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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
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\multicolumn{4}{l}{{\bf
                International Europhysics
                Conference on High Energy Physics},
                July~12,~2001,~Budapest} \\
 {\bf EPS 2001:} 
                 & Abstract:        & {\bf 822}    &\\
                 & Parallel Session & {\bf 6}   &\\ [.7em]
\multicolumn{4}{l}{{\bf
               XX International Symposium on Lepton and Photon Interactions}, 
               July~23,~2001,~Rome} \\ 
{\bf LP 2001:}  
                 & Abstract:        & {\bf 514} &\\
                 & Plenary Session  & {\bf S10, S11}   &\\ \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 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 is identical to 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 (vector)
   resonance is markedly (slightly) different from that 
   of the scattered lepton in NC DIS~\cite{H1LQ99}, a mass
   dependent cut $y>y_{\rm cut}$ allows
   the signal significance to be optimized.
The mass spectrum measured in the full $e^+ p$ data set 
is compared in Fig.~\ref{fig:dndmnc}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).
%
Fig.~\ref{fig:dndmnc}b shows the mass spectrum of the
NC DIS-like events measured in the $e^- p$
data set and the comparison with the SM prediction.
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).

% ---------- FIGURE 1: dNdM  Scalar and Vector  ----------------
%
\begin{figure}[htb]
  \begin{center}
  \begin{tabular}{cc}
     \hspace*{-0.2cm}\mbox{\epsfxsize=0.52\textwidth
        \epsffile{H1prelim-01-161.fig1a.eps}}
   &
     \hspace*{-0.8cm}\mbox{\epsfxsize=0.52\textwidth
      \epsffile{H1prelim-01-161.fig1b.eps}}
  \end{tabular}
  \end{center}
%
 \caption[]{ \label{fig:dndmnc}
 {\small Mass spectra for the events from the NC DIS selection
         for (a) $e^+ p$ and (b) $e^- p$ data (symbols),
         together with the corresponding DIS expectations (histograms).
         The data are shown before (open squares,
         dashed-line histogram) and after (filled dots, full-line histogram)
         a $y$ cut designed to maximize the significance of 
         (a) a scalar and (b) a vector leptoquark (LQ) signal.
         The grey boxes indicate the $\pm 1 \sigma$ uncertainty
         due to the systematic errors on the NC DIS
         expectation. }}
\end{figure}
%---------------------------------------------------------------------------

% 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:dndmcc}a and Fig.~\ref{fig:dndmcc}b.

% ---------- FIGURE 2: dNdM CC  ----------------
%
\begin{figure}[htb]
  \begin{tabular}{cc}
     \hspace*{-0.2cm}\mbox{\epsfxsize=0.52\textwidth
        \epsffile{H1prelim-01-161.fig2a.eps}}
   &
     \hspace*{-0.8cm}\mbox{\epsfxsize=0.52\textwidth
      \epsffile{H1prelim-01-161.fig2b.eps}}
  \end{tabular}
%
 \caption[]{ \label{fig:dndmcc}
 {\small Mass spectra for the events from the CC DIS selection
         for (a) $e^+ p$ and (b) $e^- p$ data (symbols),
         together with the corresponding DIS expectations (histograms).
         The grey boxes indicate the $\pm 1 \sigma$ uncertainty
         due to the systematic errors on the CC DIS
         expectation. }}
\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 within a
variable mass bin, adapted to the experimental mass distribution
for a given true LQ mass $M_{\rm LQ}$, and
which slides over the accessible mass range.
%
The signal efficiencies, including the mass bin
requirement, vary with the LQ mass between $30 \%$ ($20 \%$) and
$55 \%$ ($45 \%$) for scalar (vector) LQs decaying into $e q$,
and between $20 \%$ and $50 \%$ for LQs decaying into $\nu q$.

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 standard Bayesian
prescription.
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}.
The main source of experimental systematic error 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 Fig.~\ref{fig:brw}a
and Fig.~\ref{fig:brw}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 $\sqrt{s_{ep}} = 300 \GeV$.
%
Constraints corresponding to $F=2$ LQs are shown
in Fig.~\ref{fig:brw}c and Fig.~\ref{fig:brw}d.
%
%
% --------------- FIGURE 3: Limits BRW -------------------------
%
\begin{figure}[htb]
   \begin{center}
   \begin{tabular}{cc}
     \hspace*{-1.6cm}{\mbox{
     \epsfig{file=H1prelim-01-161.fig3ab.eps,
       width=0.6\textwidth}
     }}
     &
     \hspace*{-1.4cm}{\mbox{
     \epsfig{file=H1prelim-01-161.fig3cd.eps,
       width=0.6\textwidth}
     }}
    \end{tabular}
      \caption
      { \small  \label{fig:brw}
                Exclusion limits for the 14 leptoquarks (LQs) described by the 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 in~\cite{H1LQ99} using
                the partial $e^+ p$ data sample at 
                $\sqrt{s_{ep}} = 300 \GeV$, are shown in the
                rightmost part of each plot. }
 \end{center}
\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 Fig.~\ref{fig:brw} in the rightmost part of each plot.
%
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,
by the OPAL 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{H1CIOSAKA} are 
also shown.

% --------------- FIGURE 4: Limits BRW : H1 + LEP + D0    --------------
%
\begin{figure}[htb]
   \begin{center}
%
     \epsfxsize=0.73\textwidth 
      \epsffile{H1prelim-01-161.fig4a.eps} \\
     \vspace*{0.cm}

     \epsfxsize=0.73\textwidth 
      \epsffile{H1prelim-01-161.fig4b.eps}
%
      \caption
      { \small  \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 LQ with $F=0$ and
                    (bottom) a scalar LQ with $F=2$ described by
                the BRW model.
                Shaded and hatched domains are excluded. }
 \end{center}
\end{figure}
%----------------------------------------------------------------------



%
% --------------- FIGURE 5 : Limits beta vs mass  -------------------------
%
\begin{figure}[htb]
   \begin{center}
    \begin{tabular}{c}
     \mbox{\epsfxsize=0.8\textwidth
      \epsffile{H1prelim-01-161.fig5a.eps}}  \\
%
     {\mbox{\epsfxsize=0.8\textwidth
     \epsffile{H1prelim-01-161.fig5b.eps}}
     }
%
    \end{tabular}
     \vspace*{0.4cm}
      \caption
      { \small  \label{fig:betaeplus}
         Mass dependent exclusion limits at $95 \%$ CL on the branching
         ratio $\beta_e$ of a scalar leptoquark (LQ) which couples (a) to $e^+ d$
         (with the quantum numbers of the $\tilde{S}_{1/2,L}$)
         and (b) to $e^+ u$
         (with the quantum numbers of the $S_{1/2,L}$).
         In (a) and (b), the hatched region represents the domain
         excluded by the D$0$ experiment~\cite{d0}.}
%
 \end{center}
\end{figure}
%----------------------------------------------------------------------
%

%
% --------------- FIGURE 6 : Limits beta vs mass  -------------------------
%
\begin{figure}[htb]
   \begin{center}
   \vspace*{-3mm}
    \begin{tabular}{c}
     \mbox{\epsfxsize=0.8\textwidth
      \epsffile{H1prelim-01-161.fig6a.eps}}  \\
%
     {\mbox{\epsfxsize=0.8\textwidth
     \epsffile{H1prelim-01-161.fig6b.eps}}
     }
%
    \end{tabular}
      \vspace*{0.4cm}
      \caption
      { \small  \label{fig:betaeminus}
         (a) Mass dependent exclusion limits at $95 \%$ CL on the branching
         ratio $\beta_e$ of a scalar leptoquark (LQ) which couples to $e^- d$
         (with the quantum numbers of the $\tilde{S}_{0,R}$).
         The hatched region represents the domain
         excluded by the D$0$ experiment~\cite{d0}.
       (b) Domains ruled out by the combination of the NC and CC analyses,
       for a scalar LQ which couples to $e^- u$ (with the quantum
       numbers of the $S_{0,L}$)  and
       decaying only into $e q$ and $\nu q$
       for three values
       of the Yukawa coupling $\lambda$.
       The regions on the left of the full curves
       are excluded at $95 \%$ CL.
       For $\lambda=0.05$, 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.
       The hatched region represents the domain
       excluded by the D$0$ experiment~\cite{d0}, combining the
       $eq$ and $\nu q$ decay modes of the LQ..}
%
 \end{center}
\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
$\tilde{S}_{1/2,L}$ ($S_{1/2,L}$), which couples
to $e^+ d$ ($e^+ u$),
Fig.~\ref{fig:betaeplus}a (Fig.~\ref{fig:betaeplus}b) shows the part of the
$\beta_e$-$M_{\rm LQ}$ plane which is ruled out, for three 
values of  the Yukawa coupling.
The domain excluded by the
D$0$ experiment at the Tevatron~\cite{d0} is also shown.
Fig.~\ref{fig:betaeminus}a
shows exclusion areas in the same
plane, for a scalar LQ possessing the quantum numbers of the
$\tilde{S}_{0,R}$ (which couples to $e^- d$).
%
For a scalar LQ coupling to $e^- u$ (possessing the
quantum numbers of the $S_{0,L}$) and for $\lambda = 0.05$,
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:betaeminus}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 middle full curve, for $\lambda = 0.05$. 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 $\lambda=0.3$.
% for the same LQ type.
For $\lambda$ greater than $\sim 0.03$, these 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}.




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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\end{thebibliography}


\end{document}

