%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % A Search for Leptoquark Bosons in e-p Collisions at HERA % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \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 %=================================================================== %%%%%%%%%%%%% Start personal commands and re-definitions %%%%%%%%%%% % special \newcommand{\Rp}{\mbox{$\not \hspace{-0.15cm} R_p$}} \newcommand{\lsim}{\raisebox{-1.5mm}{$\:\stackrel{\textstyle{<}}{\textstyle{\sim}}\:$}} \newcommand{\gsim}{\raisebox{-0.5mm}{$\stackrel{>}{\scriptstyle{\sim}}$}} % shorthands \newcommand{\Loooo}{$\sqrt{\lambda_{11}\lambda_{11}}$} \newcommand{\Lootw}{$\sqrt{\lambda_{11}\lambda_{2j}}$} \newcommand{\Looth}{$\sqrt{\lambda_{11}\lambda_{3j}}$} \newcommand{\Lotot}{$\sqrt{\lambda_{12}\lambda_{12}}$} \newcommand{\Lottw}{$\sqrt{\lambda_{12}\lambda_{2j}}$} \newcommand{\Lotth}{$\sqrt{\lambda_{12}\lambda_{3j}}$} % units \newcommand{\cm}{\mbox{\rm ~cm}} \def\GeV{\hbox{$\;\hbox{\rm GeV}$}} \def\MeV{\hbox{$\;\hbox{\rm MeV}$}} \def\TeV{\hbox{$\;\hbox{\rm TeV}$}} \newcommand{\picob}{\mbox{{\rm ~pb}~}} % styling \def\figurename{{\bf Figure}} \def\tablename{{\bf Table}} %%%%%%%%%%%%%%%%%%% End definitions of personal commands %%%%%%%%%%%%%% % \begin{document} % \begin{titlepage} % %%\begin{flushleft} %%{\bf Draft 1.00\hspace{5mm} \today}\\ %%{\bf Editor : E. Perez }\\ %%{\bf Referee : B. Heinemann} \\ %%\end{flushleft} %%To be Submitted to the 30th International Conference on %%High-Energy Physics ICHEP00, \\ Osaka, Japan, July 2000 % \begin{flushleft} Submitted to the 30th International Conference on High-Energy Physics ICHEP2000,\\ Osaka, Japan, July 2000 \end{flushleft} \vspace{4cm} \begin{center} \begin{Large} \bf{A Search for Leptoquark Bosons in {\boldmath $e^- p$} Collisions at HERA \\ } \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} \noindent A search for scalar and vector leptoquarks (LQs) coupling to first generation fermions is performed in the H1 experiment at the $ep$ collider HERA. The analysis uses all available $e^- p$ data collected in 1998 and 1999 at a centre of mass energy of $\sim 320 \GeV$, corresponding to an integrated luminosity of $\sim 14.4 \picob^{-1}$. No evidence for the direct production of such particles is found in the high $Q^2$ neutral current deep-inelastic scattering data sample, and constraints on LQs are obtained. For a Yukawa coupling of electromagnetic strength LQs are excluded for masses up to $\sim 290 \GeV$. This analysis complements the LQs searches performed previously using data collected while HERA was operating with positrons instead of electrons. \end{abstract} \vfill \begin{flushleft} \textbf{Abstract: 954\\ Parallel Session: 11\\ Plenary Talk: 7} \end{flushleft} \end{titlepage} \newpage \section{Introduction} \label{sec:intro} The $ep$ collider HERA offers the unique possibility to search for $s$-channel resonant production of new particles which couple to lepton-parton pairs. Examples are leptoquark (LQ) 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 $27.5 \GeV$ initial state lepton with a quark of the $920 \GeV$ incoming proton, with masses up to the kinematic limit of $\sqrt{s_{ep}} \simeq 320 \GeV$. This analysis presents a search for LQs using $e^- p$ data collected in 1998 and 1999. Collisions between {\it{electrons}} and protons provide a high sensitivity to LQs coupling to $e^-$ and a {\it{valence quark}} (i.e. LQs with fermion number $F=2$) while the production of such LQs is largely suppressed in $e^+ p$ collisions where an {\it{antiquark}} should participate to the fusion. Thus this analysis complements the searches for LQs in $e^+ p$ data published recently~\cite{H1LQ99}. The search is restricted to the neutral current (NC) decay mode of the LQ which leads to final states similar to those of deep-inelastic scattering (DIS) at very high squared momentum transfer $Q^2$. The luminosity amounts to $14.41 \picob^{-1}$, an increase in statistics of a factor $\sim 35$ compared to previous LQs searches~\cite{H1LQ94} in $e^- p$ collisions. %======================================================================= \section{Leptoquark Phenomenology} %======================================================================= The phenomenology of LQs at HERA is presented in detail in~\cite{H1LQ99}. At HERA, LQs can be resonantly produced in % % --------------- FIGURE 1 : Diagrammes DIS + LQ, s/u --------------- \begin{figure}[h] \begin{center} \epsfxsize=0.7\textwidth \epsffile{H1prelim-00-061.fig1.eps} \caption[]{ \label{fig:diagdislq} {\small Diagrams (a) $s$-channel resonant production and (b) $u$-channel exchange of a leptoquark with fermion number $F = 2$. Diagrams involving a $ F = 0$ leptoquark are obtained from (a) and (b) by exchanging $q$ and $\bar{q}$. }} \end{center} \end{figure} % -------------------------------------------------------------------- % the $s$-channel or exchanged in the $u$-channel between the incoming lepton and a quark coming from the proton. This is illustrated in Fig.~\ref{fig:diagdislq}, where $\lambda$ denotes the unknown Yukawa coupling of the LQ to the $eq$ pair. Both these processes interfere with NC DIS. In contrast to~\cite{H1LQ99} where both contributions and their interference with DIS were carefully taken into account in order to probe LQs masses close to or above the kinematic limit, we only consider here the resonant process. % in which a LQ is produced at a mass $M =\sqrt{s_{ep} x}$ % where $x$ is the momentum fraction of the proton carried by the struck quark. % The case of extreme LQ masses $M_{LQ}$ and high coupling values, % where the convolution of the Breit-Wigner distribution of finite width % $\Gamma_{LQ} \propto \lambda^2 M_{LQ}$ characterizing the LQ resonance % with the steeply falling density in the proton of the incoming quark % leads to a strong distorsion of the LQ mass peak towards lower values, % is not adressed here. % % We restrict to LQ masses $M_{LQ}$ and coupling values small enough, such that % convoluting the Breit-Wigner distribution of finite width % $\Gamma_{LQ} \propto \lambda^2 M_{LQ}$ characterizing the LQ resonance % with the density in the proton of the incoming quark does not lead % This approach is valid as long as the LQ mass $M_{LQ}$ is not too high and its width $\Gamma \propto \lambda^2 M_{LQ}$ is small enough for the narrow-width approximation (NWA) to hold. In that case, the LQ mass spectrum is not distorted by the convolution of the Breit-Wigner distribution characterizing the LQ resonance with the density in the proton of the incoming quark~\cite{H1LQ99}. For $\sqrt{s_{ep}} = 320 \GeV$, this is the case for LQ masses up to $\sim 290 \GeV$ when the strength of the Yukawa coupling is of the order of $\alpha_{EM}$. 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 struck quark. Scalar LQs produced in the $s$-channel decay isotropically in their rest frame leading to a flat ${\rm d} \sigma\,/\,{\rm d}y \;$ spectrum where $y= Q^2 / s_{ep}x = \frac{1}{2}\left(1+\cos{\theta^*}\right)$ is the Bjorken scattering variable in DIS and $\theta^*$ is the decay polar angle of the lepton relative to the incident proton in the LQ centre of mass frame. In contrast, events resulting from the production and decay of vector LQs would be distributed according to ${\rm d} \sigma\,/\, {\rm d} y \propto \, (1-y)^2$. These $y$ spectra (or in other words the specific angular distributions of the decay products) from scalar or vector LQ production are markedly different from the ${\rm d} \sigma\,/\, {\rm d} y \propto \,y^{-2}$ distribution expected at fixed $x$ for the dominant $t$-channel photon exchange in neutral current DIS events. Hence, a LQ signal in the NC-like channel will be statistically most prominent at high $y$. %======================================================================= \section{Event Selection and Comparison with SM Expectations} %======================================================================= The search for first generation LQs relies essentially on an inclusive NC selection requiring an identified positron at high transverse energy. Selected events must have been accepted by a LAr trigger and survived a set of filters to reject non $ep$ colliding background, and a primary vertex is required in the range $\mid z - \bar{z} \mid < 35\cm$. %............................ \subsection{Event Selection} \label{eventselec} %............................ The selection of NC-like events is identical to that presented in~\cite{H1LQ99}. It mainly requires an isolated electron in the LAr with $E_{T,e} > 15 \GeV$ and an energy-momentum balance. A ``loose" requirement of a jet in the LAr, with $P_{T,jet} > 7 \GeV$, allows to suppress non-DIS contamination as $\gamma \gamma$ or QED Compton processes. The kinematic variables $Q^2$, $M$ and $y$ are determined using the measurement of the scattered electron energy and angle, the subscript $e$ being used in the following to label the corresponding reconstructed variables. The considered phase space is restricted to the kinematic range $Q^2_e > 2500 \GeV^2$ and $0.1 < y_e < 0.9$. The resolution in $M_e$ degrades with decreasing $y_e$ ($ \delta M_e / M_e \propto 1/ y_e$) and so the low $y$ domain is excluded. Excluding the high $y$ values avoids the region where migrations effects due to QED radiation in the initial state are largest for the $e$-method, and also suppresses down to a negligible level the photoproduction background where e.g. a jet has been misidentified as an electron. In the kinematic range considered, the NC trigger efficiency exceeds $98\%$ and is consistent with $100\%$ to within experimental error. Applying our NC selection criteria, 696 NC DIS candidates are observed in the considered kinematic range. % in good agreement % with the expectation of $675.7 \pm 50.6$ events from % standard NC DIS. The distribution of these events in the $y_e - M_e$ kinematic plane is shown in Fig.~\ref{fig:scatter}. % % --------------- FIGURE 1: Scatter plot ------------------------- % \begin{figure}[htb] \begin{center} \epsfxsize=0.6\textwidth \epsffile{H1prelim-00-061.fig2.eps} \caption {\small \label{fig:scatter} Kinematics in the $y_e -M_e$ plane of the selected NC DIS candidates. Three isocurves at $Q^2 = 2500, 15000$ and $30000 \GeV^2$ are also shown as full lines. } \end{center} \end{figure} %---------------------------------------------------------------------- In this plane, events coming from a resonantly produced scalar LQ decaying to $eq$ would accumulate in $M_e$ around the LQ mass, and be flatly distributed in $y$. %.................................. \subsection{Comparison with NC DIS} %.................................. The SM prediction for DIS is obtained using the event generator DJANGO~\cite{DJANGO} which includes QED first order radiative corrections and a modelling of the emission of QCD radiation to all orders according to the Color Dipole Model as implemented in ARIADNE~\cite{ARIADNE}. The parton densities in the proton used throughout are taken from the MRST~\cite{MRST} parametrization which includes constraints from HERA data up to $Q^2 = 5000 \GeV^2$. The systematic errors propagated on the mean SM expectations include:~ % \begin{itemize} \item the uncertainty on the integrated luminosity ($\pm 2.2 \%$); \item the uncertainty on the absolute calibration of the calorimeters for electromagnetic energies, ranging between $\pm 0.7\%$ in the central LAr wheels to $\pm 3\%$ in the forward region of the LAr calorimeter; \item the uncertainty on the calibration of the calorimeters for hadronic showers of $\pm 2\%$; \item the uncertainty on the partons densities in the proton which lead to a $7\%$ theoretical uncertainty on the predicted NC DIS cross-section. \end{itemize} Applying the requirements mentioned in section~\ref{eventselec}, $675.7 \pm 50.6$ events are expected from standard NC DIS, in good agreement with the number of observed candidates. Fig.~\ref{fig:ctrlpl} shows the distributions of the transverse energy of the electron $E_{T,e}$, its polar angle $\theta_e$, the missing transverse momentum $P_{T,miss}$ and the transverse momentum $P_{T,jet}$ of the highest $P_T$ jet, for the 696 observed candidates and for the NC DIS expectation. % % --------------- FIGURE 2: Control plot ------------------------- % \begin{figure}[htb] \begin{center} \epsfxsize=0.75\textwidth \epsffile{H1prelim-00-061.fig3.eps} \caption {\small \label{fig:ctrlpl} Distributions of (a) the transverse energy and (b) the polar angle of the electron; (c) the missing transverse momentum and (d) the transverse momentum of the highest $P_T$ jet for the selected NC DIS candidates. Symbols correspond to data events and histograms to SM simulation. } \end{center} \end{figure} %---------------------------------------------------------------------- All distributions are seen to be well described by the NC DIS simulation. The observed and expected $Q^2_e$ distributions are compared in Fig.~\ref{fig:q2pl}a. % % --------------- FIGURE 3: Q2 figure ------------------------- % \begin{figure}[htb] \begin{center} \epsfxsize=0.7\textwidth \epsffile{H1prelim-00-061.fig4.eps} \caption { \small \label{fig:q2pl}(a) $Q^2_e$ distribution of the selected NC DIS candidate events for the data ($\bullet$ symbols) and for standard NC DIS expectation (histogram); (b) ratio of the observed and expected (from NC DIS) number of events as a function of $Q^2_e$; the lines above and below unity specify the $\pm 1\sigma$ levels determined using the combination of statistical and systematic errors of the DIS expectation. } \end{center} \end{figure} %---------------------------------------------------------------------- Also shown in Fig.~\ref{fig:q2pl}b is the ratio of the observed $Q^2_e$ distribution to the NC DIS expectation. The errors resulting from the convolution of the systematic errors and the statistical error of the Monte Carlo sample are correlated for different $Q^2_e$ bins and are indicated in Fig.~\ref{fig:q2pl}b as lines above and below unity joining the $\pm 1\sigma$ errors evaluated at the centre of each bin. The NC DIS expectation agrees well with the data, with a slight deficit observed for $Q^2_e > 10000 \GeV^2$ where 42 events are observed while $49.26 \pm 5.18$ are expected from SM expectation, which is however not statistically significant. For $Q^2_e > 15000 \GeV^2$, 18 events are observed, in good agreement with the NC DIS prediction of $16.9 \pm 2.43$. %======================================================================= \section{Direct Search for Leptoquarks} %======================================================================= Starting from the NC DIS selection presented above, the significance of a possible LQ signal over the NC DIS background is enhanced by exploiting the specific angular distributions for LQ induced processes. % The LEGO~\cite{LEGO} event generator has been used to simulate events coming from the resonant production of scalar and vector LQs decaying into $eq$, for various values of the LQ mass $M_{LQ}$. For the LQ mass range considered here, % where the NWA holds, the kinematics of events coming from $eq \rightarrow LQ \rightarrow eq$ does not depend on the value of the Yukawa coupling $\lambda$, provided that $\lambda$ remains of moderate strength. These Monte-Carlo event samples have been used to optimize mass dependent lower $ y_e > y_{cut}$ cuts which maximize the signal significance. This has been achieved by finding the best compromise between the efficiency loss on the LQ signal and the important background reduction. Thus, with increasing LQ mass, the $y_{cut}$ decreases together with the NC DIS expectation. For scalar (vector) LQs, this $y_{cut}$ continuously decreases from $\sim$0.45 ($\sim$0.35) at 75 GeV to $\sim$0.35 ($\sim$0.1) at 200 GeV, reaching 0.1 (0.1) at 290 GeV. The optimized $y_{cut}$ is less stringent for vector than for scalar LQs due to the softer $y$ distribution ($\propto (1-y)^2$) of events induced by vector LQ production. %================================= \subsection{Mass Distributions} %================================= The comparison of the measured mass spectrum with SM predictions is shown in Fig.~\ref{fig:dndmlq} for the NC DIS analysis. The measured and expected NC spectra are seen before and after applying the mass dependent $y_e$ cut relevant for the search of a scalar (Fig.~\ref{fig:dndmlq}a) and a vector (Fig.~\ref{fig:dndmlq}b) LQ. After applying the $y_e$ cut optimized for scalar LQs, we observe 298 events in the mass range $M_e > 62.5 \GeV$ while $289.8 \pm 21.8$ are expected. For $M_e > 137.5 \GeV$ 21 candidate events are observed, which is slightly below the SM prediction of $29.8 \pm 3.2$. This is the reflection of the slight deficit observed above in the $Q^2$ distribution, for intermediate $Q^2$ values. % The $y_e$ cut optimized for vector LQs searches leads to % a smaller reduction of the sample The sample is less reduced when applying the $y_e$ cut optimized for vector LQs searches, which leads to 514 candidates in good agreement with the $495.2 \pm 37.2$ expected from SM. % ---------- FIGURE 4: dNdM Scalar and Vector ---------------- % \begin{figure}[htb] \begin{center} \begin{tabular}{cc} \hspace*{-0.9cm}\mbox{\epsfxsize=0.55\textwidth \epsffile{H1prelim-00-061.fig5a.eps}} & \hspace*{-0.8cm}\mbox{\epsfxsize=0.55\textwidth \epsffile{H1prelim-00-061.fig5b.eps}} \end{tabular} \end{center} % \caption[]{ \label{fig:dndmlq} {\small Mass spectra for NC DIS-like final states for data (symbols) and DIS expectation (histograms). The NC DIS-like comparison is shown before (open triangles, white histogram) and after (closed dots, hatched histogram) a $y$ cut designed to maximize the significance of an eventual (a) scalar and (b) vector LQ signal. The greyed boxes indicate the $\pm 1 \sigma$ band combining the statistical and systematic errors of the NC DIS expectation. }} \end{figure} %--------------------------------------------------------------------------- %================================= \subsection{Constraints on LQs} %================================= Since no evidence for LQ production is observed, the data is used to set constraints on LQs coupling to first generation fermions. For a given LQ mass, we use the numbers of observed and expected events within a mass bin $\left[ M_{min}, M_{max} \right]$ of variable width, adapted to the expected mass resolution (typically $3-6 \GeV$, dominated by experimental effects) and measured mass values for a given true LQ mass, and which slides over the accessible mass range. For example, only candidates with $M_e \in \left[ 187 ; 206 \right] \GeV$ will be used to constrain a $200 \GeV$ LQ undergoing a NC DIS-like decay. In the mass domain where the NWA holds, $M_{min}$ and $M_{max}$ vary linearly with the LQ mass. Typical detection efficiencies of scalar (vector) LQs including the optimized $y$ and mass cuts are found to vary between $35 \%$ ($18 \%$) at $100 \GeV$, $40 \%$ ($45 \%$) at $200 \GeV$ and $52 \%$ ($45 \%$) at 290 GeV. Assuming Poisson distributions for the SM background expectation and for the signal, an upper limit on the number of events coming from LQ production is then obtained using a standard Bayesian prescription with a flat prior for the signal cross section. The procedure which folds in the statistical and systematic errors is described in detail in~\cite{H1LQ94}. This number can be translated into a limit on the product $\sigma_{LQ}\beta_e$ of the LQ production cross section $\sigma_{LQ}$ and the branching ratio $\beta_e$ for the LQ to decay into $eq$. NLO QCD corrections to $\sigma_{LQ}$ were calculated in~\cite{SPIRA} and are taken into account here. They lead to an enhancement of the LQ cross section by $15 \% - 30 \%$ for LQ masses between 100 GeV and 290 GeV. % Assuming a specific LQ model (e.g.~\cite{BRW}) in which % the cross section $\sigma (eq \rightarrow LQ \rightarrow eq)$ % depends only on the Yukawa coupling besides $M_{LQ}$, % upper limits on $\lambda$ are thus obtained as a function of the LQ mass. % % In the NWA, $\sigma_{LQ}$ scales with the square of the Yukawa coupling, hence upper limits on $\lambda \sqrt{\beta_e}$ are obtained as a function of the LQ mass. Thus, assuming a specific LQ model (e.g.~\cite{BRW}) in which $\beta_e$ is known, mass dependent upper limits on $\lambda$ can be derived. On the other hand, assuming a given value for the coupling $\lambda$, limits on the branching ratio $\beta_e$ can be obtained as a function of the LQ mass. These two approaches are addressed in the following. %............................................................. \subsubsection{Limits on the Yukawa coupling in the BRW model} %............................................................. % --------------- FIGURE 5: Limits BRW ------------------------- % \begin{figure}[htb] \begin{center} \epsfxsize=0.8\textwidth \epsffile{H1prelim-00-061.fig6.eps} \caption { \small \label{fig:brw} Exclusion limits at $95 \%$ CL on the Yukawa coupling $\lambda$ as a function of the LQ mass for (a) scalar and (b) vector LQs with fermion number $F=2$ described by the BRW model. Domains above the curves are excluded. The upper curve on each plot indicates the limit obtained from the (less suited for $F=2$ LQs) $e^+ p$ data~\cite{H1LQ99}. } \end{center} \end{figure} %---------------------------------------------------------------------- The phenomenological model proposed by Buchm\"uller-R\"uckl-Wyler (BRW)~\cite{BRW} describes 14 LQs, half of them having a fermion number $F=2$, i.e. coupling to $e^- + q$. We focus on those LQs since LQs with $F=0$ are better constrained using $e^+ p$ data~\cite{H1LQ99}. In the BRW model the branchings $\beta_e$ are fixed and equal to 1 or 0.5 depending on the LQ type. In this framework, mass dependent upper limits on the Yukawa coupling can then be set for each LQ type. These limits are represented in Fig.~\ref{fig:brw}. % Those limits considerably extend the domain excluded by the analysis of $e^+ p$ data~\cite{H1LQ99}, represented as the most upper curve on each plot. For Yukawa coupling of the electromagnetic strength ($\lambda = 0.3$) LQ masses up to $290 \GeV$ are excluded at $95 \%$ confidence level (CL). % For such LQ mass and coupling, the NWA is still valid within % $\sim 30 \%$. Moreover it leads to conservative constraints % since the LQ cross section is underestimated by NWA. For such LQ mass and coupling, the NWA is still valid within $\sim 30 \%$ and the interference of LQ production with NC DIS remains below $1 \%$ of the LQ resonant production cross section in the kinematic domain where the signal is searched for, which justifies the approximation made in the analysis. %............................................................. \subsubsection{Mass Dependent Limits on {\boldmath $\beta(LQ \rightarrow eq)$ }} %............................................................. Moving away from the BRW model, we now consider leptoquarks which undergo NC DIS-like decays with a branching ratio $\beta_e$ and do not make any assumption on the other possible decay modes of the LQ. For a fixed value of the Yukawa coupling $\lambda$ upper limits on $\beta_e$ are derived as shown in Fig.~\ref{fig:beta}a and Fig.~\ref{fig:beta}b for a $F=2$ scalar LQ coupling to $e^- d$ and $e^- u$ respectively. % % --------------- FIGURE 6 : Limits beta ------------------------- % \begin{figure}[htb] \begin{center} \begin{tabular}{l} \mbox{\epsfxsize=0.8\textwidth \epsffile{H1prelim-00-061.fig7a.eps}} \\ \mbox{\epsfxsize=0.8\textwidth \epsffile{H1prelim-00-061.fig7b.eps}} \end{tabular} \caption { \small \label{fig:beta} Mass dependent exclusion limits at $95 \%$ CL on the branching ratio $\beta_e$ of the LQ to decay into $eq$ for scalar LQs with $F=2$ produced by (a) $e^- d$ and (b) $e^- u$ fusion. The $D\emptyset$ limit is also shown as hatched region. } \end{center} \end{figure} %---------------------------------------------------------------------- It can be seen that the domain excluded by this analysis extends considerably beyond the region excluded by the $D\emptyset$ experiment at the TeVatron, represented as the hatched domain on Fig.~\ref{fig:beta}. %========================================= \section{Conclusions} %========================================= Leptoquarks with fermion number $F=2$ have been searched using the $e^- p$ data collected by H1 in 1998 and 1999. No signal has been observed and constraints on such LQs have been set, allowing to extend beyond the domains excluded by other experiments. Moreover the constraints set here on $F=2$ LQs are more stringent than those on $F=0$ LQs obtained in~\cite{H1LQ99} from the higher statistics $e^+ p$ data sample, due to the enhanced energy in the centre of mass of the $ep$ collision. \begin{thebibliography}{99} \bibitem{H1LQ99} H1 Collaboration, C.~Adloff {\it et al.}, Eur.Phys.J. C11 (1999) 447. \vspace{-2mm} \bibitem{H1LQ94} H1 Collaboration, T.~Ahmed {\it et al.}, Z.~Phys.~C64 (1994) 545. \vspace{-2mm} \bibitem{DJANGO} DJANGO~6.2; G.A.~Schuler and H.~Spiesberger, Proc. of the Workshop Physics at HERA, W.~Buchm\"uller and G.~Ingelman (Editors), (October 1991, DESY-Hamburg) Vol. 3 p. 1419. \vspace{-2mm} \bibitem{ARIADNE} ARIADNE 4.08; L.~L\"onnblad, Comput.~Phys.~Commun. 71 (1992) 15. \vspace{-2mm} \bibitem{MRST} A.D.~Martin, R.G.~Roberts, W.J.~Stirling and R.S.~Thorne, Euro. Phys. J. 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