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\begin{titlepage}


\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
                & & & \\
\multicolumn{4}{l}{{\bf
                International Europhysics Conference 
                on High Energy Physics, EPS03},
                July~17-23,~2003,~Aachen} \\
                (Abstract {\bf 105} & Parallel Session & {\bf 13}) & \\
                & & & \\
\multicolumn{4}{l}{{\bf
                XXI International Symposium on  
                Lepton and Photon Interactions, LP03},
                August~11-16,~2003,~Fermilab} \\ 
                & & & \\
                \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
   A Search for Leptoquark Bosons in {\boldmath{$ep$}} Collisions at HERA}

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

\begin{abstract}

A search for scalar and vector leptoquarks coupling to
first generation fermions is performed in the H1 experiment
using $e^+p$ and $e^-p$ data collected from 1994 to 2000. 
No significant evidence for the direct production of such
particles is found in a data sample with a large transverse
momentum final state electron or with large missing transverse
momentum, and
constraints on leptoquark models are established. For
leptoquark couplings of electromagnetic strength,
leptoquark masses up to 290 GeV are ruled out.
 

\noindent
\end{abstract}


\end{titlepage}

\pagestyle{plain}

The $ep$ collider HERA offers the unique possibility to search for
resonant production of new particles which couple to
lepton-parton pairs.
Examples are leptoquarks (LQs), colour triplet bosons which appear naturally
in various unifying theories beyond the Standard Model (SM).
At HERA, leptoquarks could be singly produced by the fusion of the
initial state lepton of energy $27.5 \GeV$ with a quark from the
incoming proton of energy up to $920 \GeV$,
with masses up to the centre-of-mass energy $\sqrt{s_{ep}}$.

This analysis presents a search for LQs coupling to first generation fermions
using $e^+ p$ data collected
at $\sqrt{s_{ep}} = 300 \GeV$, 
$e^- p$ data collected at $\sqrt{s_{ep}} = 320 \GeV$,
and $e^+ p$ data collected at $\sqrt{s_{ep}} = 320 \GeV$.
These data sets correspond to integrated luminosities of
$37 \picob^{-1}$, $15 \picob^{-1}$ and $65 \picob^{-1}$, respectively.
They represent the full statistics accumulated by the
H1 experiment between 1994 and 2000.
The $e^+ p$ and $e^- p$ data sets are largely complementary
when searching for leptoquark resonances,
since the $e^+ p$ ($e^- p$) data provide most sensitivity to leptoquarks
with fermion number $F=0$ ($F=2$), i.e. LQs coupling to
$e^+$ ($e^-$) and a {\it{valence}} quark.
% The search reported here considers both the neutral current (NC) and
% charged current (CC) like decay modes of the LQ,
% which lead to final states
% similar to those of deep-inelastic scattering (DIS) at very high
% squared momentum transfer $Q^2$.
The search reported here considers the decays  ${\rm{LQ}} \rightarrow eq$ and
${\rm{LQ}} \rightarrow \nu q$ which lead to final states similar
to those of deep-inelastic scattering (DIS) neutral current (NC)
and charged current (CC) interactions at very high
squared momentum transfer $Q^2$.

The phenomenology of LQs at HERA was discussed in detail
in~\cite{H1LQ99}. At HERA, LQs can be resonantly produced in
the $s$-channel or exchanged in the $u$-channel between the
incoming lepton and a quark coming from the proton.
The amplitudes for both these processes interfere with those from DIS.
We shall consider here the mass domain where the resonant $s$-channel
contributions largely dominate the LQ signal cross-section.

In the $s$-channel, a LQ is produced at a mass $M =\sqrt{s_{ep} x}$
where $x$ is the momentum fraction of the proton carried by the 
interacting quark.
When the LQ decays into an electron and a quark, the mass
is reconstructed from the measured kinematics of the scattered electron,
and is henceforth labelled $M_e$. Similarly when the LQ decays into a
neutrino and a quark, the mass is labelled $M_h$ as it is
reconstructed from the hadronic final state only~\cite{H1LQ99}.

The H1 detector components most relevant to this analysis are the liquid argon
calorimeter, which measures the positions and energies of
charged and neutral particles over
the polar angular range\footnote{The polar angle $\theta$ is defined with respect
to the incident proton momentum vector (the positive $z$ axis).}
$4^\circ<\theta<154^\circ$,
and the inner tracking detectors which measure
the angles and momenta of charged particles over the range
$7^\circ<\theta<165^\circ$. A full description of the detector can be
found in~\cite{h1det}. 

This search relies essentially on
inclusive NC and CC DIS selections.
The selection of NC-like events follows that presented
in~\cite{H1LQ99}.
It requires an identified electron with transverse momentum above
$15 \GeV$ and considers the kinematic domain defined by
$Q^2 > 2500 \GeV^2$ and $0.1 < y < 0.9$, where
$y=Q^2/M^2$.
The inelasticity variable $y$ is related to
the polar angle $\theta^\ast$ of the lepton
in the centre-of-mass frame of the hard subprocess
by $y =\frac{1}{2}(1+\cos\theta^\ast)$.
Since the angular distribution of the electron coming from the decay
of a scalar resonance is markedly different from that
of the scattered lepton in NC DIS~\cite{H1LQ99}, a mass
dependent cut $y>y_{\rm cut}$ was applied previously~\cite{H1LQ99,H1LQe-}
to the $e^+p$ 1994-1997 and $e^-p$ 1998-1999 data in order to
optimize the signal sensitivity. However, the optimization power is rather
limited for a vector resonance as the angular distribution is only slightly
different from that of the DIS background. This can be seen from the
scattered event distribution in the mass$-y$ plane both for data
(Fig.~\ref{mass-y}a,b) and for a 200\,GeV NC-like scalar (vector)
(Fig.~\ref{mass-y}c (\ref{mass-y}d)), and CC-like vector LQ 
(Fig.~\ref{mass-y}e).
%
% --------------- FIGURE 1 : scattered plots  -------------------------
\begin{figure}[p]
\begin{center}
\begin{picture}(50,205)
\put(-55,137.5){\epsfig{figure=H1prelim-02-064.fig1a.eps,width=6.5cm}}
\put(-4,185){\bf (a)}
\put(-24,157.5){\footnotesize \textcolor{red}{$Q^2\!=\!10\,000$\,GeV$^2$}}
\put(25,137.5){\epsfig{figure=H1prelim-02-064.fig1b.eps,width=6.5cm}}
\put(76,185){\bf (b)}
\put(56,157.5){\footnotesize \textcolor{red}{$Q^2\!=\!10\,000$\,GeV$^2$}}
\put(-55,65){\epsfig{figure=H1prelim-02-064.fig1c.eps,width=6.5cm}}
\put(-4,110){\bf (c)}
\put(-55,-7.5){\epsfig{figure=H1prelim-02-064.fig1d.eps,width=6.5cm}}
\put(-4,40){\bf (d)}
\put(25,-7.5){\epsfig{figure=H1prelim-02-064.fig1e.eps,width=6.5cm}}
\put(76,40){\bf (e)}
\end{picture}
\end{center}
  \caption{\label{mass-y}
  Data events selected in the NC (a) and CC (b) analyses and the
    corresponding Monte Carlo events at 200 GeV for (c) NC-like scalar, 
    (d) NC-like vector LQs, and (e) CC-like vector LQ. In (a) and (b), the
      red lines are for shown value of $Q^2$ of 10\,000\,GeV$^2$.}
\end{figure} 
%
%----------------------------------------------------------------------
%
Indeed, from the ratio plot (Fig.\ref{sbratio}) of the LQ (signal) over
the DIS background, one sees that applying a mass dependent $y$ cut for a
vector LQ can hardly improve the signal significance. For this reason,
no $y$ cut is applied in the analysis of the $e^+p$ 1999-2000 data, 
instead bins with varying  size adapted to the experimental resolution are 
defined in the mass-$y$ plane to fully explore the signal sensitivity.
%
% --------------- FIGURE 2 : efficiency  -------------------------
\begin{figure}[p]
\begin{center}
\begin{picture}(50,205)
\put(-55,137.5){\epsfig{figure=H1prelim-02-064.fig2a.eps,width=7.5cm}}
\put(-42.5,153){\bf (a)}
\put(25,137.5){\epsfig{figure=H1prelim-02-064.fig2b.eps,width=7.5cm}}
\put(36.5,153){\bf (b)}
\put(-55,65){\epsfig{figure=H1prelim-02-064.fig2c.eps,width=7.5cm}}
\put(-42.5,80){\bf (c)}
\put(25,65){\epsfig{figure=H1prelim-02-064.fig2d.eps,width=7.5cm}}
\put(36.5,80){\bf (d)}
\put(-55,-7.5){\epsfig{figure=H1prelim-02-064.fig2e.eps,width=7.5cm}}
\put(-42.5,7.5){\bf (e)}
\put(25,-7.5){\epsfig{figure=H1prelim-02-064.fig2f.eps,width=7.5cm}}
\put(36.5,7.5){\bf (f)}
\end{picture}
\end{center}
  \caption{\label{sbratio}
  Leptoquarks (LQs) event distribution at 200 GeV for (a) 
    NC-like scalar, (c) NC-like vector, and (e) CC-like vector LQs, and the
    corresponding signal over the Standard Model background ratios (b), (d),
    and (e).}
\end{figure} 
%
%----------------------------------------------------------------------
%

The mass spectrum measured in the $\sqrt{s_{ep}}=320$\,GeV data set
is compared in Fig.~\ref{fig:dndm}a
with the NC SM prediction, obtained using a Monte-Carlo
calculation~\cite{DJANGO} and the MRST parametrization~\cite{mrst}
for the parton densities.
%
%The distributions are shown before and after applying the
%mass dependent lower $y$ cut
%designed to maximize the significance of a scalar LQ in
%each $e^+ p$ data set.
%This $y_{\rm cut}$ decreases from $\sim 0.5$ at $100 \GeV$
%to $\sim 0.45$ at $200 \GeV$, reaching
%$\sim 0.15$ at 290 GeV.
%
%In the mass range $M_e>62.5$\,GeV and after applying
%this $y$ cut,
%880 events are
%observed in good agreement with the SM expectation of $869 \pm 65$
%events.
%A good agreement is also observed when applying the
%$y$ cut optimized for vector LQ searches (not shown).
%
Similar mass spectrum of the
NC DIS-like events measured in the 300\,GeV $e^+p$ and 320\,GeV $e^-p$
data sets and the comparison with the SM prediction can be found in
\cite{H1LQ99, H1LQe-}.
%The distributions are shown before and after applying the
%mass dependent lower $y$ cut
%designed to maximize the significance of a vector LQ, which
%decreases from $\sim 0.25$ at $100 \GeV$ to $\sim 0.15$
%at 200 GeV, reaching 0.1 at 290 GeV.
%514 events are observed after applying the mass dependent
%$y$ cut, in good agreement with the SM expectation of $504 \pm 38$
%events.
%A good agreement is also observed in the $e^- p$ data set
%when applying the lower $y$ cut optimized for scalar LQ searches
%(not shown).

% The selection of CC-like events is described in detail  
% in~\cite{H1LQ99,H1EMINUS}.
% It mainly requires a missing transverse momentum larger
% than 25 GeV. The signal is searched for in the kinematic domain defined by
% $Q^2 > 2500 \GeV^2$. 
The selection of CC-like events follows closely that
presented in~\cite{H1LQ99,H1EMINUS}.
A missing transverse momentum exceeding $25 \GeV$
and $Q^2 > 2500 \GeV^2$ are required.
%
The domain at high $y$ where
the resolution on the mass $M_h$ degrades is removed by requiring $y<0.9$.
%For $M_h > 65 \GeV$, 692 (345) events are observed in the $e^+ p$ ($e^- p$)
%data set,
%in good agreement with the CC SM expectation of  $673 \pm 61$ 
%($350 \pm 28$) events.
The observed and expected mass spectra are in good agreement as
shown in Fig.~\ref{fig:dndm}b.
%
% ---------- FIGURE 3: dNdM  Scalar and Vector  ----------------
%
\begin{figure}[htb] 
\begin{center}
\begin{picture}(50,70)
\put(-53,-90){\epsfig{figure=H1prelim-02-064.fig3.eps,bbllx=0pt,bblly=0pt,bburx=
594pt,
bbury=842pt,width=18cm}}
\put(-32.5,25){\bf (a)}
\put(45,25){\bf (b)}
\end{picture}
\end{center}
  \caption{\label{fig:dndm}
  Mass spectra for the events from (a) neutral current (NC)
  and (b) charged current (CC) deep inelastic scattering (DIS)
  selections, together with the corresponding DIS expectations (histograms).
  The grey bands indicate the $\pm1\sigma$ uncertainty due to the systematic
  errors on the NC and CC DIS expectations.}
\end{figure} 
%---------------------------------------------------------------------------

No evidence for LQ production is observed in the NC and CC data samples.
Hence the data are 
used to set constraints on LQs which couple
to first generation fermions.
The $e^- p$ data are used to set constraints on $F=2$ LQs,
and the NC data from both $e^+ p$ data sets are used to
constrain LQs with $F=0$.

For both the NC-like and CC-like channels, we use the numbers of observed and
expected events and the signal efficiencies within the variable mass$-y$ bins 
for a given true LQ mass $M_{\rm LQ}$.
Assuming Poisson distributions for the SM background expectations and
for the signal, an upper limit on the number of events coming
from LQ production is obtained using a modified frequentist
approach~\cite{tjunk}.
This limit on the number of signal events
is then translated into an upper bound on
the LQ cross-section, which in turn leads to constraints
on LQ models.
The signal cross-section is obtained from the leading-order LQ amplitudes 
given in~\cite{BRW},
corrected by multiplicative $K$-factors~\cite{LQNLO} to account
for next-to-leading order QCD corrections.
These corrections can enhance the LQ cross-section by ${\cal{O}}(10 \%)$.


%The procedure which folds in the
%statistical and systematic errors is described in detail
%in~\cite{H1LQ94}.
Both the statistical and the systematic errors are taken into account in the 
limit derivation.
The main source of experimental systematic error considered is the uncertainty
on the electromagnetic energy scale (between $0.7 \%$ and
$3 \%$) for the NC analysis, and the
uncertainty on the hadronic energy scale ($2 \%$)
for the CC analysis.
Furthermore, an error of $\pm 7 \%$ on the DIS expectations is attributed
to the limited knowledge of proton structure. An additional systematic
error arises from the theoretical uncertainty on the signal cross-section,
originating mainly from the uncertainties on the parton densities.
This uncertainty is $7 \%$ for $F=2$ ($F=0$) LQs coupling to 
$e^- u$ ($e^+ u$), and varies
between $7 \%$
at low LQ masses up to $50 \%$ around 290\,GeV for 
$F=2$ ($F=0$) LQs coupling to $e^- d$ ($e^+ d$).
Moreover, choosing alternatively $Q^2$ or the square of the transverse momentum
of the final state lepton instead of $M_{\rm LQ}^2$ as the hard scale at which
the parton distributions are estimated yields an additional uncertainty of
$\pm 7 \%$ on the signal cross-section.

The phenomenological model proposed by
Buchm\"uller, R\"uckl and Wyler (BRW)~\cite{BRW}
describes
7 LQs with $F=0$ and 7 LQs with $F=2$.
We use here the nomenclature of~\cite{LQNAME}
to label the various scalar $S_{I,L}$
($\tilde{S}^{\mbox{\tiny
\hspace{-3mm}\raisebox{1.5mm}{(}\hspace{2mm}\raisebox{1.5mm}{)}}}_{I,R}$)
or vector $\tilde{V}^{\mbox{\tiny
\hspace{-3mm}\raisebox{1.5mm}{(}\hspace{2mm}\raisebox{1.5mm}{)}}}_{I,L}$ ($V_{I,R}$) LQ
types of weak
isospin $I$, which
couple to a left-handed (right-handed) electron. The tilde is used to
distinguish LQs which differ only by their 
hypercharge.
%
In the BRW model the branching ratios $\beta_e$ ($\beta_{\nu}$)
for the LQ decays
into $e q$ ($\nu q$) are fixed and equal
to 1 or 0.5 (0 or 0.5) depending on the LQ quantum numbers.
Table~\ref{tab:lqbrw} lists the 14 LQ types described by the
BRW model.

% ------------------ TABLE : Scalar Leptoquarks  -------------------------
\begin{table*}[htb]
  \renewcommand{\doublerulesep}{0.4pt}
  \renewcommand{\arraystretch}{1.2}
 \vspace{-0.1cm}

\begin{center}
    \begin{tabular}{|c|c|c||c|c|c|}
      \hline
       $F=2$ & Prod./Decay & $\beta_e$
              & $F=0$ & Prod./Decay & $\beta_e$  \\

      \hline
%
% -> Scalar LQ :
     \multicolumn{6}{|c|}{Scalar Leptoquarks} \\ \hline
    $^{1/3}S_0$     & $e^-_L u_L\rightarrow e^- u$ & $1/2$
  & $^{5/3}S_{1/2}$ & $e^+_R u_R \rightarrow e^+ u$            & $1$  \\
                          & $e^-_R u_R\rightarrow e^- u$ & $1$
  &                       & $e^+_L u_L \rightarrow e^+ u$            & $1$ \\
      \cline{1-3}
      $^{4/3}\tilde{S}_0$
        & $e^-_R d_R\rightarrow e^- d$ & $1$
  & $^{2/3}S_{1/2}$ & $e^+_L d_L \rightarrow e^+ d$            & $1$ \\
      \hline
      $^{4/3}S_1$
        & $e^-_L d_L \rightarrow e^- d$
         & $1$
  & $^{2/3}\tilde{S}_{1/2}$ & $e^+_R d_R \rightarrow e^+ d$ & $1$ \\
      $^{1/3}S_1$
        & $e^-_L u_L \rightarrow e^- u$
         & $1/2$
             & & &  \\
      \hline
%
% -> Vector LQ :
     \multicolumn{6}{|c|}{Vector Leptoquarks} \\ \hline
    $^{4/3}V_{1/2}$ & $e^-_R d_L\rightarrow e^-  d$ & $1$
  & $^{2/3}V_{0}$   & $e^+_L d_R \rightarrow e^+ d$              & $1$ \\
                          & $e^-_L d_R \rightarrow e^-  d$ & $1$
  &                       & $e^+_R d_L \rightarrow e^+ d$              & $1/2$ \\
      \cline{4-6}
    $^{1/3}V_{1/2}$ & $e^-_R u_L\rightarrow e^-  u$ & $1$
  & $^{5/3}\tilde{V}_0$
        & $e^+_L u_R \rightarrow e^+ u$ & $1$ \\
      \hline
    $^{1/3}\tilde{V}_{1/2}$
        & $e^-_L u_R\rightarrow e^- u$ & $1$
  & $^{5/3}V_{1}$    & $e^+_R u_L \rightarrow e^+ u$              & $1$ \\
                          &                                            &
  & $^{2/3}V_{1}$    & $e^+_R d_L \rightarrow e^+ d$              & $1/2$ \\
      \hline
      \hline
    \end{tabular}
    \caption {\small \label{tab:lqbrw}
               Leptoquark isospin families in the Buchm\"uller-R\"uckl-Wyler
               model.
               For each leptoquark, the superscript corresponds to its
               electric charge, while the subscript denotes its weak
               isospin.
               The leptoquarks are conventionally indexed
               with the chirality of the incoming {\it{electron}} which
               could mediate their production in $e^-p$ collisions.
               }
\end{center}
\end{table*}
% ------------------------------------------------------------------------
%
For LQs with $F=0$, the upper limits on the 
Yukawa coupling $\lambda$ at the $e \, q \, {\rm LQ}$ vertex
obtained at $95 \%$ confidence level (CL) are
shown as a function of the LQ mass in Figs.~\ref{fig:brw}a and b, 
for scalar and vector LQs respectively.
For masses above $\sim 270 \GeV$, these bounds improve by a factor
of about 5 the limits obtained in~\cite{H1LQ99} 
from the analysis of $e^+ p$ data at $\sqrt{s_{ep}} = 300 \GeV$.
For mass values beyond the kinematic limit, the constraints from a contact 
interaction analysis~\cite{ci} are also shown.
%
Constraints corresponding to $F=2$ LQs are shown
in Figs.~\ref{fig:brw}c and d. 
%
% --------------- FIGURE 4: Limits BRW : H1    --------------
%
\begin{figure}[htbp] 
\begin{center}
\begin{picture}(50,80)
\put(-57.5,-7.5){\epsfig{figure=H1prelim-02-064.fig4ab.eps,width=8.75cm}}
\put(25,-7.5){\epsfig{figure=H1prelim-02-064.fig4cd.eps,width=8.75cm}}
\end{picture}
\end{center}
  \caption{\label{fig:brw}
  Exclusion limits for the 7 $F=0$ leptoquarks (LQs) described by the
  Buchm\"uller, R\"uckl and Wyler (BRW) model. The limits are expressed at
  95\% CL on the Yukawa coupling $\lambda$ as a function of the leptoquark
  mass for the (a) scalar LQs with $F=0$, (b) vector LQs with $F=0$, (c)
  scalar LQs with $F=2$ and (d) vector LQs with $F=2$.
  Domains above the curves are
  excluded. Constraints on LQs with masses above the HERA centre-of-mass
  energy, obtained from a contact interaction (CI) analysis and using the
  partial $e^+p$ data sample at $\sqrt{s_{ep}}=300$\,GeV, are shown in the
  rightmost part of figures (a-b) and (c-d), respectively.}
  \end{figure} 
%----------------------------------------------------------------------
%
Constraints on LQs with masses above the HERA centre-of-mass energy
were set in~\cite{H1LQ99}, where the interference between the LQ
production and DIS processes  was taken into account.
These are shown 
%for completeness
in the rightmost part in Fig.~\ref{fig:brw}c,d.
%
For a Yukawa coupling of electromagnetic strength $\alpha_{\rm em}$
($\lambda = \sqrt{4\pi\alpha_{\rm em}}=0.3$)
this analysis rules out LQ masses below 275 to $290 \GeV$, depending
on the LQ type.

Fig.~\ref{fig:brwcompar} summarizes the constraints on the
$\tilde{S}_{1/2,L}$ and on the $S_{0,L}$ obtained by H1,
%020718 by the OPAL experiment at LEP~\cite{LQLEP}, 
by the L3 experiment at LEP~\cite{LQLEP}, 
and by the Tevatron experiments~\cite{d0}.
For LQ masses above the HERA centre-of-mass energy, the H1 constraints
obtained from a contact interaction approach~\cite{ci} are 
also shown.

% --------------- FIGURE 5: Limits BRW : H1 + LEP + D0    --------------
%
\begin{figure}[p]
\begin{center}
\begin{picture}(50,180)
\put(-30,60){\epsfig{figure=H1prelim-02-064.fig5a.eps,width=10.5cm}}
\put(-30,-30){\epsfig{figure=H1prelim-02-064.fig5b.eps,width=10.5cm}}
\end{picture}
\end{center}
  \caption{\label{fig:brwcompar}
  Exclusion limits at 95\% CL on the Yukawa coupling $\lambda$ as a
  function of the leptoquark (LQ) mass for (top) a scalar with $F=0$ and
  (bottom) a scalar LQ with $F=2$ described by the BRW model. Shaded and
  hatched domains are excluded.}
\end{figure} 
%----------------------------------------------------------------------

Beyond the BRW ansatz, generic LQ models can also be considered, where
other LQ decay modes are allowed such that the branching ratios $\beta_e$
and $\beta_\nu$ are free parameters.
Mass dependent constraints on the LQ branching ratios
can then be set for a given
value of $\lambda$.
For a scalar LQ possessing the quantum numbers of the
$S_{1/2,L}$, which couples to $e^+ u$,
Fig.~\ref{fig:betaeplus}a shows the part of the
$\beta_e$-$M_{\rm LQ}$ plane which is ruled out by the NC analysis, for four
values of the Yukawa coupling.
For a vector LQ coupling to $e^- d$ (possessing the
quantum numbers of the $V_{0,L}$) and for $\lambda = 0.05$ and 0.3,
the domain of the $\beta_e$-$M_{\rm LQ}$ ($\beta_{\nu}$-$M_{\rm LQ}$) plane
excluded by the NC (CC) analysis is shown in Fig.~\ref{fig:betaeplus}b.
If the LQ decays into $e q$ or $\nu q$
only\footnote{It should be noted that $\beta_e + \beta_{\nu} = 1$ does
   not imply $\beta_e = \beta_{\nu}$ even when
   invariance under $SU(2)_L$ transformations is required.
   For example, when LQs belonging to a given isospin multiplet are not
   mass eigenstates, their mixing usually leads to different branching
   ratios in both channels for the physical LQ states. },
the combination
of both channels rules out the part of the plane on the left of
the second and fourth full curves from the left, respectively 
for $\lambda = 0.05$ and 0.3. The resulting
combined bound is largely independent of the individual values
of $\beta_e$ and $\beta_{\nu}$.
Combined bounds are also shown for $\lambda=0.03$ and $\lambda=0.1$.
Fig.~\ref{fig:betaeplus}c
shows exclusion areas in the same plane as for Fig.~\ref{fig:betaeplus}a, 
for a scalar LQ possessing the quantum numbers of the
$\tilde{S}_{0,R}$ (which couples to $e^- d$).
Fig.~\ref{fig:betaeplus}d
shows similar exclusion limits as for Fig.~\ref{fig:betaeplus}(b), 
for a scalar LQ possessing the quantum numbers of the
$S_{0,L}$ (which couples to $e^- u$).
%
% for the same LQ type.
The domain excluded by the D$0$ experiment at the Tevatron~\cite{d0} is 
also shown. For $\lambda$ greater than $\sim 0.03$, the H1 limits extend 
considerably beyond the
% region excluded by the D$0$ experiment at the Tevatron~\cite{d0},
region excluded by the D$0$ experiment~\cite{d0}.
%
% --------------- FIGURE 6 : Limits beta vs mass  -------------------------
%
\begin{figure}[htbp] 
\begin{center}
\begin{picture}(50,90)
\put(-60,-10){\epsfig{figure=H1prelim-02-064.fig6ab.eps,width=9cm}}
\put(14,85){(a)}
\put(14,30){(b)}
\put(27.5,50){\epsfig{figure=H1prelim-02-064.fig6c.eps,width=9cm,height=6cm}}
\put(27.5,-10){\epsfig{figure=H1prelim-02-064.fig6d.eps,width=9cm,height=6cm}}
\end{picture}
\end{center}
  \caption{\label{fig:betaeplus}
  (a) Mass dependent exclusion limits at 95\% CL on the branching
  ratio $\beta_e$ of a scalar leptoquark (LQ) which couples to $e^+u$ (with
  the quantum numbers of the $S_{1/2, L}$). (b) Domains ruled out by the
  combination of the NC and CC analyses, for a vector LQ which couples to
  $e^+d$ (with the quantum numbers of the $V_{0,L}$) and decaying only into
  $eq$ and $\nu q$ for four values of the Yukawa coupling $\lambda$.
  (c) Same as for (a), here the scalar LQ couples to $e^-d$ (with the
  quantum numbers of the $\tilde{S}_{0,R}$)~\cite{H1LQe-}.
  (d) Same as for (b), here the scalar LQ couples to $e^-u$ (with the
  quantum numbers of the $S_{0,L}$)~\cite{H1LQe-}.
  The regions on the left of the full curves are excluded at 95\% CL. For
  $\lambda=0.05$ (also 0.3 in (b)), the part of the $\beta_e-M_{\rm LQ}$ 
  ($\beta_\nu-M_{\rm LQ}$) plane on the left of the dashed (dotted) curve 
  is excluded by the NC (CC) analysis. The branching ratios $\beta_e$ and 
  $\beta_\nu$ are shown on the left and right axes respectively. 
  In (a-d), the hatched region represents the domain excluded by the D0 
  experiment. The D0 bounds do not depend on the value of the Yukawa coupling.}
\end{figure} 
%----------------------------------------------------------------------
%

To summarize, a search for resonantly produced leptoquarks 
% with fermion numbers $F=2$ and $F=0$
has been performed
using all $e^+p$ and $e^-p$ data collected by H1 between 1994 and 2000.
No signal has been observed and constraints on leptoquarks have been
set, which extend beyond the domains excluded by other experiments.
For a Yukawa coupling of electromagnetic strength, leptoquark masses
up to 290 GeV can be ruled out.
% This represents the most stringent direct bound on $F=2$ leptoquarks.

\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 in constructing and now
maintaining the H1 detector, our funding agencies for
financial support, the
DESY technical staff for continual assistance
and the DESY directorate for the
hospitality which they extend to the non DESY
members of the collaboration.

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%
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%
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% 
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% \vspace{-2mm}
% 
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%
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\vspace{-2mm}


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\vspace{-2mm}


%\bibitem{H1CIOSAKA}
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%\vspace{-2mm}

\bibitem{ci}
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\vspace{-2mm}

\bibitem{LQLEP}
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\vspace{-2mm}

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%%CITATION = HEP-EX 9707033;%%
%
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%%CITATION = HEP-EX 9710032;%%
\vspace{-2mm}

\end{thebibliography}

\end{document}
