%================================================================
% LaTeX file with preferred layout for the contributed papers to
% the ICHEP Conference 98 in Vancouver
% process with:  latex hep98.tex
%                dvips -D600 hep98
%================================================================
\documentclass[12pt]{article}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{hhline}
\usepackage{amssymb}
%\usepackage{times}

\newcommand{\odd}{{\textit{\textsf{I}}\hspace{-0.3em} O}}

\newcommand{\txtodd}{{\textit{\textsf{I}}\hspace{-0.38em} O}}
\newcommand{\txtpom}{{I\hspace{-0.31em}P}}


\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}
%\newcommand{\odd}{\mathbb{O}}
\newcommand{\Odd}{O\hspace{-0.91em}O\hspace{+0.09em}}%\hspace{-0.05em}\odd}
%\newcommand{\pom}{{I\hspace{-0.28em}P}}
\newcommand{\pom}{{I\hspace{-0.23em}P}}
\newcommand{\regge}[1]{{I\hspace{-0.10cm}#1}}
\newlength{\dinwidth}
\newlength{\dinmargin}
\setlength{\dinwidth}{21.0cm}
\textheight23.5cm \textwidth16.0cm
\setlength{\dinmargin}{\dinwidth}
\setlength{\unitlength}{1mm}
\addtolength{\dinmargin}{-\textwidth}
\setlength{\dinmargin}{0.5\dinmargin}
\oddsidemargin -1.0in
\addtolength{\oddsidemargin}{\dinmargin}
\setlength{\evensidemargin}{\oddsidemargin}
\setlength{\marginparwidth}{0.9\dinmargin}
\marginparsep 8pt \marginparpush 5pt
\topmargin -42pt
\headheight 12pt
\headsep 30pt \footskip 24pt
\parskip 3mm plus 2mm minus 2mm

%===============================title page=============================

% Some useful tex commands
%
\newcommand{\GeV}{\rm GeV}
\newcommand{\TeV}{\rm TeV}
\newcommand{\pb}{\rm pb}
\newcommand{\cm}{\rm cm}
\newcommand{\hdick}{\noalign{\hrule height1.4pt}}

\begin{document}

\pagestyle{empty}

\begin{titlepage}

\noindent
\begin{center}
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                31st International Conference 
                on High Energy Physics, ICHEP02},
                July~24,~2002,~Amsterdam} \\
                 & Abstract:        & {\bf 997}    &\\
                 & Parallel Session & {\bf 6}   &\\ \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 
     Investigation of Pomeron- and Odderon Induced\\  
     Photoproduction of Mesons Decaying to Pure\\ Multiphoton Final States 
     at HERA\\}

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

\begin{abstract}

\noindent
%Quasi-elastic photoproduction of pseudoscalar, vector-, axial vector-,
%and tensor - mesons is thought to be mediated by either Pomeron or
%Odderon $t$-channel exchange. Considering only meson decays to net
%multiphoton final states, one classifies these simply according to their
%$C$ - parity eigenvalues: Vector- and axial vector - mesons, with an odd
%number of final state photons, carry odd $C$ - parity, while pseudoscalar
%and tensor mesons, with an even number of final state photons, carry even
%$C$ - parity. The $C$ - parity of the meson determines its production
%mechanism via either Pomeron (even $C$ - parity) or Odderon 
%(odd $C$ - parity)
%exchange between the proton and the final state meson. 
This paper reports on cross section measurements made at HERA
for the reactions $\gamma p \rightarrow \omega p$ and $\gamma p \rightarrow
\omega \pi^0 X$, and on
searches for the reactions $\gamma p \rightarrow \pi^0 N^*$, $\gamma p
\rightarrow f_2(1270) X$, and $\gamma p \rightarrow a_2^0(1320) X$, 
where $N^{\ast}$ denotes an excited nucleon state. The
average photon - proton centre-of-mass energy at HERA were 
$\langle W \rangle$ = 200 GeV and 210 GeV. 
Cross sections for the Pomeron - mediated reactions 
were determined in agreement
with previous measurements and theoretical expectations. Processes 
mediated by Odderon - photon fusion could not be observed; upper limits
on cross sections are below predictions from a non-perturbative 
QCD model.
 
\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}
The Pomeranchuk trajectory (``Pomeron'', $\txtpom$)
was introduced, in the framework of Regge
theory, in order to explain the high energy behaviour of hadron-hadron
scattering. It was named after I. Ya. Pomeranchuk whose famous conjecture
(``Pomeranchuk Theorem'' \cite{pom}) states that, in the limit of very large 
energies, the difference between particle-particle and particle-antiparticle 
total cross sections vanishes.

The Pomeranchuk theorem might, however, be violated by means of 
an additional
``odd under crossing'' trajectory which contributes with different signs
to particle-particle and particle-antiparticle total cross sections,
and thus leads to a finite difference in these cross sections at high 
energies \cite{nico}.
%The effect of this trajectory which 
%is named ``Odderon'' \cite{odd} in 
%analogy to the ``Pomeron'' has not yet been observed by experiment.
No effects of this trajectory named ``Odderon'' ($\txtodd$) 
have been experimentally observed so far. The
Pomeron and the Odderon are believed to be close relatives inasmuch as
both trajectories are given the same intercept (close to one) and the
same slope. In short,
the soft (non-perturbative) Odderon is introduced in elastic
hadron-hadron scattering as the $C=P=-1$ partner of the Pomeron.
Fig.~\ref{fig:nano01} shows a generic graph which describes 
photon - Pomeron and photon - Odderon induced exclusive processes.


The HERA electron beam acts as an intense source of quasi-real photons.
The interactions of these with the proton beam provide a unique
opportunity to study the photoproduction of mesons at very high energy.
Vector meson production, mediated by Pomeron exchange, has been 
extensively investigated. Pseudoscalar or tensor mesons cannot be
produced via Pomeron exchange, but require the Odderon
%HERA, with its electron beam as an intense source of very high energy
%quasi-real photons, opens a new stage for both Pomeron and Odderon
%dominated processes. Classical diffractive reactions such as vector meson 
%photoproduction are confronted with a class of processes which, if
%observed, carry the clear signature of Odderon contribution: Quasi-elastic
%production of pseudoscalar or tensor mesons cannot be mediated by
%Pomeron exchange but needs the Odderon 
with its ($C = - 1$) - assignment.
Thus, HERA offers the possibility to simultaneously investigate Pomeron-
and Odderon induced processes, both of which we will call ``diffractive''
because of the similarity of the trajectories, and the lack of colour-
or isospin exchange in these reactions. 
%In short,
%the soft (non-perturbative) Odderon $\txtodd$ is introduced in elastic
%hadron-hadron scattering as the $C=P=-1$ partner of the Pomeron
%$\txtpom$. Fig. \ref{fig:nano01} shows a generic graph which describes 
%photon - Pomeron and photon - Odderon induced exclusive processes.

This paper reports on cross section measurements
for the reactions $\gamma p \rightarrow \omega p$ and $\gamma p \rightarrow
\omega \pi^0 X$, and on
searches for the reactions $\gamma p \rightarrow \pi^0 N^*$, $\gamma p
\rightarrow f_2(1270) X$, and $\gamma p \rightarrow a_2^0(1320) X$. 
$N^*$ denotes an ($I = 1/2$) - nucleonic state. The
former two processes are mediated by Pomeron exchange and have been 
observed before \cite{before}, the latter three are believed to proceed
via photon - Odderon fusion and have not been observed so far. 

A common feature of all the above reactions is that the mesons produced 
are reconsructed from their decays to pure photon final states with the
help of the H1 backward calorimeters: The neutral 
pion decays into two photons with a branching ratio (BR) of 98.8 \%, the
$\omega$ meson decays into $\pi^0 \gamma$ with a BR of 8.5 \%, the 
$f_2(1270)$ decays into $\pi$ $\pi$ with a BR of 84.7 \%, and hence
into $\pi^0 \pi^0$ with a BR of 84.7~\%/3 = 28.2 \%. 
the $a_2^0(1320)$ decays into $\pi^0 \eta$ with a BR of 14.5 \%, and 
the $\eta$ meson decays into two photons with a BR of 39.3 \%
\cite{PDG}.
A possible source for an exclusive $\omega \pi^0$ final state is the
$b_1(1235)$ which decays dominantly into these particles.
Considering only meson decays to net
multiphoton final states, one classifies these simply according to their
$C$ - parity eigenvalues: Vector- and axial vector - mesons, with an odd
number of final state photons, carry odd $C$ - parity, while pseudoscalar
and tensor mesons, with an even number of final state photons, carry even
$C$ - parity. The $C$ - parity of the meson determines its production
mechanism via either Pomeron (even $C$ - parity) or Odderon (odd $C$ - parity)
exchange between the proton and the final state meson. 

Total cross sections have been measured with good precision up to
high energies, and their behaviour as a function of energy can be 
described well by phenomenological models such as that of Donnachie  
and Landshoff \cite{DoLa} or Cudell \cite{Cudell}. These were
extended to describe
elastic vector meson production by Schuler and
Sj\"ostrand \cite{SS90} and were used here to parametrize the cross 
section for $\gamma p \rightarrow \omega~p$.

For Odderon induced processes, there exist some predictions which
have to be confronted with experiment \cite{ber, a2Do}. The non -
observation of Odderon contributions in proton - proton and proton -
%antiproton reactions \cite{nooddpro} is, in these models, explained 
antiproton reactions is, in these models, explained using
a possible quark - diquark structure of the proton which leads to 
a suppression of the proton - Odderon coupling due to parity arguments.

For quantitative predictions a model in the framework 
of non-perturbative QCD, the
Stochastic Vacuum Model (SVM) \cite{dos}, is used and applied to 
high energy scattering by functional methods \cite{nac} in which the
proton is treated as a quark-diquark system in transverse space.
At HERA, a sizeable Odderon contribution to single
pseudoscalar or tensor meson photoproduction is expected
if simultaneously the 
proton is excited into an ($I = 1/2$) -- nucleonic state with 
negative parity.

%The
%production of an isobar, verified through the detection of a high energy
%``leading'' neutron, is an explicit requirement which was 
%experimentally imposed only on
%the reaction $\gamma p \rightarrow \pi^0 N^{\ast}$. 

%In the case of the tensor
%mesons, no experimental distinction between elastic and proton -
%dissociative production was made in the analysis presented here. 
%The same is true for ($\omega \pi^0$) 
%production. In the case of $\omega$ production a condition designed
%to suppress inelastic reactions was imposed.

SVM Model calculations were performed at a photon - proton centre-of-mass
energy $W = 20$ GeV \cite{ber, a2Do, dos, nac}. 
For the extrapolation to HERA energies, the
intercept of the Odderon trajectory was assumed as $\alpha(t=0) = 1$
which leads to an energy independent cross section.
 

\section{Event Selection}

All mesons investigated in these analyses have decay channels to pure
photonic final states, either through intermediate $\pi^0$
or $\eta$ mesons or directly: 
The number of final state photons varies between two 
and five. Since in diffractive photoproduction the quasi-elastically
produced mesons take over the incoming photon's energy and momentum,
the decay products are detected in the ``backward'' region of the detector,
i.e. in the electron beam direction.
At H1 (for a general description see \cite{H1}), 
part of this region is covered by two
electromagnetic calorimeters, the SpaCal \cite{spa} 
(``Spaghetti Calorimeter''
at $z\approx -155$ cm) and the VLQ \cite{vlq} (``Very Low 
%$\text{Q}^{2}$ calorimeter'' at $z\approx -302$ cm) 
%(see Fig. \ref{fig:sign}).
$\text{Q}^{2}$ calorimeter'' at $z\approx -302$ cm). 
Here $z$ represents the distance from the nominal interaction point.
%(see Fig. \ref{fig:nano01})
%The two calorimeters cover together,
%expressed in terms of $Q^2$ for scattered DIS electrons, 
%the phase space region $0.03 < Q^2 < 100~\text{GeV}^2$.


The analyses presented here are based on data taken in 1996 where
electrons of 27.56 GeV were collided
with protons of 820 GeV, and on data taken in 1999 and 2000
where electrons (respectively positrons) were collided with a
proton beam of 920 GeV.
The data correspond to integrated luminosities of $4.5~\text{pb}^{-1}$ 
and $30.6~\text{pb}^{-1}$, respectively. 
Photoproduction
events with $Q^2<0.01\;\text{GeV}^{2}$ and $0.3<y<0.7$
($Q^2=4EE'\cos^2{\theta/2}$, $y=1-E'/E$, where $E$ and $E'$ are the
energies of the incoming and scattered electron, respectively,
and $\theta$ is the scattering angle measured w.r.t. the proton
beam direction) were
selected by measuring the almost undeflected electron in a low-angle
electron detector 33 m downstream from the interaction point.

The analysis of the reaction $\gamma p \rightarrow \pi^0~N^{\ast}$ 
differs from the others by its trigger conditions: In that, 
in addition to the
general photoproduction condition, an energy deposit of at least 6 GeV
in the VLQ and a hit in the Forward
Neutron Calorimeter (FNC) with an energy deposition of more than
100 GeV were required. The last requirement ensures the presence of an 
intermediate excited nucleonic state $N^{\ast}$. 
(Only $N^{\ast}$'s are believed to lead to a considerable
contribution since Regge exchange decreases strongly at high energies,
and the production of $\Delta$ baryons and the
transformation of a proton into a neutron - without excitation - require 
isospin and charge exchange, respectively.)
Neutral pions in this reaction are reconstructed from two photons where
a) either both are found in the VLQ, or b) one photon is
found in the SpaCal, and the second in the VLQ.
A photon in the SpaCal or the VLQ is 
experimentally defined as a cluster with an energy
larger than 90 MeV (100 MeV for the 1996 data)
or 2 GeV, respectively. To ensure exclusive production 
of the final state mesons, no further cluster in the
above calorimeters or any charged particle in the track detectors,
from which an interaction vertex can be reconstructed, is allowed. 
As there are no charged particles in the events
the position of the vertex cannot be measured, and the
kinematics is reconstructed using the nominal interaction vertex.
A more detailed description of the investigation of the reaction
$\gamma p \rightarrow \pi^0~N^{\ast}$ can be found in \cite{buda01}.
The $\pi^0$ data sample has been collected during the 1999 - 2000
run period with a proton beam energy of 920 GeV. This corresponds to
an average $\gamma p$ centre-of-mass energy $\langle W \rangle$ = 
210 GeV. All other analyses were carried out at a lower proton beam
energy leading to $\langle W \rangle$ = 200 GeV.


In the case of the tensor
mesons, no experimental distinction between elastic and proton -
dissociative production was made in the analysis presented here. 
The same is true for ($\omega \pi^0$) 
production. In the case of $\omega$ production a condition designed
to suppress inelastic reactions was imposed, namely cuts on detectors
in the forward region were applied to reject events where the proton
breaks up. This cut rejects events where the mass of the forward 
baryonic system exceeds 1.6 GeV/c$^2$. The remaining background
of inelastic events amounts to about 10 \%.

For all but the $\pi^0$ analysis,
the trigger contained, in addition to the 
general photoproduction tagging
condition, requirements on the energy registered in the electromagnetic
SpaCal. Thus, at least one SpaCal energy cluster (i.e. an isolated energy
deposit, separated from neighbouring energy depositions by the
clustering algorithm) had to exceed 2 GeV and at the same time have 
%a radial distance to the beam axis of more than approximately 16 cm. 
a radial distance to the beam axis of more than 16 cm. 
Photon candidates were reconstructed from SpaCal clusters only.

The ability to reconstruct neutral pions in the SpaCal was shown
in a study on inclusive $\pi^0$ photoproduction \cite{Martin}.
In order to demonstrate the ability to reconstruct $\pi^{0}$s with 
the help of the VLQ, 
%vertex, Fig. \ref{fig:incl} shows the two-photon invariant mass for events
Fig.~\ref{fig:nano02} shows the two-photon invariant mass for events
with exactly one cluster in the SpaCal and one in the VLQ. Using the
nominal interaction vertex, a clear $\pi^0$ signal is observed.

The exclusiveness of the reactions studied was ensured with the help
of the variable $\Sigma$ which is the sum of all $(E - P_{z})$ of 
all particles in the electromagnetic calorimeters in the backward
region, and takes a value equal to twice the electron beam energy
if no particles escape undetected in the backward hemisphere. A cut of
$49\;\text{GeV} < \Sigma < 60\;\text{GeV}$
serves to reject non-exclusive or radiative events.
For the 1996 data, the lower limit was 50 GeV.


%$\sum_{i}(E-P_{z})_{i}$, 
%where $i$ runs over all particles in the final state,
%takes a value equal to twice the electron beam energy
%if no particles escape undetected in the backward hemisphere. A cut of
%$49\;\text{GeV}<\sum_{i=e',\text{all~photons}}(E-P_{z})_{i}<
%60\;\text{GeV}$ serves to reject non-exclusive or radiative events.
%For the 1996 data, the lower limit was 50 GeV.

The remaining selection criteria simply reflect the topology of
the events under study: The number of photon candidates reconstructed
had to equal the number of final state photons expected, and for 
final states with $\pi^0$'s and $\eta$'s, appropriate mass restrictions
had to be obeyed.


\section{Monte Carlo Models}
The simulation programs used are PYTHIA \cite{pyt} and
DIFFVM \cite{dif}. The original DIFFVM event generator produces
exclusive vector mesons by Pomeron exchange based on the Vector Meson
Dominance model. This generator has been extended to 
include Odderon exchange according to the SVM
with a single $\pi^{0}$, $f_2(1270)$, or
$a_2^0(1320)$ in the final state
with $t$-distributions for the signal processes as calculated in 
\cite{ber, a2Do}.
The extended event generator is called OPIUM\footnote{An acronym for 
``Odderon and Pomeron Induced Unified Meson maker''}~\cite{opi}.

PYTHIA is a universal tool for describing $\gamma p$ interactions. 
It is used to simulate the non-resonant $\omega \pi^0$ production
(there is most likely an additional 
contribution from resonant $\omega \pi^0$ production
via production of the $b_1(1235)$ meson which decays dominantly into
these particles \cite{PDG})
and the background contributing to exclusive meson production. The
purely diffractive events (either Pomeron- or Odderon- induced) are
modelled with the help of DIFFVM and OPIUM. The contribution from
resonant $b_1(1235) \rightarrow \omega \pi^0$ was generated 
with the help of OPIUM where
the cross section was adjusted to fit the signal observed in 
this analysis. The generator PYTHIA does not provide resonant $b_1$
production and decay. Due to the large cross section of this channel
the $b_1$ represents a substantial background for the investigation
of lower photon multiplicities if one or more photons escape
detection. The final state $\omega \pi^0$
represents, through its feed-down into the four photon sample,
a background source for the investigation of $f_2(1270)$ and
$a_2^0(1320)$ production.

Following advice by the author of PYTHIA \cite{pyt}, a modified
version of this program is used for the background description. 
%referred to as ``PYTHIA-mod''. 
Here, certain processes are excluded
in which isospin conservation is not explicitly taken care of. 
%It is
%expected that background kinematical distributions will lie between 
%the predictions of these two versions of the model.

%The channel $\gamma p \rightarrow \pi^0~N^{\ast}$ is sensitive to background
%from exclusive $\rho^0$ and $\omega$ photoproduction where the vector
%mesons decay into $\pi^{0}~\gamma$. 

Contributions from Regge
exchange ($\omega$-trajectory) or $\gamma\gamma$ fusion (``Primakoff 
effect''), leading to elastic single pseudoscalar and tensor
meson production, are negligible. 
A remaining background is low multiplicity events
which can be modelled with the PYTHIA generator. 


\section{Results}

In this section we discuss our results in the order dictated by the
number of final state photons. The number of photons
defines the $C$ - parity of the meson produced, and thus the $C$ - parity
of the assumed exchange trajectory: an even number of photons is
correlated with Odderon, an odd number with Pomeron exchange.

We first present our findings on searches for Odderon contributions
to the measurement of the reaction $\gamma p \rightarrow \pi^0 N^{\ast}$. 
Next, we present cross section measurements for
$\gamma p \rightarrow \omega p$, followed by the search for $f_2(1270)$
and $a_2^0(1320)$ production by photon - Odderon fusion. Finally, we
present the cross section measurement for the reaction
$\gamma p \rightarrow \omega \pi^0 X$.

Since the reaction $\gamma p \rightarrow \pi^0 N^{\ast}$ has been
discussed in \cite{buda01}, we will repeat here only the
salient features of the analysis:

\noindent 
Figure~\ref{fig:nano03} shows the final two-photon mass distribution, with 
all selection criteria applied. The two dotted vertical lines
indicate the two photon mass range within which
$\pi^0$ candidates were accepted. The expectation from PYTHIA is
four events. The Odderon-photon fusion \cite{ber}, as modelled in 
OPIUM, predicts 110 events; 13 events are observed in the data.

Fig.~\ref{fig:nano04} shows the differential cross section
$d\sigma/d|t|$ for the reaction $\gamma p \to (\gamma\gamma) 
N^{\ast}$, where the invariant mass of the two photons lies in the
pion mass region defined in Fig.~\ref{fig:nano03}. The squared 
four-momentum transfer at the nucleon vertex is approximated as
$|t| = p_\perp^2(\pi^0)$.
In addition, the
background expectation and the SVM signal prediction are shown. 
Integrating the differential cross section in the accessible $|t|$ - range,
i.e. for $0.02 < |t| < 0.3$ GeV$^2$, and applying the prescriptions
of \cite{Cou1} and \cite{Cou2}, one arrives at an upper limit of
\begin{equation}
  \label{eq:limit}
%  \sigma_{\text{acc},\gamma p \to \pi^{0}N^{*}}(\gamma\txtodd\;\text{-fusion}) <
%  39\; \text{nb \hspace{1.5cm} (95~\%~CL)}.
\sigma_{\text{acc}}(\gamma p\stackrel{\odd}{\to} \pi^0 N^*) < 39\,\text{nb}
\hspace{1.5cm}(95~\%~\text{CL})
\end{equation}
This has again to be compared with the predicted value of 200 nb at
HERA energies, which is clearly incompatible with observation.

The reaction $\gamma p \rightarrow \omega p$ was investigated in the
exclusive three photon sample, i.e. the $\omega$ meson was reconstructed
from its decay to $\pi^0 \gamma$. Fig.~\ref{fig:nano05} shows the 
two-photon invariant mass distribution, with a clear $\pi^0$ signal. Also
shown are the expectations from the signal (DIFFVM) and background
Monte Carlo simulations (PYTHIA and feed-down from $b_1$ and non-resonant
$\omega \pi^0$ production). 
>From this distribution a $\pi^0$
mass window is derived which is defined by 
$|m_{\gamma \gamma} - m_{\pi^0,\text{PDG}}| < 40$ MeV/c$^2$.

The three photon invariant mass distribution, where one photon pair
is required to have its invariant mass in the $\pi^0$ mass window, 
is displayed in Fig.~\ref{fig:nano06} and shows the $\omega$ signal. 
In addition, the signal and background Monte Carlo expectations 
are shown. 

%For the fit, the mass 
%range of the $\omega$ was defined by $0.65 < m_{\pi^0 \gamma} < 1.0$ GeV.
%
%The partial cross section for $\gamma p \rightarrow \omega p$,
%integrated over the accessible $|t|$ range, amounts to
%$$ \sigma(\gamma p \rightarrow \omega p) = 
%   (1.25 \pm 0.17~(\text{stat}) \pm 0.22~(\text{syst}))~\mu\text{b}.$$
The cross section was determined by fitting the line shape and
subtracting the non - $\omega$ background statistically.
The background was determined with the PYTHIA and OPIUM Monte Carlo
programs. The latter is used to desribe the feed-down from $b_1$
decays into five photons where two photons have not been detected.
In addition, a remaining background of 10 \% inelastic
$\omega$ production was removed. The cross section then
amounts to 
$$ \sigma(\gamma p \rightarrow \omega p) = 
(1.25 \pm 0.17~(\text{stat}) \pm 0.22~(\text{syst}))~\mu\text{b}.$$  
   
The four - momentum transfer squared ($|t|$-) distribution for the
reaction $\gamma p \rightarrow \omega p$ at the proton vertex (with
the approximation $|t| = p_\perp^2(\omega)$) is shown in 
Fig.~\ref{fig:nano07}. Events subjected to the fit were chosen to be
$\omega$ - candidates , i.e. they had to fulfil the requirement $0.65
< m_{\pi^0 \gamma} < 1.00$ GeV/c$^2$.  A fit of an exponential of the
form $dN/d|t| = A~\exp{(-b|t|)}$ to the data in the range $|t| < 0.4$
GeV$^2$, gives a slope of 
$$
b = (10.5 \pm 1.2~(\text{stat}) \pm 0.5~(\text{syst}))~\text{GeV}^{-2}
$$
which is in the range typical for elastic vector meson photoproduction
at this energy.
Fig.~\ref{fig:nano08} shows the slope values measured 
for elastic diffractive $\omega$ photoproduction reactions,
and Fig.~\ref{fig:nano09} shows the partial cross sections 
for diffractive photoproduction cross sections, as a function
of the photon - proton centre-of-mass energy $W$. One observes that the
values presented in this paper fit excellently in the general pattern.


The exclusive four photon sample was searched for evidence of Odderon
exchange leading to $f_2(1270)$ and $a_2^0(1320)$ production. 
Fig.~\ref{fig:nano10} shows the invariant mass of all $\gamma \gamma$ 
pairs, together with
the sum of the
signal Monte Carlo predictions for $f_2(1270)$ and $a_2^0(1320)$ and
the background Monte Carlo expectation (PYTHIA and feed-down from
$b_1$ and non-resonant $\omega \pi^0$ production). 
A $\pi^0$ signal is visible but weaker than expected from the SVM. 
Fig.~\ref{fig:nano11} shows an extended two photon invariant mass
distribution, this time the $\gamma \gamma$ system ``recoiling'' against 
the $\pi^0$ which is defined by an invariant mass cut as above. 
According to the Odderon exchange
models, in this plot, a second $\pi^0$
signal is expected in the case of $f_2(1270)$, and an $\eta$ signal
in the case of $a_2^0(1320)$ production. No $\eta$ and less
$\pi^0$'s are seen than expected in OPIUM. 
The expected signals are also shown in the figure.
The data distribution is compatible with the bare background
expectation. The same conclusion can be drawn from
the $\pi^0$ - $\eta$ invariant mass distribution shown in 
Fig.~\ref{fig:nano12} where the $\pi^0$ mass range
definition is as above, and the
$\eta$ region is defined by $|m_{\gamma \gamma} - m_{\eta,\text{PDG}}| 
< 100$ MeV/c$^2$. The signal prediction from the SVM is added. 
Again, the data
distribution is compatible with the background expectation.
Finally, the two $\pi^0$ invariant mass distribution is presented in
Fig.~\ref{fig:nano13}. The data is shown together with the background
Monte Carlo expectation and the $f_2(1270)$ SVM prediction.

Converting the findings of the exclusive four photon analysis into
numbers, one arrives, applying again the prescriptions
of \cite{Cou1} and \cite{Cou2},  
at the following limit for $a_2^0(1320)$ production:
%$$\sigma_{\gamma p \to a_2 X}(\gamma\txtodd\;\text{-fusion}) <
%  96\; \text{nb \hspace{1.5cm} (95~\%~CL)},  $$
$$  
\sigma(\gamma p\stackrel{\odd}{\to} a_2 X) < 96\,\text{nb}
\hspace{1.5cm}(95~\%~\text{CL})
$$  
to be compared with the SVM prediction for
%$\sigma_{\gamma p \to a_2 N^{\ast}}(\gamma\txtodd\;\text{-fusion}) =
%190~\text{nb}$.
$\sigma(\gamma p\stackrel{\odd}{\to} a_2 N^*) = 190\,\text{nb}.$
The corresponding numbers for $f_2(1270)$ production 
%$$\sigma_{\gamma p \to f_2 X}(\gamma\txtodd\;\text{-fusion}) <
%  16\; \text{nb \hspace{1.5cm} (95~\%~CL)}  $$
$$  
\sigma(\gamma p\stackrel{\odd}{\to} f_2 X) < 16\,\text{nb}
\hspace{1.5cm}(95~\%~\text{CL})
$$  
are to be compared with the model prediction
%$\sigma(\gamma p \to f_2 N^{\ast}}(\gamma\txtodd\;\text{-fusion}) =
%21~\text{nb}$.
$\sigma(\gamma p\stackrel{\odd}{\to} f_2 N^*) = 21\,\text{nb}.$


Finally we discuss the five photon sample.
Fig.~\ref{fig:nano14} shows the invariant mass of all 
ten $\gamma \gamma$ combinations with a clear
$\pi^0$ signal. The data distribution is compared with the sum of the
background expectation (PYTHIA, non-resonant $\omega \pi^0$
production, and contribution from $b_1 \to \omega \pi^0$ where the
$\omega$ decays into $\pi^+ \pi^- \pi^0$)
and the prediction of a signal Monte Carlo for
$b_1(1235)$ production. The $b_1$ decays dominantly to $\omega \pi^0$
and hence can produce purely photonic final states. 
%where the $b_1$ whose dominant decay channel is
%$\omega \pi^0$ decays to purely photonic final states. 
%There is excellent agreement between data and prediction in the shape  
%of the distribution. 
Fig.~\ref{fig:nano15} shows the three
photon invariant mass ``recoiling'' against the $\pi^0$. A clear
$\omega$ peak is observed. For further analysis, the $\omega$ mass range
is defined by $|m_{3\gamma} - 0.76~\text{GeV/c}^2| < 0.15~\text{GeV/c}^2$.
The $\omega$ central mass results from the fit which also served to
derive the $\omega \pi^0$ cross section by determining the number of
$\omega$'s in the sample.
The shape of the $\omega \pi^0$ invariant mass distribution
displayed in Fig.~\ref{fig:nano16} shows very good agreement
with the model prediction. The absolute normalization of the
resonant $b_1$ contribution to the $\omega \pi^0$ final state 
has been taken from the OPIUM generator
which was adjusted to fit the observed data. The non-resonant 
contribution is taken from the PYTHIA prediction. The
conclusion is that there is substantial $\omega \pi^0$ diffractive
photoproduction which might well proceed via 
dominant resonant $b_1(1235)$
production. The corresponding cross section is
$$ \sigma(\gamma p \rightarrow \omega \pi^0 X) = (980 \pm 
200~\text{(stat)} \pm 200~\text{(syst)})~\text{nb}.$$
This has to be compared 
with the sum of the non-resonant prediction by PYTHIA 
$$\sigma_{\text{PYTHIA}}(\gamma p \rightarrow \omega \pi^0 X) = 
  190~\text{nb}$$ 
and a cross section value measured for $b_1$ photoproduction at lower
energies (8 GeV, \cite{before}) which, after extrapolation to HERA energies
reads 
$$\sigma_{extrap}(\gamma p \rightarrow b_1 p) 
   = (660 \pm 250)~\text{nb}.$$
 
The extrapolation followed \cite{Cudell, SS90} in complete analogy to
the ordinary vector mesons with the $\gamma \txtpom V$ coupling
adapted to match the low energy data.
%Fig. \ref{fig:nano15} shows the slope values measured 
%for elastic diffractive $\omega$ photoproduction reactions,
%and Fig. \ref{fig:nano16} shows the partial cross sections 
%for diffractive photoproduction cross sections, as a function
%of the photon - proton centre-of-mass energy $W$. One observes that the
%values presented in this paper fit excellently in the general pattern.


\section{Conclusion}

Our findings provide a rather clear picture. We have observed
Pomeron induced reactions in complete agreement with previous measurements,
expectations, and extrapolations from lower energy experiments, but: 
we see no trace of Odderon induced reactions as predicted by the 
Stochastic Vacuum Model (SVM).

\noindent
Possible explanations include:
\begin{enumerate}
\item 
  The energy dependence of the cross section is different from that 
  assumed. This would imply that the
  Odderon intercept $\alpha_{\odd}(0)$ is considerably smaller than one.
  A value of $\alpha_{\odd}(0)<0.65$ would be compatible with the
  $\pi^0$ cross section limit,
  but this would mean that the object exchanged is not 
  a ``genuine'' Odderon for which $\alpha_{\odd}(0)\approx~1$. 
\item The absence of elastic $\pi^0$ production could be understood
  in that the coupling at the $\gamma\txtodd\pi$-vertex is small due to
  the Goldstone Boson nature of the~$\pi^{0}$ \cite{ona}. 
  This explanation does, however, not hold in the case 
  of the $f_2(1270)$ and the $a_2(1320)$.
\end{enumerate}

%The situation is surely challenging, and a strong gain in insight is 
%desirable. It could come from HERA II data to be traken with a special 
%trigger, in combination with a much higher luminosity. To overcome the
%problem of strongly restricted acceptance, which cannot be solved at
%HERA II, one would have to think of new concepts.

The level of understanding of this sector of nonperturbative QCD is 
still unsatisfactory, and new theoretical ideas are needed. 
%The development of 
%these may be aided by data
%taken during high luminosity HERA II running, which will require
%dedicated triggers. If the restricted acceptance for these events of the
%HERA detectors remains a problem, new experimental techniques 
%will have to be sought.



\section*{Acknowledgements}
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 constructing and maintaining the H1
detector, our funding agencies for financial support, the DESY technical
staff for continuous assistance, and the DESY Directorate for the
hospitality which they extend to the non-DESY members of the collaboration.
For many stimulating and helpful discussions, the authors wish to thank
E. R. Berger, H. G. Dosch, O. Nachtmann, and T. Sj\"ostrand.



\begin{thebibliography}{99}

%\bibitem{nico} L. Lukaszuk and B. Nicolescu, \Journal{\NCL}{8}{405}{1973}

\bibitem{pom}  I. Ya. Pomeranchuk, Zh. Eksp. Teor. Fiz. {\bf 34}
               (1958) 725, and Sov. Phys. JETP {\bf 7} (1958) 499.
               
\bibitem{nico}  L. Lukaszuk and B. Nicolescu,
                Lett. Nuov. Cim. {\bf 8} (1973) 405. 
                
\bibitem{odd}   D. Joynson, E. Leader, B. Nicolescu, C. Lopez,
                Nuov. Cim. {\bf 30A} (1975) 345.
                                
\bibitem{before}  The Omega Photon Collaboration, M. Atkinson et al.,
                  Nucl. Phys. {\bf B243} (1984) 1;
                  ZEUS Collaboration, M. Derrick et al., 
                  Z. Phys. {\bf C73} (1996) 73
                 
\bibitem{PDG}   The Particle Data Group, D. E. Groom et al.,
                Eur. Phys. J. {\bf 15} (2000) 1
                
\bibitem{DoLa}  A. Donnachie and P. V. Landshoff,
                Phys. Lett. {\bf B296} (1992) 227.

%\bibitem{nooddpro}  No Odderon in pp and ppbar -> Quelle!

\bibitem{Cudell}  J. Cudell et al., Phys. Rev. {\bf D61} (2000) 34019

\bibitem{SS90}  G. A. Schuler and T. Sj\"ostrand, 
                Nucl. Phys. {\bf B407} (1993) 539.


\bibitem{ber}  E. R. Berger, A. Donnachie, H. G. Dosch, W. Kilian,
               O. Nachtmann, M. R\"uter, Eur. Phys. J. {\bf C9}
               (1999) 491; 
               E. R. Berger et al., Eur. Phys. J. {\bf C14} (2000) 673.
               
%\bibitem{f2calc}  f2 - calculation

\bibitem{a2Do}  H. G. Dosch, private communication

%\bibitem{dos} H. G. Dosch, Yu. A. Simonov, \Journal{\PLB}{B205}{339}{1988} 
\bibitem{dos}  H. G. Dosch and Yu. A. Simonov,
               Phys. Lett. {\bf B205} (1988) 339.

\bibitem{nac} O. Nachtmann, Ann. Phys. {\bf 209} (1991) 436.

\bibitem{H1}  H1 Coll., I. Abt et al., Nucl. Instrum. Methods
              {\bf A386} (1997) 310 and 348.

\bibitem{spa}     H1 SpaCal Group, T. Nicholls et al., 
                  Nucl. Instrum. Methods {\bf A374} (1996) 149;
\newline
                  H1 SpaCal Group, R.D. Appuhn et al.,
                  Nucl. Instrum. Methods {\bf A382} (1996) 395;
\newline
                  H1 SpaCal Group, R.D. Appuhn et al., 
                  Nucl. Instrum. Methods {\bf A386} (1997) 397. 

\bibitem{vlq}     M. Keller et al., Nucl. Instr. Methods {\bf A409}
                  (1998) 604. 
                  
\bibitem{buda01}  H1 Collaboration, ``Search for Odderon Induced
                  Contributions to Exclusive $\pi^0$ Photoproduction
                  at HERA'', to appear in the Proceedings of the
                  9th International Workshop on Deep Inelastic
                  Scattering DIS2001, Bologna, 27 April - 1 May, 2001.
                  
                  
\bibitem{Martin}   C. Adloff et al., H1 - Collaboration, 
                   Eur. Phys. J. {\bf C18} (2000) 29
                   

%\bibitem{pi0buda}  H1 Collaboration, ``Search for Odderon Induced
%                   Contributions to Exclusive $\pi^0$ Photoproduction
%                   at HERA'', submitted to the International
%                   Europhysics Conference on High Energy Physics,
%                   Budapest, Hungary, July 12 - 18, 2001.

\bibitem{pyt}  T. Sj\"ostrand, Comp. Phys. Comm. {\bf 82} (1994) 74;
  private communication (2001). 

\bibitem{dif}  B. List and A. Mastroberardino, ``DIFFVM - A Monte
               Carlo Generator for Diffractive Processes in ep
               Scattering'', available as:\newline
               {\tt http://www.desy.de/$\sim$heramc/mclist.html.}

\bibitem{opi}  W. Kornelis, private communication, Heidelberg (2000).

%\bibitem{PDG}   The Particle Data Group, D. E. Groom et al.,
%                Eur. Phys. J. {\bf 15} (2000) 1

%\bibitem{Sjo}  T. Sj\"ostrand, private communication.

\bibitem{Cou1}  R. D. Cousins and G. J. Feldman, 
                Phys. Rev. {\bf D57} (1998) 3873.

\bibitem{Cou2}  R. D. Cousins and V. L. Highland, 
                Nucl. Instr. Meth. {\bf A320} (1992) 331.
                    
%\bibitem{Braunschw}  M. Braunschweig et al., Phys. Lett. {\bf 26B}
%                     (1968) 405.
                     

\bibitem{ona} O. Nachtmann, private communication, Heidelberg (2001).

\end{thebibliography}


\clearpage
\vspace{3cm}
\


\begin{figure}
  \centerline{
%  \epsfxsize=32pc 
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/feynman.eps}}
  \epsfig{file=H1prelim-01-117.fig1.eps, width=12cm}}
%  \epsfig{file=H1prelim_01_117.fig1.eps, width=12cm}}
  \caption{Generic diagram illustrating photon - Pomeron and photon - Odderon
           induced exclusive processes.
    \label{fig:nano01}}
%  \end{center}
\end{figure}

%--------------------------------------------------------------------
% Two photons / odd:

\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/pi0_inc.eps}} 
  \epsfig{file=H1prelim-01-117.fig2.eps, width=12cm}}
  \caption{Two photon sample:
           Invariant mass spectrum of the two-photon candidates for
           events where one photon is detected in the VLQ and one in the
           SpaCal. In addition, a neutron and the scattered electron 
           are detected. The full line shows the result of a fit of a
           Gaussian plus a fourth order polynomial.
    \label{fig:nano02}}
%  \end{center}
\end{figure}


\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/pi0_2g.eps}}
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/pi0_2g.eps, width=12cm}}  
  \epsfig{file=H1prelim-01-117.fig3.eps, width=12cm}} 
  \caption{Two photon sample: Distribution of two photon invariant
           mass, with either both photons detected in the VLQ,
           or one photon detected in the VLQ and the second
           one in the SpaCal, after all selection cuts.
           Also shown are the model expectation (hatched area)
           and the prediction from the background MC (white histogram). 
           The two vertical lines indicate the mass
           region for $\pi^0$ candidates.
    \label{fig:nano03}}
%  \end{center}
\end{figure}



\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/pi0_tlim.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/pi0_tlim.eps, width=12cm}} 
  \epsfig{file=H1prelim-01-117.fig4.eps, width=12cm}} 
  \caption{Differential cross section for the reaction $\gamma p 
           \rightarrow (\gamma \gamma) N^{\ast}$, with the two photon
           invariant mass inside the $\pi^0$ candidate range (see text).
           Also shown are the background Monte Carlo expectation and
           the SVM signal prediction.
    \label{fig:nano04}}
%  \end{center}
\end{figure}

%--------------------------------------------------------------------
% Three photons:


\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/omega_2g.eps}}
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/omega_2g.eps, width=12cm}}  
  \epsfig{file=H1prelim-01-117.fig5.eps, width=12cm}}  
  \caption{Three photon sample: Two photon invariant mass distribution,
           for data, background Monte Carlo (see text), 
           and model expectation.
    \label{fig:nano05}}
%  \end{center}
\end{figure}




\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/omega_3g.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/omega_3g.eps, width=12cm}} 
  \epsfig{file=H1prelim-01-117.fig6.eps, width=12cm}} 
  \caption{Three photon sample: Three photon invariant mass distribution,
           with one $\gamma \gamma$ invariant mass in the $\pi^0$ mass window,
           for data, background Monte Carlo (see text), and model expectation. 
    \label{fig:nano06}}
%  \end{center}
\end{figure}


\begin{figure}[t]
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/omega_slope.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/omega_slope.eps, width =12cm}}
  \epsfig{file=H1prelim-01-117.fig7.eps, width =12cm}}
  \caption{Three photon sample: Distribution of four - momentum transfer
           squared ($|t|$) at the proton vertex. The full line shows the
           result of a fit of an exponential $|t|$ - distribution to the
           data.
    \label{fig:nano07}}
%  \end{center}
\end{figure}

%----------------------------------------------------------------------
%%% tommy's playing around
\newpage
%Tommy's starting\ldots
\begin{figure}
  \centerline{
%    \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/vm_slopes.eps, width=12cm} }
    \epsfig{file=H1prelim-01-117.fig8.eps, width=12cm} }
  \caption{A compilation of slopes of $|t|$ - distributions for elastic
    $\omega$ photoproduction as a function
    of the photon - proton centre-of-mass energy, from fixed
    target to HERA experiments.           
    \label{fig:nano08}}
\end{figure}

\begin{figure}
  \centerline{
%    \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/vmxs.eps, width=12cm} }
    \epsfig{file=H1prelim-01-117.fig9.eps, width=12cm} }
  \caption{A synopsis of elastic vector meson photoproduction cross
    sections as a function of the photon - proton centre-of-mass
    energy, from fixed target to HERA experiments. 
    \label{fig:nano09}}
\end{figure}
%Tommy's finished
\newpage
%--------------------------------------------------------------------------------

%------------------------------------------------------------------------
% Four photons:

\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/af2_pi.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/af2_pi.eps, width=12cm}} 
  \epsfig{file=H1prelim-01-117.fig10.eps, width=12cm}} 
  \caption{Four photon sample: Two photon invariant mass distribution,
           for data, background Monte Carlo (see text), and model expectations.
    \label{fig:nano10}}
%  \end{center}
\end{figure}


\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/af2_eta.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/af2_eta.eps, width=12cm}} 
  \epsfig{file=H1prelim-01-117.fig11.eps, width=12cm}} 
  \caption{Four photon sample: Two photon invariant mass 
           ``recoiling'' against $\pi^0$, for data, background Monte
           Carlo (see text), and model expectations.
    \label{fig:nano11}}
%  \end{center}
\end{figure}



\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/a2_4g.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/a2_4g.eps, width=12cm}}  
  \epsfig{file=H1prelim-01-117.fig12.eps, width=12cm}} 
  \caption{Four photon sample: $\pi^0$ - $\eta$ invariant mass, 
           for data, background Monte Carlo (see text), and model expectation. 
           For $\pi^0$ and $\eta$ mass definitions, see text.    
    \label{fig:nano12}}
%  \end{center}
\end{figure}


\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/f2_4g.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/f2_4g.eps, width=12cm}}   
  \epsfig{file=H1prelim-01-117.fig13.eps, width=12cm}} 
  \caption{Four photon sample: Two $\pi^0$ invariant mass distribution,
           for data, background Monte Carlo (see text), and model expectations.
           For $\pi^0$ mass definition, see text.
    \label{fig:nano13}}
%  \end{center}
\end{figure}


%-----------------------------------------------------------------------
% Five photons:

\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/b1_pi.eps}}
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/b1_pi.eps, width=12cm}} 
  \epsfig{file=H1prelim-01-117.fig14.eps, width=12cm}} 
  \caption{Five photon sample: Two photon invariant mass distribution
           for data, background Monte Carlo (see text), and model expectations
           (ten entries per event).
    \label{fig:nano14}}
%  \end{center}
\end{figure}


\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/b1_omega.eps}}
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/b1_omega.eps, width=12cm}}  
  \epsfig{file=H1prelim-01-117.fig15.eps, width=12cm}} 
  \caption{Five photon sample: Three photon invariant mass ``recoiling''
           against $\pi^0$, for data, background Monte Carlo
           (see text), and
           model expectations. For $\omega$ mass definition, see text. 
    \label{fig:nano15}}
%  \end{center}
\end{figure}


\begin{figure}
  \centerline{
%  \epsfxsize=32pc
%  \epsfbox{/u12/home/golling/TEX/Budapest_talk/Budaplots/b1_5g.eps}} 
%   \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/b1_5g.eps, width=12cm}} 
  \epsfig{file=H1prelim-01-117.fig16.eps, width=12cm}} 
  \caption{Five photon sample: $\omega$ - $\pi^0$ invariant mass,
           for data, background MC (see text), and model expectation.
           For $\omega$ and $\pi^0$ mass definitions, see text. 
    \label{fig:nano16}}
%  \end{center}
\end{figure}

%----------------------------------------------------------------------
%----------------------------------------------------------------------
%%% tommy's playing around
%\newpage
%%Tommy's starting\ldots
%\begin{figure}
%  \centerline{
%    \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/vm_slopes.eps, width=12cm} }
%%    \epsfig{file=H1prelim-01-117.fig15.eps, width=12cm} }
%  \caption{A compilation of slopes of $|t|$ - distributions for elastic
%    $\omega$ photoproduction as a function
%    of the photon - proton centre-of-mass energy, from fixed
%    target to HERA experiments.           
%    \label{fig:nano15}}
%\end{figure}

%\begin{figure}
%  \centerline{
%    \epsfig{file=/u12/home/golling/TEX/Budapest_talk/Budaplots/vmxs.eps, width=12cm} }
%%    \epsfig{file=H1prelim-01-117.fig16.eps, width=12cm} }
%  \caption{A synopsis of elastic vector meson photoproduction cross
%    sections as a function of the photon - proton centre-of-mass
%    energy, from fixed target to HERA experiments. 
%    \label{fig:nano16}}
%\end{figure}
%%Tommy's finished
%\newpage
%--------------------------------------------------------------------------------


\end{document}

