requiring that $\ypom < 0.018$,
where
\begin{equation}
\ypom = \frac{p.(q-X)}{q.p} \simeq \frac{\sum_Y(E-P_z)}{2E_{\gamma}}.
\end{equation}
Here, $p$ and $q$ are the 4-vectors of the incoming proton and photon
respectively and $X$ is the 4-vector of the scattered photon. The
quantity is calculated experimentally by summing the $E-P_z$ of all
hadronic final state objects in the event (i.e. all measured particles
except the scattered electron and high $p_t$ photon), and dividing by
twice the incoming photon energy $E_\gamma$. This method has the
experimental advantage that particles lost in the forward beam pipe do
not contribute much to the numerator. As $\ypom \simeq e^{-\Delta
  \eta}$, this cut ensures that there is a large rapidity gap between
the photon and the proton dissociative system \footnote{To ensure
  efficient background rejection, a minimum rapidity gap of $\Delta
  \eta = 2$ is required between the photon candidate and the edge of
  the proton dissociative system. This requirement is corrected for in
  the final cross sections.}. However, no proton dissociative system
is required to be seen in the detector.

\noindent
In addition to the kinematic variables defined above, the variable
$\xpom$ is defined as
\begin{equation}
\label{xpom}
\xpom = \frac{q.(p-Y)}{q.p} \simeq \frac{(E+P_z)_\gamma}{2E_{p}},
\end{equation}   
where $Y$ is the 4-vector of the proton dissociative system,
$(E+P_z)_\gamma$ is the $E+P_z$ of the photon candidate and $E_{p}$ is
the energy of the incident proton.

\section{Monte Carlo simulations and data corrections}
\label{mc}
The \herwig~6.1 \cite{HERWIG} Monte Carlo event generator was used to
correct the data for detector acceptance and bin migration effects,
and to make model comparisons. \herwig~is the only event generator at
present in which the diffractive high-$t$ photon sub-process has been
implemented. Details can be found in \cite{Cox:1999kv}. The
calculation has been completed within the leading logarithmic
approximation (LLA) of BFKL, and includes contributions from both real
and virtual incoming photons \cite{Ivanov:1998jw,Evanson:1999zb}. At
leading logarithmic accuracy, the strong coupling constant $\alpha_s$
is a fixed parameter. This means that there are two independent free
parameters in the calculation: the value of $\alpha_s$ in the
pre-factor of the cross section (which enters to the fourth power) and
the value of $\alpha_s$ in the pomeron intercept $1 + \omega_0$, where
$\omega_0 = (3\alpha_s/{\pi})4{\rm ln}2$ in the LLA. In all that
follows, we chose these two values of $\alpha_s$ to be
equal ($\alpha_s$ will henceforth be refered to as
$\overline{\alpha_s}$). Note, however, that this is an arbitrary
choice. In particular, to the accuracy of the present calculations
\begin{equation}
\frac{{\rm d}\sigma}{{\rm d}\xpom} \sim \frac{1}{W^2}\left(\frac{1}{\xpom}\right)^{2\omega_0+2},
\end{equation}
so the slope of the $\xpom$ distribution is affected only by the
choice of $\overline{\alpha_s}$ in the pomeron intercept.

\noindent
A \herwig~sample with $\overline{\alpha_s}=0.17$ was passed through a full
simulation of the H1 detector and used to correct the data for
detector acceptance and bin migration effects. This sample was found
to give a good description of the data for all kinematic distributions
considered. In order to investigate the model dependence of the
detector correction procedure, the Monte Carlo sample was reweighted
in $\xpom$, $p_{t({\gamma})}$ and $M_Y$, the mass of the proton
dissociative system. The model dependence of the detector acceptance
corrections was included in the systematic errors as detailed in
section \ref{results}.
  
\noindent
The photon-proton ($\gamma p$) cross sections were extracted by
dividing the $ep$ cross sections by the effective photon flux \cite{WWApprox}
integrated over the $W$ and $Q^2$ range of the measurement.
 
\noindent
The background from inclusive diffractive photoproduction events, in
which a single electromagnetic particle fakes the photon candidate in
the SPACAL or escapes detection, and all other hadronic activity falls
below the SPACAL noise cuts, was simulated using the {\sc PHOJET}
Monte Carlo generator \cite{Bopp:1998rc}.  There was a small
contamination from this background of less than $9 \%$ for all bins. A
bin-by-bin subtraction was made to remove this background.  In order
to investigate the background from high-$t$ diffractive $\omega$
production, where the $\omega$ decays in the $\pi^0\gamma$ channel, a
sample was generated using the {\sc DIFFVM} Monte Carlo \cite{diffvm}.
The contribution was found to be negligible.  Background from standard
DIS events, in which the scattered electron fakes the photon candidate
and an overlapping photoproduction or Bethe-Heitler event produces an
electron in the 33m tagger, was also considered and found to be
negligible.

\section{Results and Discussion}
\label{results}

\noindent
The $\gamma p$ cross section differential in $\xpom$, in the range
$175 < W < 247$~GeV, $p_{t(\gamma)} > 2$ GeV, $\ypom < 0.018$, is
shown in figure \ref{xpcs}. The cross section is defined at the level
of stable hadrons. The inner error bars show the statistical error and
the outer error bars show the statistical and systematic errors added
in quadrature. The largest systematic error is due to the error in the
noise subtracted from the LAr calorimeter.  The total systematic
uncertainty is small compared to the statistical error. Also shown are
the LLA BFKL predictions from the \herwig~Monte Carlo. As described in
section \ref{mc}, the data are sensitive to the choice of the
$\overline{\alpha_s}$ parameter in the prediction in two ways. The first is the
slope of the $\xpom$ distribution which, as equation \ref{xpom} shows,
is related to the BFKL pomeron intercept. The cross section clearly
rises steeply as $\xpom$ becomes small - the classic signature of a
diffractive process. Within the errors, it is difficult to distinguish
between the slopes of the 3 choices of $\overline{\alpha_s}$, although perhaps
$\overline{\alpha_s} = 0.15$ (a pomeron intercept of $\sim 1.4$) leads to too
shallow a rise with $1/\xpom$. The second point of interest is the
normalisation of the cross section predictions. Here, a choice of
$\overline{\alpha_s} = 0.17$ gives too large a cross section. It should be noted
however that there is some normalisation uncertainty within the LLA,
even given a choice of $\overline{\alpha_s}$. It may therefore be possible to fix
both $\overline{\alpha_s}$ values at $0.17$ and obtain a good description of the
data in both normalisation and shape. This is in comparison to the
value $\overline{\alpha_s} = 0.18$ as used for recent H1 measurements
\cite{Aktas:2003zi,Gaps}.

\noindent
The $\gamma p$ cross section differential in the squared 4-momentum
transfer $t$ between proton and the incoming photon (where in
photoproduction $-t \sim p_{t(\gamma)}^2$), in the range $175 < W <
247$~GeV, $0.0001 < \xpom < 0.0007$, $\ypom < 0.018$, is shown in
figure \ref{tcs}. The largest systematic error is due to the error in
the noise subtracted from the LAr calorimeter . The total systematic
uncertainty is small compared to the statistical error. In this case,
the agreement in the shape of the cross section between the
\herwig~predictions and the data is perhaps more questionable, for all
values of $\overline{\alpha_s}$ chosen here.

\noindent
It is worth bearing in mind that there may be important contributions
from higher order effects beyond the LLA, so strong statements about
the agreement with the LLA may be premature.  This said, however, the
fact that the measured cross section exhibits such a dramatic rise
with energy is a striking result, and there is an reasonable overall
agreement with the LLA BFKL predictions.

\section{Conclusions}

The process $\gamma p \rightarrow \gamma Y$ where the photon carries a
large transverse momentum and is well separated from the proton
dissociative system $Y$ has been studied. Cross sections have been
measured differentially in the appropriate energy variable $\xpom$ and
the squared 4-momentum transfer at the proton vertex, $t$. The cross
sections are found to be in reasonable agreement in both normalisation
and shape with the predictions of the leading logarithmic
approximation of BFKL. In particular, the cross section is found to
rise very steeply with decreasing $\xpom$.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgements}
\noindent
We thank Jeff Forshaw for many useful discussions and suggestions. We
are grateful to the HERA machine group whose outstanding efforts have
made and continue to make this experiment possible.  We thank the
engineers and technicians for their work in constructing and now
maintaining the H1 detector, our funding agencies for financial
support, the DESY technical staff for continual assistance, and the
DESY directorate for the hospitality which they extend to the non DESY
members of the collaboration.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}

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\end{thebibliography}


\begin{figure}
\centering
\begin{picture}(200,150)

\put(-12,130){\epsfig{file=./H1prelim-03-012.fig2.eps,width=.78\textwidth,angle=270}}

\end{picture}
\caption{The $\gamma p$ cross section differential in $\xpom$. The inner error bars show the statistical error and the outer error bars show the statistical and  systematic errors added in quadrature. The dotted line shows the prediction of the leading logarithmic approximation of BFKL as implemented in \herwig, for the choice of fixed $\overline{\alpha_s} = 0.15$ in the prefactor and pomeron intercept, as described in the text. The dashed line and solid line show the same calculation, for $\overline{\alpha_s} = 0.16$ and $\overline{\alpha_s} = 0.17$ respectively.}
\label{xpcs}
\end{figure}

\begin{figure}
  \centering
\begin{picture}(200,150)

\put(-12,130){\epsfig{file=./H1prelim-03-012.fig3.eps,width=.78\textwidth,angle=270}}

\end{picture}
\caption{The $\gamma p$ cross section differential in the squared 4-momentum transfer $t$ at the proton vertex. The inner error bars show the statistical error and the outer error bars show the statistical and  systematic errors added in quadrature. The dotted line shows the prediction of the leading logarithmic approximation of BFKL as implemented in \herwig, for the choice of fixed $\overline{\alpha_s} = 0.15$ in the prefactor and pomeron intercept, as described in the text. The dashed line and solid line show the same calculation, for $\overline{\alpha_s} = 0.16$ and $\overline{\alpha_s} = 0.17$ respectively.}
\label{tcs}
\end{figure}


\end{document}

