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\begin{document}

\title{Photo- and Electroproduction of Single Hadrons and Resonances}

\author{F.~CORRIVEAU}

\address{McGill University, \\
Department of Physics,\\
3600 University Street,\\
Montr\'eal, Qc,\\
Canada, H3A 2T8\\
E-mail: corriveau@physics.mcgill.ca}

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\maketitle

\abstracts{
Production of single hadrons and resonances emerges as a promising
field for the study of Quantum Chromodynamics at HERA.
Four recent studies are presented here to illustrate the scope and reach
of the technique:  light mesons and resonances test the universality of
hadroproduction, strange particles challenge the hadronisation models or
directly probe the quark content of the proton sea while the first
observation of $K-K$ resonant states offers a glueball candidate.
}

\section{Introduction}

The process by which quarks and gluons convert into colorless hadrons is
not well described by Quantum Chromodynamics (QCD) processes.  This is
particularly true for light quarks, where perturbative QCD does not apply.  
As a consequence, phenomenological hadronisation models such as the Lund
String Model or the Cluster Fragmentation Model are
widely used to represent the processes.

Production studies of particles such as some of the light mesons or baryons
containing a strange quark, or light resonances, should therefore
contribute to the understanding of the hadronisation mechanisms.
In many ways, HERA lags behind LEP in several of such measurements,
but its different kinematical reach and the presence of quarks in the
initial state strongly enhances its potential.

This paper will cover four examples of photo- and electroproduction
processes:   neutral hadronic resonances, strange particles,
the use of strange mesons to probe the proton sea content and the
study of $K_s^0K_s^0$ resonances in the search for special states of
matter.

\section{Neutral Hadronic Resonances at HERA}

This first extensive set of measurements done by the H1 experiment at 
HERA on light hadronic mesons and resonances used the
39~$pb^{-1}$ of the 2000 data, covering the laboratory rapidity region of
$|y_{lab}|$$<$$1$ with an average energy of 210~GeV in the photon-proton system.
The production rates of $\eta$, $\rho^0$, $f_0(980)$ and
$f_2(1270)$ were investigated\cite{hkrop}.

A large fraction of the $\eta$'s decay in a pair of photons which can be
identified by clusters in the liquid argon detector, as illustrated in
figure~\ref{krop1}.  The other states
are predominantly decaying in $\pi^+\pi^-$ pairs, easily detected as
charged tracks in the jet chambers.  However, as shown in 
figure~\ref{krop2}, the low-mass background is considerable and special 
care had to be taken in its combinatorial representation and in the assumptions 
regarding reflections from $\omega$ and $K^*$ states.  The $\rho^0$ peak 
is shifted to low values from the expectations, but this is also 
partly due to the acceptance limitations in that range and introduces but 
a negligible bias on the $f_0$ and $f_2$ resonant peaks. 

\begin{figure}[htb]
\vspace*{-6mm}
\centerline{\epsfxsize=2.9in\epsfbox{corriveau01.eps}}
\caption{The two-photon mass spectrum.  The curves were obtained from 
a fit to a Gaussian distribution and a polynomial background 
function.}
\label{krop1}
\vspace*{-2mm}
\end{figure}

When the single isospin data is corrected for spin and plotted
as function of the sum of the meson mass and its transverse momentum 
(figure~\ref{krop3}), one observes a striking scaling as the same 
behaviour of light, long-lived hadrons is reproduced, thus testing the 
universality of hadroproduction. 

\begin{figure}[htb]
%\vspace*{-6mm}
\centerline{\epsfxsize=2.9in\epsfbox{corriveau02.eps}}
\caption{The $\pi^+\pi^-$ invariant mass spectrum before and 
after subtraction of the background and of the estimated 
low-energy contributions from reflections. The curves contain 
relativistic Breit-Wigner shapes from the fit.}
\label{krop2}
\end{figure}

\begin{figure}[htb]
%\vspace*{-6mm}
\centerline{\epsfxsize=2.9in\epsfbox{corriveau03.eps}}
\caption{The differential photoproduction cross sections of light mesons
as function of the sum of the meson mass and its transverse momentum $p_T$.}
\label{krop3}
\end{figure}

\clearpage
\section{Strangeness Production}

Strange quarks may be produced by flavour excitation, QCD Compton,
gluon-splitting, boson-gluon fusion, various hadronisation processes,
decay from higher mass states or diffractive processes, most of which are not 
always readily differentiated.  Strange particle production becomes very 
useful because of the associated low masses, copious rates and unambiguous 
signals.  $K_s^0$'s and $\Lambda$'s have been studied previously at 
HERA in deep inelastic scattering (DIS) and photoproduction, but only from very 
early data sets\cite{zkaon,hstra,hkaon,zchar}, and no cross-section had
as yet been determined.

Using the 60~$pb^{-1}$ of the ZEUS 1999-2000 data\cite{zzieg,hlevs}
in the DIS regime
(50$<$$Q^2$$<$500~GeV$^2$), and restricting the particle $p_T$ range to the
0.5--5~GeV interval, figure~\ref{zieg1} shows the quality
of the particle identification for the main decays of the particles.
Table~\ref{zieg9} compares the results to HERWIG and the Lund Color Dipole
Model (under ARIADNE) for two configurations of the strangeness
suppression factor $\lambda_s = P(s)/P(d)$, whereby $P(d)=P(u)$. The
measurements fall between the values of 0.2 and 0.3 in Lund model
while HERWIG fails to predict the total cross sections. The ratio between
$\Lambda$ and $\overline{\Lambda}$ remains however unity.

\begin{figure}[htb]
\vspace*{-6mm}
\begin{tabular}{cc}
\begin{minipage}{54mm}
\centerline{\epsfxsize=54mm\epsfbox{corriveau04.eps}}
\end{minipage}
&
\begin{minipage}{54mm}
\centerline{\epsfxsize=54mm\epsfbox{corriveau05.eps}}
\end{minipage}
\end{tabular}
\caption{The $K_s^0$ (left) and $\Lambda$ (right) invariant mass spectra.}
\label{zieg1}
\vspace*{-2mm}
\end{figure}

\begin{figure}[htb]
\vspace*{-6mm}
\centerline{\epsfxsize=3.3in\epsfbox{corriveau06.eps}}
\centerline{\epsfxsize=3.3in\epsfbox{corriveau07.eps}}
\caption{Differential cross sections for $K_s^0$ and $\Lambda$ as
function of the transverse momentum $p_T$ and the pseudorapidity $\eta$
in the laboratory frame.}
\label{zieg3}
\end{figure}

\begin{table}[htb]
\tbl{Preliminary cross-sections and ratios thereof for $K_s^0$ and $\Lambda$.}
{
\begin{tabular}{|c||c|c|c|}
\hline
                    &$\sigma(K_s^0)$ [$pb$]&
                     $\sigma(\Lambda+\overline{\Lambda})$ [$pb$]&
                     $\sigma(\Lambda+\overline{\Lambda})/\sigma(K_s^0)$\\
\hline
\hline
ZEUS (prelim.)      &2454$\pm$   18$^{   +32}_{  -102}$&
                      567$\pm$   12$^{   +13}_{   -34}$&
                    0.231$\pm$0.005$^{+0.005}_{-0.006}$\\
CDM ($\lambda_s=0.3$)&2762& 603&0.218\\
CDM ($\lambda_s=0.2$)&2257& 483&0.214\\
HERWIG               &1854&1329&0.717\\
\hline
\multicolumn{4}{c}{}\\
\hline
                    &$\sigma(\Lambda)$ [$pb$]&
                     $\sigma(\overline{\Lambda})$ [$pb$]&
                     $\sigma(\Lambda)/\sigma(\overline{\Lambda})$\\
\hline
\hline
ZEUS (prelim.)      & 292$\pm$    9$^{    +7}_{   -18}$&
                      279$\pm$    9$^{   +12}_{   -18}$&
                     1.05$\pm$ 0.05$^{ +0.05}_{ -0.05}$\\
CDM ($\lambda_s=0.3$)&302&301&1.00\\
CDM ($\lambda_s=0.2$)&240&243&0.99\\
HERWIG               &661&668&0.99\\
\hline
\end{tabular}
\label{zieg9}
}
\end{table}

In figure~\ref{zieg3}, drawn in the laboratory frame, even
a renormalized HERWIG simulation does not reproduce the shapes of the
distributions. Moreover, the effect of changing the value of $\lambda_s$ is
shown to be non-uniform according to the type of particle or its
transverse momentum. From the pseudorapidity ($\eta$) plot, there is an
indication of increased baryon to meson production in the forward region.

This last observation motivated further investigation in the Breit Frame,
where the
radiation from the struck quark is naturally separated from the proton
remnant (figure~\ref{zieg4}).  The variable $x_p$ represents the
particle scaled momentum.  The current region is equivalent to one
hemisphere of a $e^+e^-$ collider system and the results confirm the
low sensitivity to the $\lambda_s$ parameter.  In the target region,
associated to the proton remnant, the data tend towards the higher
value $\lambda_s=0.3$, which may suggest that this parameter could be
related to the gluon density.
A single parameter might not be adequate
to estimate the production rates of strange particle over such
kinematical ranges.  Studies of the heavier strange particles $\Sigma$
and $\Xi$ are currently being done in ZEUS to further extend the scope
of this study.

\begin{figure}[htb]
\vspace*{-6mm}
\centerline{\epsfxsize=3.3in\epsfbox{corriveau08.eps}}
\centerline{\epsfxsize=3.3in\epsfbox{corriveau09.eps}}
\caption{Differential cross sections for $K_s^0$ and $\Lambda$ as
function of the scaled momentum $x_p$ in the Breit Frame.}
\label{zieg4}
\end{figure}

%\clearpage
\section{Strange Content of the Sea}

The $\phi$-meson is another strange particle with a clean decay mode
of a pair of kaons at the vertex which can be used to study not only
hadron production in yet another channel, but also to probe directly the
content of the proton sea.  Detection of $\phi$'s in the 1995-1997 ZEUS
data sample\cite{zssea} reveals a high background but exhibits a clear
signal in the
laboratory frame, which becomes even more enhanced in spite of low
statistics in the current region of the Breit Frame (figure~\ref{ssea1}).

\begin{figure}[htb]
\vspace*{-6mm}
\centerline{\epsfxsize=3.1in\epsfbox{corriveau10.eps}}
\caption{Invariant mass plot of $K^+K^-$ pairs in the laboratory and in
the Breit Frame.}
\label{ssea1}
\end{figure}

\begin{figure}[htb]
\vspace*{-3mm}
\centerline{\epsfxsize=3.15in\epsfbox{corriveau11.eps}}
\caption{Differential $\phi$-meson cross-sections as function of
the kinematic variables $p_T$, $\eta$, $x_p$ (current and target
regions) and $Q^2$.  Contributions of subprocesses of Boson-Gluon
Fusion, Quark Parton Model or QCD Compton are also indicated.}
\label{ssea2}
\end{figure}

The cross-section measured in the selected kinematical range,
$\sigma(e^+p\rightarrow{}e^+\phi{}X)=0.57\pm{}0.022^{+0.010}_{-0.008}~nb$
agrees very well with the LEPTO (0.0501~$nb$) and ARIADNE (0.509~$nb$)
simulations while establishing a preliminary value of $0.22\pm{}0.02$
for $\lambda_s$ in that range.  The plots of figure~\ref{ssea2}, whereby
the Monte-Carlo inputs can be controlled, 
illustrate some of the observations:  the hard QCD processes give very
significant relative contributions in the current region of the Breit Frame 
while
vanishing in the target region.  This, coupled to the fact that their
fraction increases as function of $p_T$ or $x_p$, points to important
involvement of the sea $s$-quarks.

By concentrating on the leading $\phi$-mesons ($x_p$$>$0.8), one realizes
that uncertainties in the QCD processes and hadronisation are very small
at high $p_T$, that gluon emissions become negligible and that
the photon scattering on s-quarks is a QED process, i.e. well described.
The main uncertainties left arise from the modellisations themselves and the
allowed $\lambda_s$
range, which is taken to be 0.2--0.3.  Under such conditions, the
leading $\phi$-mesons in figure~\ref{ssea3} unambiguously require
s-quark scattering, thus showing direct evidence of the proton strange sea
contribution to hadron production at low values of the scaled momentum $x$.

\begin{figure}[htb]
\vspace*{-3mm}
\centerline{\epsfxsize=2.6in\epsfbox{corriveau12.eps}}
\caption{Cross sections for leading $\phi$-mesons as function of $x_p$ in
the current region of the Breit Frame.  The hatched bands represent the
full range of uncertainties in the simulations.}
\label{ssea3}
\end{figure}

\clearpage
\section{$K_s^0K_s^0$ Resonances}

With the maturity of the experiments and the recent developments in the
field, there is now considerable interest in ``meson spectroscopy'' at HERA.
The striking example of the $K_s^0K_s^0$ resonant states in DIS with the
ZEUS experiment\cite{hlevt,zksks} illustrates the potential for discoveries.

Kaons are again chosen in
this search because of their high detection efficiency, good
acceptance and low background in the central rapidity  region.
The $K_s^0$ momentum threshold is chosen to be 200~MeV.  A special cut on
the opening angle $\theta_{KK}$ between the 2 kaons is applied to reject the
$f_0/a_0$(980) state.  2553 candidates are found.  Their invariant mass
plot of the system is displayed in figure~\ref{ksks1} and fitted with
three relativistic modified Breit-Wigner distributions and one
background function.

\begin{figure}[htb]
\vspace*{-1mm}
\centerline{\epsfxsize=3.3in\epsfbox{corriveau13.eps}}
\caption{Invariant mass plot of the $K_s-K_s$ pairs.  The lines identify
the residual combinatorial background and the peaks used in the
overall fit to the data (full dots).  The open dots describe the
already rejected $f_0/a_0$ background.}
\label{ksks1}
\end{figure}

Three regions are identified.  Below 1500~MeV, the contributions from
the $f_2$(1270) and $a_2^0$(1320) merge over the acceptance threshold.
The $\theta_{KK}$ cut is shown to leave negligible possible contributions
under  the remaining two peaks.  The first of these, at 1537$\pm$9~MeV and
with a width of $\sim$50~MeV, is consistent with the known $f_2'$(1525)
state. The second peak, at 1726$\pm$7~MeV, contains 79$^{+29}_{-23}$
events and has a measured width of 38$^{+20}_{-14}$~MeV.  This width
is in open contradiction from the observations from BES, Belle and L3,
which published 167, 323 and 200~MeV respectively.  A large number of
permutations and assumptions has been tested in the fits to the data,
the other state widths, the background shapes, etc..
but results in this high mass range were proven to be rather insensitive
to them.  A further check in the Breit Frame revealed that 93\% of the
candidates are found in the target region, i.e. associated with the
proton remnant.  The expected sizeable initial state gluon radiation
thus strengthens the hypothesis that the state could
be a glueball candidate.

%\clearpage
\section{Summary}

First measurements of inclusive photoproduction cross-sections of the light
resonances $\eta$, $\rho^0$, $f_0$(980) and $f_2$(1270) have been
reported.  Strangeness production studies in deep inelastic scattering
reveal details of hadronisation processes and inconsistencies in some
of the currently available simulation packages.  $\phi$-mesons were
further used to provide direct evidence of the strangeness content of
the proton sea.  Finally, in a first case of complex resonant system
of $K_s^0$ pairs, two high mass states have been clearly identified,
offering one glueball candidate.

\section*{Acknowledgments}

This work has been partly supported by the National Sciences and
Engineering Research Council of Canada and by DESY.

I would like to thank the organisers of this workshop for creating such
a stimulating environment in a truly congenial setting.

\appendix

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\begin{thebibliography}{0}

\bibitem{hkrop} The H1 Collaboration, presented by A. Kropivnitskaia,
{\it Measurements of the Inclusive Photoproduction of $\eta$, $\rho^0$,
$f_0(980)$ and $f_2(1270)$ Mesons at HERA},
International Europhysics Conference on High Energy Physics,
EPS03, Aachen, July 17--23, 2003.

\bibitem{zkaon} The ZEUS Collaboration, M. Derrick et al.,
{\it Neutral Strange Particle Production in Deep Inelastic Scattering at
HERA},
DESY-95-084 (April 1995),
{\it Zeitschrift f. Physik} {\bf C68}, 29--42 (1995).

\bibitem{hstra} The H1 Collaboration, S. Aid et al.,
{\it Strangeness Production in Deep Inelastic Positron-Proton Scattering
at HERA},
DESY-96-122 (June 1996),
{\it Nucl. Phys.} {\bf B480}, 3 (1996).

\bibitem{hkaon} The H1 Collaboration, C. Adloff et al.,
{\it Photoproduction of $K^0$ and $\Lambda$ at HERA and a Comparison
with Deep Inelastic Scattering},
DESY-97-095 (May 1997),
{\it Zeitschrift f. Physik} {\bf C76}, 213 (1997).

\bibitem{zchar} The ZEUS Collaboration, J. Breitweg et al.,
{\it Charged Particles and Neutral Kaons in Photoproduced Jets at HERA},
DESY-97-229 (November 1997),
{\it Eur. Phys. Journal.} {\bf C2}, 77--93 (1997).

\bibitem{zzieg} The ZEUS Collaboration, presented by A. Ziegler,
{\it Strange Particle Production in DIS at HERA},
International Workshop in Deep Inelastic Scattering,
DIS2003, St.~Petersburg, April 23-27, 2003.

\bibitem{hlevs} The ZEUS Collaboration, presented by B. Levtchenko,
{\it Measurements of Strange Particle Production in Deep Inelastic $e^+p
\rightarrow e^+X$ Scattering at HERA},
International Europhysics Conference on High Energy Physics,
EPS03, Aachen, July 17--23, 2003.

\bibitem{zssea} The ZEUS Collaboration, S. Chekanov et al.,
{\it Observation of the Strange Sea in the Proton via Inclusive
$\phi$-Meson Production in Neutral Current Deep Inleastic Scattering at
HERA},
DESY-02-184 (October 2002),
{\it Phys. Lett.} {\bf B553}, 141--158 (2002).

\bibitem{hlevt} The ZEUS Collaboration, presented by B. Levtchenko,
{\it Observation of $K_s^0K_s^0$ Resonances in Deep Inelastic Scattering
at HERA},
International Europhysics Conference on High Energy Physics,
EPS03, Aachen, July 17--23, 2003.

\bibitem{zksks} The ZEUS Collaboration, S. Chekanov et al.,
{\it Observation of $K_s^0K_s^0$ resonances in deep inelastic
scattering at HERA},
DESY-03-098 (July 2003),
accepted for publication by {\it Phys. Lett. B}.

\end{thebibliography}

\end{document}
