%================================================================ % 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} %{\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=/u12/home/golling/TEX/DIS2001/H1logo.ps ,width=2.cm} \\[.2em] \hline \multicolumn{4}{l}{{\bf International Europhysics Conference on High Energy Physics}, July~12,~2001,~Budapest} \\ {\bf EPS 2001:} & Abstract: & {\bf 795} &\\ & Parallel Session & {\bf 2} &\\ % & Plenary Session & {\bf } &\\[.7em] \multicolumn{4}{l}{{\bf XX International Symposium on Lepton and Photon Interactions}, July~23,~2001,~Rome} \\ {\bf LP 2001:} & Abstract: & {\bf 488} &\\ % & Parallel Session & {\bf } &\\ & Plenary Session & {\bf S08} &\\ \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 $0.3From 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=/u12/home/golling/TEX/Budapest_talk/Budaplots/feynman_old.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=/u12/home/golling/TEX/Budapest_talk/Budaplots/pi0_inc.eps, width=12cm}} % \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.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:nano08}} \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: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.fig8.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.fig9.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.fig10.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.fig11.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.fig12.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.fig13.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.fig14.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}