%================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ \documentstyle[12pt,epsfig,hhline,times]{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 \def\GeV{\hbox{$\;\hbox{\rm GeV}$}} %===============================title page============================= \begin{document} % The rest \newcommand{\pom}{{I\!\!P}} \newcommand{\reg}{{I\!\!R}} \newcommand{\slowpi}{\pi_{\mathit{slow}}} %\newcommand{\gevsq}{\mathrm{GeV}^2} \newcommand{\fiidiii}{F_2^{D(3)}} \newcommand{\fiidiiiarg}{\fiidiii\,(\beta,\,Q^2,\,x)} \newcommand{\n}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand{\nz}{1.30\pm 0.08 (stat.)^{+0.08}_{-0.14} (syst.)} \newcommand{\fiidiiiful}{F_2^{D(4)}\,(\beta,\,Q^2,\,x,\,t)} \newcommand{\fiipom}{\tilde F_2^D} \newcommand{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)} \newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (syst.)} \newcommand{\fiipomarg}{\fiipom\,(\beta,\,Q^2)} \newcommand{\pomflux}{f_{\pom / p}} \newcommand{\nxpom}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand {\gapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim}$}} \newcommand {\lapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim}$}} \def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle >$}\,} \def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle <$}\,} \newcommand{\pomfluxarg}{f_{\pom / p}\,(x_\pom)} \newcommand{\dsf}{\mbox{$F_2^{D(3)}$}} \newcommand{\dsfva}{\mbox{$F_2^{D(3)}(\beta,Q^2,x_{I\!\!P})$}} \newcommand{\dsfvb}{\mbox{$F_2^{D(3)}(\beta,Q^2,x)$}} \newcommand{\dsfpom}{$F_2^{I\!\!P}$} \newcommand{\gap}{\stackrel{>}{\sim}} \newcommand{\lap}{\stackrel{<}{\sim}} \newcommand{\fem}{$F_2^{em}$} \newcommand{\tsnmp}{$\tilde{\sigma}_{NC}(e^{\mp})$} \newcommand{\tsnm}{$\tilde{\sigma}_{NC}(e^-)$} \newcommand{\tsnp}{$\tilde{\sigma}_{NC}(e^+)$} \newcommand{\st}{$\star$} \newcommand{\sst}{$\star \star$} \newcommand{\ssst}{$\star \star \star$} \newcommand{\sssst}{$\star \star \star \star$} \newcommand{\tw}{\theta_W} \newcommand{\sw}{\sin{\theta_W}} \newcommand{\cw}{\cos{\theta_W}} \newcommand{\sww}{\sin^2{\theta_W}} \newcommand{\cww}{\cos^2{\theta_W}} \newcommand{\trm}{m_{\perp}} \newcommand{\trp}{p_{\perp}} \newcommand{\trmm}{m_{\perp}^2} \newcommand{\trpp}{p_{\perp}^2} \newcommand{\alp}{\alpha_s} \newcommand{\alps}{\alpha_s} \newcommand{\sqrts}{$\sqrt{s}$} \newcommand{\LO}{$O(\alpha_s^0)$} \newcommand{\Oa}{$O(\alpha_s)$} \newcommand{\Oaa}{$O(\alpha_s^2)$} \newcommand{\PT}{p_{\perp}} \newcommand{\JPSI}{J/\psi} \newcommand{\sh}{\hat{s}} %\newcommand{\th}{\hat{t}} \newcommand{\uh}{\hat{u}} \newcommand{\MP}{m_{J/\psi}} %\newcommand{\PO}{\mbox{l}\!\mbox{P}} \newcommand{\PO}{I\!\!P} \newcommand{\xbj}{x} \newcommand{\xpom}{x_{\PO}} \newcommand{\ttbs}{\char'134} \newcommand{\xpomlo}{3\times10^{-4}} \newcommand{\xpomup}{0.05} \newcommand{\dgr}{^\circ} \newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}} \newcommand{\gev}{\,\mbox{GeV}$\;$} \newcommand{\WBoson}{\mbox{$W$}} \newcommand{\fbarn}{\,\mbox{{\rm fb}}} \newcommand{\fbarnt}{\,\mbox{{\rm fb$^{-1}$}}} % % Some useful tex commands % \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } \newcommand{\et}{\ensuremath{E_t^*} } \newcommand{\rap}{\ensuremath{\eta^*} } \newcommand{\gp}{\ensuremath{\gamma^*}p } \newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} } \newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} } % \newcommand{\ptcalo}{$P_T^{\mathrm calo}\;$} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}} \def\NPB{{\em Nucl. Phys.} {\bf B}} \def\PLB{{\em Phys. Lett.} {\bf B}} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} {\bf D}} \def\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \noindent %Submitted to the 30th International Conference on %High-Energy Physics ICHEP2000, \\ %Osaka, Japan, July 2000 %{\bf %Draft Version : 0.1 \\ %Date : \today \\ %Editors : C.Diaconu, J.Dingfelder, F.Keil, E.Perez \\ %Referee : M.Erdmann }\\ %\vspace*{3.0cm} \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=H1logo_bw_small.epsi ,width=2.cm} \\[.2em] \hline \multicolumn{4}{l}{{\bf International Europhysics Conference on High Energy Physics}, July~12,~2001,~Budapest} \\ {\bf EPS 2001:} & Abstract: & {\bf 824} &\\ & Parallel Session & {\bf S11} &\\[.7em] % & Plenary Session & {\bf S11} &\\[.7em] \multicolumn{4}{l}{{\bf XX International Symposium on Lepton and Photon Interactions}, July~23,~2001,~Rome} \\ {\bf LP 2001:} & Abstract: & {\bf 512} &\\ & Parallel Session & {\bf S6} &\\ % & Plenary Session & {\bf S6} &\\ \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} %\vspace{2cm} \begin{center} \begin{Large} {\bf Search for Single Top Production in e$^\pm$p collisions at HERA } \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{1cm} \begin{abstract} %%%%%%%%%%%%%%%%%%% ABSTRACT%%%%%%%%%%%%%%%%%%%%% A search for anomalous top quark production mediated by a flavour changing neutral current via a $\gamma$-$u$-$t$ coupling is performed in $e^{\pm}p$ collisions at HERA. The search exploits data collected from 1994 to 2000 and is motivated by the previous observation of outstanding events with isolated leptons, missing transverse momentum and a jet with large transverse momentum. The top decay into a $b$-jet and a $W$-boson is considered in both the leptonic and hadronic decay modes of the $W$. In leptonic decay modes, five events are found to be compatible with the hypothesis of anomalous top quark production while $1.8$ events are expected from Standard Model. No excess above the Standard Model expectation is found in the analysis of the hadronic decay channel. % A limit on the effective photon-$u$-$t$ coupling of % $\kappa_\gamma=0.23$ is determined. An upper limit on the anomalous $\gamma$-$u$-$t$ coupling is established in the framework of recent NLO calculations. The sensitivity of HERA to flavour changing neutral currents is found to be competitive with that at other existing high energy colliders. \end{abstract} %\vfill %\begin{flushleft} % {\bf Abstract: 961 } \\ % {\bf Parallel session: 11} \\ % {\bf Plenary talk: 7~b } %\end{flushleft} \end{titlepage} % % COPY THE AUTHOR AND INSTITUTE LISTS % AT THE TIME OF THE T0-TALK INTO YOUR AREA % % from /h1/iww/ipublications/h1auts.tex %\include{h1auts} % from /h1/iww/ipublications/h1inst.tex %\include{h1inst} \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% body \section{Introduction} The H1 collaboration has first reported~\cite{h1isol} the observation of events with high-$P_T$ isolated leptons and missing transverse momentum in the positron-proton data collected in 1994-1997. % Within 36.5~$pb^{-1}$ of $e^+p$ data, H1 has observed 1 electron event % for $2.4\pm0.5$ expected and 5 muon events for $0.8\pm0.2$ expected. % Three muon events were found in a region of large transverse momentum % of the hadronic system. % In more recent data collected from 1998 to 2000, new events with the same topology have been observed~\cite{h1isolbudapest}. Some of the events were further characterized by a large transverse momentum of the hadronic system, which % This characteristics turned out to be an atypical kinematic property when compared to the Standard Model (SM) calculations which are dominated by direct production of $W$-bosons. % In the more recent data, new events with %% this topology have been % the same topology have been % observed~\cite{h1isolbudapest}. \par % The lepton and the missing transverse momentum are likely to be associated % with a $W$-boson decaying % into the lepton and a neutrino. % leptonically. % The large transverse momentum of the hadronic system, however, This may indicate presence of a further production mechanism involving beyond Standard Model. % $W$ production. A possible origin of these events is production of top quarks which predominantly decay into a $b$-quark jet and a $W$-boson. The lepton and the missing transverse momentum would then be associated with a $W$-boson decaying leptonically. Within the Standard Model, top quark production is negligible in $e^{\pm}p$ collisions. % In the framework of physics beyond the Standard Model, however, top % production is predicted to occur via the flavour changing neutral % current % (FCNC) mechanism. However, in several extensions of the SM, the top quark is predicted to have significantly large flavour changing neutral current (FCNC) interactions, which could lead to a sizeable single top production cross-section at HERA. % \par In this paper we present a search % the first search for top quark production using the H1 detector at HERA. % With respect to \cite{h1toposaka} the luminosity in the leptonic decay channel % has been updated giving a total integrated luminosity of $115.2$ pb$^{-1}$. The analysis for the leptonic decay channel makes uses of all data collected from 1994 to 2000 and corresponding to an integrated luminosity of $115.2$ pb$^{-1}$. In addition to the leptonic decay channel, hadronic decays of the top quark into $3$ or more jets are exploited using a data sample corresponding to an integrated luminosity of $36.5$~pb$^{-1}$. The large jet transverse momenta involved ensure that a potential signal can be found above the jet production expected from QCD processes. %============================ \section{Phenomenology} %============================ In the Standard Model neutral current interactions preserve the involved flavours in the leading order. Therefore flavour changing neutral current processes only arise via higher order radiative corrections and are highly suppressed. Their low SM rates make FCNC processes an ideal place to look for new physics at high energy colliders. Due to the large top quark mass close to the electroweak symmetry breaking scale, deviations from the SM might be observed first in the top sector. FCNC interactions involving the top quark have thus received considerable interest since the discovery of the top at the Fermilab Tevatron. Such interactions are present in many extensions of the SM like models with an extended Higgs sector~\cite{ATWOOD}, supersymmetry~\cite{SUSY}, dynamical breaking of the electroweak symmetry~\cite{PECCEI} or of an additional symmetry~\cite{FRITZSCH}. At HERA, FCNC interactions coupling a top quark to a light quark ($u$ or $c$) and a gauge boson would lead to single top production as illustrated in Fig.~\ref{fig:diagtop}. The crossed process $e^+ e^- \rightarrow t \bar{q} (\bar{t} q)$ is actively searched for at the LEP collider since its centre-of-mass energy is above the top production threshold. %----------------------------------------------------------- We consider here the most general effective Lagrangian proposed in~\cite{JOANNE} to describe FCNC top interactions involving electroweak bosons. It reads as~: $$ {\cal{L}}_{eff} = \sum_{U = u,c} i \frac{e e_U}{\Lambda} \bar{t} \sigma_{\mu \nu} q^{\nu} \kappa_{\gamma,U} U A^{\mu} + \frac{g}{2 \cos \theta_W} \bar{t} \left[ \gamma_{\mu} (v_{Z,U} - a_{Z,U} \gamma^5) + i \frac{1}{\Lambda} \sigma_{\mu \nu} q^{\nu} K_{Z,U} \right] U Z^{\mu} \quad + {\mbox {h.c.}} ,$$ where $\sigma_{\mu \nu} = (i/2) \left[ \gamma^{\mu}, \gamma^{\nu} \right]$, $\theta_W$ is the Weinberg angle, $q$ the four-momentum of the exchanged boson, $e$ and $g$ denote the gauge couplings relative to $U(1)$ and $SU(2)$ symmetries respectively, $e_U$ denotes the electric charge of up-type quarks, $A^{\mu}$ and $Z^{\mu}$ the fields of the photon and $Z$ boson, and $\Lambda$ denotes the scale up to which the effective theory is assumed to hold. By convention we set $\Lambda = m_t$ in the following. Only magnetic operators allow FCNC $t q \gamma$ couplings denoted by $\kappa_{\gamma, q}$, while $q-t$ transitions involving the $Z$ boson may also occur via vector interactions due to the non-vanishing $Z$ mass. The single top production in $ep$ collision is however largely dominated by the $t$-channel exchange of a $\gamma$ % with very low virtuality $Q^2$ and therefore we concentrate on the $\kappa_{\gamma,q}$ couplings only\footnote{ A different convention for the $\kappa_\gamma$ coupling is used here with respect to~\cite{h1toposaka}( $\kappa^0_\gamma$). The difference is that the quark electric charge introduced here in the normalization of the anomalous coupling $\kappa_\gamma=\kappa^0_\gamma/e_u =3/2*\kappa_\gamma^0 $. With this notation the limit on $\kappa^0_\gamma$ obtained in ~\cite{h1toposaka} $\kappa^0_\gamma<0.25$ reads $\kappa_\gamma<0.375$.} The possibility of anomalous single top production at HERA was first investigated in~\cite{FRITZSCH} where a model was built in which $\kappa_{\gamma, q} \propto m^2_{q}$, and therefore only the $tc \gamma$ coupling was relevant. We do not rely here on any assumption concerning the underlying theory and thus allow both couplings $\kappa_{\gamma,c}$ and $\kappa_{\gamma,u}$ to be present and not necessarily related to each other. The sensivity of HERA is naturally much higher for the coupling $\kappa_{\gamma,u}$ than for $\kappa_{\gamma,c}$ due to the more favourable parton density. The most stringent existing bound on $\kappa_{\gamma, u}$ comes from upper limits on radiative top decays set by the CDF Collaboration~\cite{CDF}~: $BR ( t \rightarrow u \gamma) < 3.2 \%$ at $95 \%$ confidence level (CL), leading to $\kappa_{\gamma, u} < 0.42$~\cite{JOANNE}. When $\kappa_{\gamma, u}$ is saturated to its upper bound, the single top cross-section at HERA has been calculated to be $\sim 1$ pb, sufficiently large to allow several single top events to be produced with the current integrated luminosity. Cross section calculations have recently been improved for next-to-leading order terms~\cite{nlotop}. The correction increases the leading order value by roughly 20\%, and is taken into account in the results derived in section 7. %====================================== \section{Monte-Carlo Event Generators} %====================================== A complete Monte Carlo simulation of the H1 detector response is performed for each possible SM background source and for the single top signal. For the neutral current (NC) or charged current (CC) deep inelastic scattering (DIS) background estimates we use the DJANGO~\cite{DJANGO} event generator, which includes first order QED radiative corrections. Simulation of real bremsstrahlung photons, based on HERACLES~\cite{HERACLES}, is also included. % QCD radiation at all orders is treated following the approach of the Color Dipole Model~\cite{CDM} and are implemented using ARIADNE~\cite{ARIADNE}. The hadronic final state is generated using the string fragmentation model~\cite{JETSET74}. The parton densities in the proton used to estimate DIS expectations are taken from the MRST~\cite{MRST} parametrization. The RAPGAP~\cite{rapgap} generator has also been used for the study of multijet production in NC DIS. For the direct and resolved photoproduction of light and heavy flavours, we use the PYTHIA MC event generator~\cite{PYTHIA} which relies on first order QCD matrix element % corrections to first order in $\alpha_s$, and uses leading-log parton showers and string fragmentation~\cite{JETSET74}. The GRV LO (GRV-G LO) parton densities~\cite{SFGRVGLO} in the proton (photon) are used. The photoproduction expectation has also been calculated using JetVip~\cite{jvp} program. The production of electroweak vector bosons $Z^0$ and $W^{\pm}$ was modelled using the EPVEC~\cite{EPVEC} event generator. Contributions from two-photon processes where one $\gamma$ originates from the proton were calculated using the LPAIR~\cite{LPAIR} event generator. The simulation of the single top signal relies on a specific event generator ANOTOP using the matrix elements of the complete $e + q \rightarrow e + t \rightarrow e + b + W \rightarrow e + b + f + \bar{f'}$ process as obtained from the CompHEP~\cite{COMPHEP} program. This allows a proper description of angular distributions. The BASES/SPRING~\cite{BASES} package is used to perform the numerical integration of the amplitudes and to generate events according to the differential cross-section. The parton showers approach~\cite{JETSET74} relying on the DGLAP~\cite{DGLAP} evolution equations is used to simulate QCD corrections in the initial and final states. The parton densities used~\cite{MRST} are evaluated at the scale of the top mass, in analogy with leptoproduction of heavy quarks. \section{Experimental Conditions} This analysis is based on $e^{\pm}p$ collisions recorded by the H1 experiment in the 1994-2000 period. It is restricted to periods where the central drift chambers, the liquid argon calorimeter and the luminosity system are active and fully operational. \par A detailed description of the H1 detector can be found in \cite{H1detector}. Only components essential for this analysis are shortly described here. A tracking system of central and forward drift chambers is used to measure the charged particle trajectories and to determine the interaction vertex. Particle transverse momenta are determined from the curvature of the trajectories in a magnetic field of 1.15 Tesla. %yields a measurement of the particle momenta with a nominal %resolution $\sigma_{P}/P^2=3\times10^{-3}$ GeV$^{-1}$. Hadronic and electromagnetic final state particles are absorbed in a highly segmented calorimeter \cite{h1cal}, which is 5 to 8 interaction lengths deep depending on the polar angle of the particle. %Electromagnetic shower energies are measured with a precision of %$\sigma (E)/E = 12 \% / \sqrt{E/\mathrm{GeV}} \oplus 1\%$ and % hadronic shower energies with %$\sigma (E)/E = 50 \% / \sqrt{E/\mathrm{GeV}} \oplus 2 \%$. %The electro-magnetic energy scale is known to the level of 0.7-3\% %depending on the polar angle. The hadronic energy scale is understood at the 2\% %level when comparing to the Monte Carlo expectations. The calorimeter is surrounded by a superconducting coil and an iron yoke instrumented with streamer tubes. Leakage of hadronic showers outside the calorimeter is measured from an analogue charge sampling of the streamer tubes (Tail Catcher). % with a resolution of $\sigma (E)/E = 100 \% / \sqrt{E/\mathrm{GeV}}$ . Tracks of penetrating charged particles, such as muons, escaping the calorimeter are reconstructed from their hit pattern in the streamer tubes with an efficiency higher than 90\%. The trigger condition for high transverse energy interactions is based on calorimeter signals. The trigger efficiency is higher than 95\% for events with a scattered electron with an energy above 10 GeV, and higher than 85\% for events with a calorimetric missing transverse momentum greater than 25 GeV. For multi-jet events the trigger efficiency is 100\%. \section{Search for Single Top Production in the Leptonic Channel} The search of top quark decays in the leptonic channel is based on the selection of events with isolated leptons and missing transverse energy performed in~\cite{h1isolbudapest}. The basic criteria are the presence of a lepton at high transverse momentum $P_T^\ell >10$~GeV with missing $P_T$ in the event above 12 GeV. This selection (W search criteria) is further optimized to separate top production from Standard Model W production: \begin{itemize} \item {\bf Cut on the transverse momentum of the hadronic system}\\ In the top decays, the hadronic system is expected to have a high transverse momentum. The events are accepted if the transverse momentum of the hadronic system $P_T^X$ is higher than 25~GeV. The expected $P_T$ distributions of the highest $P_T$ jet in two angular domains are presented in the figure~\ref{ptthcut}. The highest $P_T$ hadronic jet is required to have $P_T^{jet} >25$ GeV. This threshold is set to 35 GeV in the case where the highest $P_T$ jet has a polar angle with respect to the proton direction of $\theta_{jet}<35^\circ$. \item {\bf Transverse mass of lepton-neutrino system}\\ This quantity is defined as the invariant mass of the two massless vectors obtained by projecting the lepton and neutrino momenta in the transverse plane, where the transverse neutrino momentum is calculated from the missing transverse momentum $P_T^{miss}$ in the event: \begin{equation} M_T^{\ell \nu} = \sqrt{\left(|\vec{P}_T^\ell|+|\vec{P}_T^{miss}| \right)^2 - \left(\vec{P}_T^\ell+\vec{P}_T^{miss} \right)^2} . \label{eq:mt} \end{equation} For W leptonic decays, the transverse mass of the lepton-neutrino system is centered around the W mass and has a tail towards low masses. In the standard model W production, the production of the charged lepton and neutrino can also proceed through photon-W scattering, while only real W decays produce leptonic final states in top induced events. In order to reduce the contribution from off-shell processes, a cut is applied on the transverse mass $M_T^{\ell\nu}>10$~GeV. \item {\bf Charge of the observed lepton}\\ The production of top quarks in $\gamma-u$ fusion yields t-quarks with charge $+2/3$ (the $\bar{\mathrm t}$ production via fusion with sea quarks $\gamma-\bar{u}$ is supressed by a factor of ~80). The subsequent decay $t \rightarrow bW^+ (\rightarrow \ell^+\bar{\nu})$ produces only positively charged isolated leptons. In order % to reduce the standard $W^\pm$ production contribution to reduce contributions other than top to the final sample, leptons for which the charge measurement yields the wrong sign with a precision better than $2\sigma$ are rejected. The reliability of the charge measurement at high $P_T$ has been tested using a sample of neutral current events collected in e$^+$p collisons. The scattered electrons are required to have transverse momentum measured from calorimeter deposit above 20 GeV and corresponding track transverse momentum above 10 GeV. The track corresponding to the scattered electron has to be isolated and must have a momentum measurement better than two standard deviations. The wrong sign assignment rate is below 1\% in this sample. In a subsample of forward electrons with the polar angle $\theta <50^\circ$, where most of the searched signal is expected, the wrong charge assignment has been measured in the data to be less than 2\%. \end{itemize} \par The overall results are presented in the tables~\ref{tableback1} and \ref{tableback2} for an analysed data sample corresponding to 101.6~pb$^{-1}$ in e$^+$p collisons and 13.6~pb$^{-1}$ in e$^-$p collisions. In $e^+p$ data 4 events containing electrons and 6 events containing muons have been observed at $P_T^X>25 $ GeV~\cite{h1isolbudapest}. After the full top selection described above, 3 electron events and 2 muon events remain as top candidates for an expectation of $0.75\pm0.18$ ($e^+p$) plus $0.13\pm0.04$ ($e^-p$) for the electron channel and $0.77\pm0.21$ ($e^+p$) plus $0.12\pm0.03$ ($e^-p$) for the muon channel. %No candidate is found in the $e^-p$ data sample. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[hhh] \begin{center} \begin{tabular}{|c|c|c|c|c||} \hline & \multicolumn{2}{|c|}{W search cuts and $P_T^X>25$~GeV} & \multicolumn{2}{c|}{Top selection} \\ \hline & Electron Channel & Muon Channel & Electron Channel & Muon Channel \\ \hline \hline Data & 4 & 6 & 3 & 2 \\ \hline \hline Total SM & $1.29\pm 0.33$ & $1.54\pm 0.41$ & $0.75\pm 0.18$ & $0.77\pm 0.21$ \\ \hline W only & $1.05\pm 0.32$ & $1.29\pm 0.39$ & $0.51\pm 0.16$ & $0.68\pm 0.19$ \\ \hline Top efficiency & 43\% & 51\% & 37\% & 45\% \\ \hline \end{tabular} \caption{Observed and predicted number of events with isolated leptons and missing transverse momentum for $e^+p$ data in $101.6$ pb$^{-1}$} \label{tableback1} \end{center} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[hhh] \begin{center} \begin{tabular}{|c|c|c|c|c||} \hline & \multicolumn{2}{|c|}{W search cuts and $P_T^X>25$~GeV} & \multicolumn{2}{c|}{Top selection} \\ \hline & Electron Channel & Muon Channel & Electron Channel & Muon Channel \\ \hline \hline Data & 0 &0 & 0 & 0 \\ \hline \hline Total SM & $0.26 \pm 0.06 $ & $ 0.20 \pm 0.06 $ & $0.13\pm0.04$& $0.12\pm0.03$ \\ \hline $W$ only & $0.16 \pm 0.05 $ & $ 0.18 \pm 0.07$ & $0.07\pm0.02$& $0.10\pm0.03$\\ \hline Top efficiency & 43\% & 51\% & 37\% & 45\% \\ \hline \end{tabular} \caption{Observed and predicted number of events with isolated leptons and missing transverse momentum for $e^-p$ data in $13.6$ pb$^{-1}$ } \label{tableback2} \end{center} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \par In order to calculate the invariant masses of the lepton-neutrino and lepton-neutrino-hadrons systems, the event kinematics has to be reconstructed. The following variables are used to quantify the event kinematics: \begin{itemize} \item $\vec{P}_T^\ell$: Transverse momentum vector of the isolated lepton. The calculation of the transverse momentum is performed using calorimetric information for electrons and central tracker information for muons. %\item $\theta^\ell$ : Polar angle of the isolated lepton. The polar angle %is measured relative to the $z$-axis which points in the direction of the %incoming proton. \item $E^\ell$: Energy of the isolated lepton. \item $\vec{P}_T^X$: Transverse momentum vector of the hadronic system. It is calculated as the vector sum of all energy deposits in the liquid argon calorimeter and the tail catcher calorimeter not including energy deposited by any additional leptons. %(i.e. the positron in event MUON-3 and ELECTRON-3). %\item $\theta^X$ : Polar angle of the hadronic system. \item $E^X$: Energy of the hadronic system. \item $\vec{P}_T^{miss}$: Total missing transverse momentum vector of the event. It is defined as the vector sum of transverse momenta of all final state particles: $\vec{P}_T^{miss} =-(\vec{P}_T^{lepton(s)} + \vec{P}_T^{X})$. The missing transverse momentum is attributed to the hypothetical neutrino. \item $\delta^{vis}$: Total visible event balance in longitudinal momentum, defined as the scalar sum of $\left( E-P_z \right)$ over all final state particles: $\delta^{vis} = \left( E-P_z \right)^{lepton(s)} + \left( E-P_z \right)^X$ %\item $M_T^{\ell \nu} = \sqrt{\left(|\vec{P}_T^\ell|+|\vec{P}_T^{miss}| \right)^2 - \left(\vec{P}_T^\ell+\vec{P}_T^{miss} \right)^2}$ : Transverse mass of the lepton-neutrino system. The missing transverse momentum is attributed to the hypothetical neutrino. \item Transverse mass of the lepton-neutrino system defined in equation~\ref{eq:mt}. \end{itemize} \par In order to compute the complete event kinematics the neutrino four-vector must be reconstructed. The transverse momentum of the neutrino corresponds to the total missing transverse momentum $\vec{P}_T^{miss}$ of the event. Regarding the longitudinal momentum of the neutrino two cases have to be treated separately: \begin{itemize} \item {\it Tagged events:} In this case the scattered electron is detected in one of the calorimeters. In the muon channel this means that the event contains an identified electron and in the electron channel the event contains an additional electron of lower transverse momentum. For tagged events, the invariant mass of the lepton-neutrino-hadron system is computed using the neutrino kinematics deduced from longitudinal energy conservation. We obtain $\left( E-P_z \right)^{\nu} = 55$ GeV $- \delta^{vis}$ using the event balance in longitudinal momentum as mentioned above. For two events out of the ten with $P_T^X>25$~GeV which are quoted in table~\ref{tableback1} this method can be applied. \item {\it Untagged events} The scattered electron is not detected and therefore its longitudinal momentum unknown. A constraint on the invariant mass of the lepton and neutrino from the $W$ decay has to be applied: \begin{equation} M_{\ell\nu} = \sqrt{P_\ell^2 + P_\nu^2 + 2P_eP_\nu}\ \approx \sqrt{2P_eP_\nu} = M_W = \ 80.2 \ \mbox{GeV} \end{equation} with $P_l, P_\nu$ denoting the four-vectors of the lepton and neutrino respectively. This constraint on the $W$ mass yields two possible solutions for $\left( E-p_z \right)^{\nu}$, one corresponding to a backward neutrino (solution 1), the other to a forward neutrino (solution 2) relative to the lepton direction. Using the two possible solutions for the neutrino, the invariant mass of the lepton-neutrino-hadrons system $M(\ell\nu X)$ can be calculated. All solutions that do not meet one of the following requirements are rejected as being unphysical: \begin{itemize} \item $M(\ell\nu X)<\sqrt{s}$ where $\sqrt{s}$ is the electron-proton cms energy (300 GeV or 320 GeV depending on data taking period). \item $0$ GeV $<\left( E-P_z \right)^{\nu}<55$ GeV \item $\left( E-P_z \right)^{\nu} + \delta^{vis} <75$ GeV \item $E^\nu+E^X+E^{lepton(s)} < 1000$ GeV \end{itemize} The latter two requirements ensuring energy and $E-p_z$ conservation were optimized on a sample of generated top events in order to leave some scope for fluctuations in the energy measurement. \\ In case no such solution exists, the measurement errors on the energy of the hadronic final state $E^X$ (electron channel) or the transverse momentum of the muon $P_T^\mu$ (muon channel) are taken into account being the dominant errors in the particular channel. New masses are computed using values of $E^X$ or $P_T^\mu$ varied by $\pm 1\sigma$. If a solution is still not found then a $\pm 2\sigma$ variation is performed. The solution yielding the lowest mass is chosen as lower $1\sigma$ or $2\sigma$ limit. \end{itemize} This mass reconstruction procedure has 80\% reconstruction efficiency in the electron channel and 65\% in the muon channel for Monte Carlo top events. In figure \ref{topmasres} distributions of the reconstructed top mass are shown for ANOTOP Monte Carlo events in both electron and muon channel. The widths of the mass distributions are determined to $\sigma (M_{top})= 20$ GeV for electrons and $\sigma (M_{top})= 22$ GeV for muons.\\ The mass solutions thus obtained for the isolated lepton events with $P_T^X > 25$~GeV can be found in table \ref{tab_topmasses}. Two events (one electron and one muon) contain the scattered electron and therefore the ``tagged'' method can be applied. For the two tagged events, masses reconstructed with the ``tagged'' and one of the solutions of the ``untagged'' method are compatible. In the final top selection as defined above, the first three of the four observed electron events and the two last muon events in table~\ref{tab_topmasses} are selected as top candidates. \begin{table}[htb] \begin{tabular}{|l|l|cc|cc|c|} \hline & PT(X) & \multicolumn{2}{|c|}{Untagged Solution 1} & \multicolumn{2}{|c|}{Untagged Solution 2} & Tagged Solution\\ & & Mass & $E-P_z$ & Mass & $E-P_z$ & Mass\\ \hline $e^+$ top cand. & 41& $ 159\pm 7$ & 61& $ 136\pm 6$ & 21 & -- \\ $e^+$ top cand. & 43& -- & -- & $ 166\pm 8$ & 54 & $ 165\pm 6$ \\ $e^+$ top cand. & 39& $ 178\pm 5$ & 39& $ 156\pm 7$ & 21 & -- \\ $e^+$ & 27& $ 234 \pm 15 $ & 65 & $ 199 \pm 14 $ & 38 & -- \\ \hline $\mu^+$ & 42& -- & -- & $ 146\pm 7$ & 19 & --\\ $\mu^-$ & 27& $ 152\pm 12$ & 53& $ 129\pm 6$& 34& $ 156\pm 10$\\ $\mu^-$$ (1\sigma)$ & 59& $ 180 $ & 67& $ 188 $ & 37 & --\\ $\mu $ $(2\sigma)$ & 30& $ 157$ & 53& $ 139$ & 22 & --\\ $\mu^+$ top cand. & 67& -- & -- & $ 181\pm 10$& 19 & --\\ $\mu^+$ top cand. & 50& -- & -- & $ 174\pm 12$ & 39 & -- \\ \hline \end{tabular} \caption{$M_{\ell\nu X}$ calculation for the ten events with $P_T^X > 25$~GeV. ``Untagged'' solutions (mass and total $E-P_z$) using a W constraint are presented for all the events. In two events the scattered electron is detected and the ``tagged'' mass solution using an $E-P_z$ constraint can be obtained. The events selected as top candidates are indicated.} \label{tab_topmasses} \end{table} The total lepton-neutrino-hadrons mass distributions of the final top candidates are compared to the Standard Model prediction in figure~\ref{mtmlnux}. \section{Search for Single Top Production in the Hadronic Channel} \label{sec:hadrons} The top hadronic channel has been searched in a smaller data sample taken in the period 1994-1997 in $e^+p$ mode at $\sqrt{s}=300$~GeV, corresponding to an integrated luminosity of 36.5~pb$^{-1}$. The decay cascade $t\rightarrow bW(\rightarrow q\bar q)$ yields events with at least three jets with high transverse momentum $P_T$. The main Standard Model QCD background is the electro- or photoproduction of high $P_T$ jets. The search for those events is performed using a $K_T$ algorithm \cite{kt} based on calorimetric energy deposits. Events with at least three jets fulfilling $P_T^{Jet1}>25$ GeV, $P_T^{Jet2}>15$ GeV and $P_T^{Jet3}>10$ GeV are selected. In order to reduce the neutral current (NC DIS) contribution, events with an identified electron are removed from the sample. NC DIS events where the electron is being misidentified as a hadronic jet are supressed by requiring either the electromagnetic energy fraction of the reconstructed jets to be less than 90\% or the jet size defined in the $\eta -\phi$ plane to be larger than 0.1. In figure \ref{jet:control} the number of selected events is shown as a function of the transverse momentum of the first jet $P_T^{Jet1}$ and the invariant mass $M_{ij}$ of the three dijet systems together with the prediction of the Monte Carlo generator PYTHIA \cite{PYTHIA}. Using an overall normalization factor of 1.2 determined to fit the measured cross sections, which could account for corrections to PYTHIA (leading order with parton showers) calculation, the data are well described by the MC prediction. The remaining NC background estimated with the Monte Carlo model RAPGAP \cite{rapgap} is less than 7\% on average. Top induced events are expected to have high total transverse energy and 2- and 3-jet invariant masses close to the $W$ and top mass, respectively. To select top candidates in the data sample defined above the invariant dijet mass of at least one of the three dijet systems has to fulfill $70