%================================================================ % LaTeX file with preferred layout for the contributed papers to % the ICHEP Conference 98 in Vancouver % process with: latex hep98.tex % dvips -D600 hep98 %================================================================ \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 %===============================title page============================= % Some useful tex commands % \newcommand{\GeV}{\rm GeV} \newcommand{\TeV}{\rm TeV} \newcommand{\pb}{\rm pb} \newcommand{\cm}{\rm cm} \newcommand{\hdick}{\noalign{\hrule height1.4pt}} % Higgs Commands % \newcommand{\mhpp}{\mbox{$M_{H^{\pm\pm}}$}} \newcommand{\mhpp}{\mbox{$M_H$}} \newcommand{\hpp}{\mbox{$H^{\pm\pm}$}} % \begin{document} \pagestyle{empty} \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 104} & 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 Search for Doubly-Charged Higgs Production at HERA } \vspace*{1cm} {\Large H1 Collaboration} \end{center} \begin{abstract} \noindent A search for the single production of doubly-charged Higgs bosons (\hpp) is performed in the framework of models where a Higgs triplet is coupled to leptons of the $i^{th}$ generation via Yukawa couplings $h_{ii}$. % The search is motivated by the observation of a few multi-electron events with a large di-electron mass, in a domain where the Standard Model expectation is small. % % The signal is searched for in di- and tri-electron % (di-muon) final states, % using a sample of $e^{\pm}p$ events corresponding to % $115.2$ ($70.9$)~pb$^{-1}$ of data collected with the H1 detector at HERA. % The signal is searched for in decay modes of the \hpp~in either electrons or muons, using a sample of $e^{\pm}p$ events corresponding up to $115.2$~pb$^{-1}$ of data collected with the H1 detector at HERA. % % A good overall agreement is found with the Standard Model expectation, % although the number of events observed % in a general multi-electron analysis % with a high di-electron mass % is in slight excess compared to the Standard Model prediction. % Only one of the multi-electron events is found to be compatible with the hypothesis of the decay of a heavy Higgs boson. Assuming that the doubly-charged Higgs only decays to electrons, we set a lower limit of about $131$~GeV on the \hpp~mass for a value $h_{ee} = 0.3$ of the coupling, which corresponds to an interaction of the electromagnetic strength. This is the first search for doubly-charged Higgs production at HERA. \end{abstract} \end{titlepage} \pagestyle{plain} % ======================= \section{Introduction} % ======================= The H1 collaboration recently reported~\cite{me} a preliminary measurement of multi-electron production at high transverse momentum at HERA. % At large di-electron masses, the % number of observed events is in slight excess compared % to the Standard Model (SM) prediction. Six events were observed with a di-electron mass above 100~GeV, a domain where the Standard Model (SM) prediction is low. A preliminary measurement of multi-muon production in H1~\cite{mm} showed a good agreement between the data and the SM expectation over the whole mass range. Based on these analyses, a search for the single production of doubly-charged Higgs bosons (\hpp), which may lead to high mass multi-lepton events, has been performed and is presented in this paper. % % In this paper, we present % a search for the single production % of doubly-charged Higgs bosons (\hpp), % which may lead % to high mass multi-lepton events. % In the mass range covered by this analysis, the decay mode of the doubly-charged Higgs boson into a pair of like-sign charged leptons is expected to be dominant. % In the mass range covered by this analysis, % the dominant decay mode of the doubly-charged Higgs boson % is expected % to be a pair of like-sign charged leptons. Other decay modes are considered to be either theoretically suppressed or kinematically forbidden. This signal is searched for in di- and tri-electron as well as di-muon final states. % The analysis makes use of all data collected from % 1994 to 2000 corresponding to an integrated luminosity of % 115.2~pb$^{-1}$. For the electron final states, the analysis makes use of all data collected from 1994 to 2000 corresponding to an integrated luminosity of 115.2~pb$^{-1}$. For the muon final state 70.9 pb$^{-1}$ are used. % This is the first search for doubly-charged Higgs production at HERA. % ========================== \section{Phenomenology} % ========================== Doubly-charged Higgs bosons appear in various extensions of the Standard Model, in which the usual Higgs sector is extended by one or more %triplet(s) with non-zero hypercharge~\cite{HTM,pati,moha1,moha2}. triplet(s) with non-zero hypercharge~\cite{HTM,pati,moha1}. Examples are provided by some Left-Right Symmetric (LRS) models~\cite{moha3,moha4}, where the extended symmetry $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ is spontaneously broken to the SM symmetry $SU(2)_L \times U(1)_Y$ by a $SU(2)_R$ triplet of scalar fields, whose neutral component acquires a non-vanishing vacuum expectation value (vev). The Higgs triplet(s) may be coupled to matter fields via Yukawa couplings. Whereas all charged fermions acquire their masses via their couplings with Higgs doublet(s), the vev of the neutral component of a Higgs triplet can give a Majorana mass to neutrinos, which is of particular interest since the existence of non-zero neutrino masses is suggested by recent experimental data. At the tree level, doubly-charged Higgs bosons couple only to charged leptons and to other Higgs and gauge bosons. Couplings to quark pairs are not allowed by charge conservation. % Although doubly-charged Higgs bosons may arise in various scenarios extending the SM, their couplings to charged leptons can be generically described by the Lagrangian~: % \begin{equation} {\cal{L}} = h^{L,R}_{ij} H^{--} \bar{\ l_i}^c P_{L,R} \ l_j \qquad {\mbox{ + \ h.c.}} \label{eq:lag} \end{equation} % where $i,j = e, \mu, \tau$ denote generation indices, $P_{L,R} = (1 \mp \gamma^5)/2$, $l$ are the charged lepton fields, and the superscript $^c$ denotes the charge conjugate spinors. The Yukawa couplings $h^{L,R}_{ij}$ are free parameters of the model. % If the $H^{--}$ field belongs to a $SU(2)_L$ triplet, $H^{--}$ couples only to left-handed leptons; only the projector $P_L$ and the couplings $h^L_{i,j}$ are then involved in equation~(\ref{eq:lag}). Models with an additional group $SU(2)_R$ and a $SU(2)_R$ Higgs triplet provide a $H^{--}$ field coupling to right-handed leptons via $h^R_{i,j}$. In the particular case of LRS models two doubly-charged Higgs bosons $H^{--}_L$ and $H^{--}_R$ are present, which couple to left-handed and right-handed leptons respectively. % Since the production processes at HERA are insensitive to the chirality of the lepton fields, we consider here the generic case of a doubly-charged Higgs boson, which couples to either left-handed or right-handed leptons, and denote its Yukawa couplings by $h_{ij}$ in the following. For a non-vanishing coupling $h_{ee}$ the single production of a doubly-charged Higgs boson is possible via the diagrams shown in Fig.~\ref{feyn}, where a photon is radiated by the proton or one of its constituent quarks\footnote{The contribution of $Z$ exchange in the diagrams shown in Fig.~\ref{feyn} can be safely neglected.}. The proton may be broken or remain intact during this interaction, leading to an inelastic or elastic reaction, respectively. % The phenomenology of doubly-charged Higgs production at HERA was first discussed in Ref.~\cite{zeus}, in which only the elastic channel was considered. % When only diagonal couplings $h_{ii}$ are present in equation (\ref{eq:lag}), the production process $e^{\pm}p\rightarrow e^{\mp}H^{\pm\pm}X$ is followed by the decays $H^{\pm\pm} \rightarrow e^{\pm} e^{\pm} (\mu^{\pm} \mu^{\pm}, \tau^{\pm} \tau^{\pm} )$. Non-diagonal couplings ($h_{ij}$ with $i \ne j$) would allow e.g. $e^{\pm}p\rightarrow \mu^{\mp}H^{\pm\pm}X$ followed by the decays $H^{\pm\pm} \rightarrow e^{\pm}\mu^{\pm}$ ($e^{\pm} \tau^{\pm}$, $\mu^{\pm} \tau^{\pm}$ ). %\section{Existing Limits} The indirect constraints~\cite{indlim1,indlim2,indlim3,indlim4} on doubly-charged Higgs can be parameterized in terms of the Higgs mass \mhpp~and the Higgs couplings to leptons. % $h_{ij}$ % where $i,j=e,\mu,\tau$~\cite{indlim1,indlim2,indlim3,indlim4}. The off-diagonal products $h_{ij}h_{i'j'}$ with either $i\ne j$ or $i'\ne j'$ suffer from stringent constraints for the first and second generation charged leptons from bounds on $\mu \rightarrow e^+e^-e^-$ and $\mu \rightarrow e\gamma$ decays~\cite{indlim4}. Constraints on purely diagonal couplings are less stringent. % Assuming that only purely diagonal couplings are non-vanishing, % the existing constraints are less stringent. They come from the possible contribution of virtual $H^{\pm\pm}$ exchange to Bhabha scattering in $e^+e^-$ collisions which yields~\cite{indlim1} $h_{ee} \le 3.1 \times 10^{-3} {\rm GeV}^{-1} M_{H}$, using $e^+ e^-$ data taken at center of mass energies of $\sim 30$~GeV, and from the search for muonium $(\mu^+e^-$) to anti-muonium $(\mu^-e^+$) conversion~\cite{indlim1,indlim4} which yields $\sqrt{h_{ee}h_{\mu\mu}} \le 7.6 \times 10^{-3} {\rm GeV}^{-1} M_{H}$. For the coupling $h_{\mu\mu}$ alone, avoiding possible extra contributions to $(g-2)_{\mu}$ yields $h_{\mu\mu} \le 5 \times 10^{-3} {\rm GeV}^{-1}\mhpp$. No constraint involving the $\tau$ lepton has been established. % For a coupling of electromagnetic strength, % $h_{ee}=e$ with $e= \sqrt{4\pi\alpha}$, % doubly charged Higgs wich would decay with 100\% branching ratio % into like-sign and like-flavour charged leptons are allowed for masses % $M_{H^{\pm\pm}} > 100 geV$. Previous direct searches for $H^{\pm\pm}$ pair production have been performed by the LEP experiments. For pair production in $e^+e^-$ collisions, the kinematic reach is restricted to $\mhpp < \sqrt{s}/2$. Masses $\mhpp \leq 45.6$~GeV have been excluded by the OPAL experiment analyzing $Z$ decays at LEP~I~\cite{opallep1}. This was extended by OPAL to $\mhpp \leq 98.5$~GeV in a search~\cite{opallep2} for \hpp~pair production % in the $s$-channel at center of mass energies between $189$ and $209$ GeV. Similar results are derived for any relative values of the $h_{ee}$, $h_{\mu\mu}$ and $h_{\tau\tau}$ couplings assuming a $100\%$ decay branching fraction into charged leptons pairs. A similar lower limit on $\mhpp$ was obtained recently by the DELPHI experiment at LEP~II~\cite{delphi} assuming that the Higgs dominantly decays into a pair of $\tau$ leptons. % in the $\hpp \rightarrow \tau^{\pm}\tau^{\pm}$ channel. In this paper we only consider diagonal couplings for which the existing bounds are less stringent and the Higgs decays into electrons and muons. This leads to final states with three leptons, with two of them like-sign and expected at large invariant mass. It should be noted that the $e^{\pm}$ which does not come from the Higgs decay is often backscattered in the direction of the incident proton momentum and may be lost in the beam pipe. % ================================================================== \section{Simulation of the Signal and Standard Model Backgrounds} % ================================================================== The simulation of the doubly-charged Higgs signal, as well as the calculation of the signal cross-section, %on a Monte Carlo program is performed using the CompHEP~\cite{comphep} package to evaluate the (lowest order) squared amplitudes corresponding to the elastic and inelastic processes\footnote{ The CompHEP implementation of the doubly-charged Higgs Lagrangian was used in~\cite{ROMANENKO} to calculate $e^- \gamma \rightarrow e^+ \mu^+ \mu^-$ cross-sections. Note that the $e^- \gamma \rightarrow e^+ H^{--}$ cross-sections obtained with CompHEP do not seem to agree with those obtained from PYTHIA 6.206~\cite{pythia}.}. The differential cross-sections are integrated with the VEGAS~\cite{VEGAS} package. The parton densities in the proton used to estimate the inelastic contribution to the cross-section are taken from the CTEQ4L~\cite{cteq} parametrization. These are evaluated at the scale $\sqrt{Q^2}$, where $Q^2$ denotes the squared momentum transfer at the hadronic vertex. The inelastic cross-section is calculated in the range $Q^2 > 4$~GeV$^2$. % The contribution to the inelastic cross-section of the exchange of lower $Q^2$ photons (``quasi-elastic" cross-section) has not been estimated yet and is conservatively neglected. % At the generator level, 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 hadronization of colored particles is then performed via an interface to the PYTHIA~\cite{pythia} program. For the elastic contribution, the $e^{\pm} p \rightarrow e^{\mp} H^{\pm \pm} p$ cross-section is calculated by adding explicitely the proton to the particle contents of CompHEP. The photon-proton-proton current is described by the electric and magnetic form factors $G_E$ and $G_M$. The usual dipole fit $$ G_E(Q^2) \simeq G_M(Q^2) / \mu_p \simeq G_D(Q^2) \equiv (1 + Q^2 / (0.71\rm~GeV^2))^{-2} $$ is used, where $\mu_p = 2.973$ is the magnetic moment of the proton. Using a linear fit for $G_E$ which takes into account the experimentally observed~\cite{JLAB} decrease of $\mu_p G_E / G_M$ with increasing $Q^2$ changes the elastic cross-section by less than $\sim 2\%$. For a Yukawa coupling $h_{ee}=0.3$, the sum of the elastic and inelastic contributions leads to a cross-section of $\sim 0.28$ pb ($\sim 0.03$ pb) for a Higgs mass of $100$ GeV ($150$ GeV). The inelastic contribution is found to be $\sim 1/3$ of the elastic contribution in the mass range $80-150$~GeV. The theoretical uncertainty on the obtained cross-section is $\sim 4\%$ in this mass range. This is obtained by assessing an uncertainty of $\pm 2 \%$ on the ratio $G_M(Q^2) / G_D(Q^2)$~\cite{SLAC}, and by varying the scale at which the parton densities are evaluated to calculate the inelastic contribution between $\sqrt{Q^2} / 2$ and $2 \sqrt{Q^2}$. % $4 \% - 6 \%$ in this mass range. It is largely dominated by % the uncertainty due to the choice of the scale at which the % parton densities are evaluated to calculate the inelastic contribution. % The above numbers were obtained by varying this scale between % $\sqrt{Q^2} / 2$ and $2 \sqrt{Q^2}$. % Simulation of the signal events and cross-section computations % have been done using a Higgs Triplet Model~\cite{modelHTM} % implemented in COMPHEP~\cite{comphep} interfaced with PYTHIA~\cite{pythia} % which takes care of the hadronization and fragmentation of the decay particles, % using the CTEQ4L~\cite{cteq} parton distributions functions. % The inelastic cross-section contribution is found to be $\sim 1/3$ % of the elastic contribution in the range $\mhpp=80-150$~GeV. % The Monte Carlo samples are subject to a full simulation of the H1 detector % which takes into account the effects of energy loss, multiples scattering and % showering in the detector. The dominant SM contributions involved in multi-lepton production at HERA come from the interaction of two photons radiated from the incident electron and proton. Among these, the Bethe-Heitler process, where a lepton is exchanged in the $t$-~or $u$-channel, is dominant. The Cabibbo-Parisi process, which involves an $e^+e^-$ interaction where one of the electrons comes from a photon radiated from the proton, contributes at high transverse momentum only. The Drell-Yan process was calculated in~\cite{dy} and was found to be negligible. % The Drell-Yan process is negligible in the entire measured % phased space~\cite{dy}. All these processes are simulated with the GRAPE Monte Carlo generator~\cite{grape}, which also takes into account contributions from Bremsstrahlung with subsequent photon conversion into a lepton pair and electroweak contributions like real $Z$ production with decay to $l^+ l^-$. For multi-muon production additional contributions are considered, using DIFFVM~\cite{DIFFVM} for the $\Upsilon$ resonance, LPAIR~\cite{lpair1,lpair2} for muons arising from $\gamma\gamma \rightarrow \tau \tau$ and AROMA~\cite{aroma} for muons stemming from semi-leptonic decays in open heavy quark production ($c\bar{c}$ and $b\bar{b}$). Experimental backgrounds are also present for multi-electron production, i.e. processes where, in addition to the scattered electron, one or more final state particles may be misidentified as electrons. They come dominantly from Neutral Current Deep Inelastic Scattering (NC-DIS) and from elastic Compton scattering, where a jet or a photon is misidentified as an electron. These processes are simulated with the DJANGO~\cite{django} and WABGEN~\cite{wabgen} generators. All Monte Carlo samples are subject to a full simulation of the H1 detector which takes into account the effects of energy loss, multiple scattering and showering in the detector. % ======================== \section{Data Analysis} % ======================== For the $e^{\pm}p \rightarrow e^{\mp}\hpp X \rightarrow e^{\mp}e^{\pm}e^{\pm}X$ analysis we use the full $e^{\pm}p$ dataset recorded by the H1 experiment in the period 1994-2000. The total integrated luminosity of $115.2$~pb$^{-1}$ is shared between $36.5$~pb$^{-1}$ and $65.1$~pb$^{-1}$ of $e^+p$ collisions recorded at center of mass energies $\sqrt{s}$ of $300$~GeV and $318$~GeV respectively, and $13.6$~pb$^{-1}$ of $e^-p$ collisions recorded at $\sqrt{s}=318$~GeV. For the $e^{\pm}p \rightarrow e^{\mp}\hpp X \rightarrow e^{\mp}\mu^{\pm}\mu^{\pm}X$ analysis we use an $e^{\pm}p$ sample of $70.9$~pb$^{-1}$ at $\sqrt{s}=318$~GeV. % The data selection and the SM backgrounds estimations are % identical to those used in multi-electron~\cite{me} % and muon pair~\cite{mm} production measurements performed at H1. % ... dire que ce qui suit = preselection; ensuite on a les % ... cuts specifiques au signal.. % This analysis uses the sample of multi-lepton events selected % to measure multi-electron~\cite{me} and muon pair~\cite{mm} production % in H1. This analysis is based on the H1 measurements of multi-electron production at high transverse momentum~\cite{me} and of multi-muon production~\cite{mm}. % The main selection criteria are summarized below and in Table 1. % The selection of multi-electron events requires two central electron\footnote{Unless otherwise stated, the term ``electron'' is used in this paper to describe generically electrons or positrons.} candidates ($20^{\circ} < \theta^e < 150^{\circ}$, where $\theta^e$ is the electron polar angle measured with respect to the proton beam direction) one of which must have a transverse momentum $P_T^{e1} > 10$~GeV and the second $P_T^{e2} > 5$~GeV. Additional electron candidates are selected in the region ($5^{\circ} < \theta^e < 175^{\circ}$) when % no explicit $P_T^e$ cut. their energy is above 5~GeV (10~GeV if $5^{\circ} < \theta^e < 20^{\circ}$). % The selected events are classified as di-electron (``2e'') in the case that only the two central electron candidates are visible, and tri-electron (``3e'') in the case in which exactly one additional electron candidate is identified. The muon-pair selection requires two central muon candidates ($20^{\circ} < \theta^{\mu} < 160^{\circ}$), with minimal transverse momentum requirements ($P_T^{\mu1} > 2$~GeV, $P_T^{\mu2} > 1.75$~GeV), and a muon pair invariant mass % $M_{\mu\mu} > 5$~GeV. % M_{ll} est reserve (cf plus bas...) plutot garder M_{12} above 5~GeV. % After this selection, we observe $105$ ($16$) data events in the di-(tri-) electron final state, which is to be compared with $118.2 \pm 12.8$ ($21.6\pm 3.0$) from SM expectation, and $1243$ data events in the di-muon final state which is to be compared with $1253\pm 125$ % $1189\pm 119$ from SM expectation. % The distributions of the invariant mass $M_{12}$ of the two highest $P_T$ electrons and of the two muons $M_{\mu\mu}$ are shown in Fig.~\ref{invmass}. % superimposed with the expected invariant % mass from a Higgs of 130~GeV (arbitrary normalization). Overall, a good agreement is observed between data and SM expectation. % although a few events are observed at large invariant mass in % the multi-electron analysis. As can been seen in Fig.~\ref{invmass}, the SM expectation is largely dominated by $\gamma \gamma$ contributions. In the multi-electron analysis and for masses $M_{12} > 100$~GeV, three ``2e" events and three ``3e" events are observed, compared to SM expectations of $0.25 \pm 0.05$ and $0.23 \pm 0.04$ respectively. Further selection criteria are then applied, which are designed to maximize the sensitivity of the analysis to an eventual \hpp~signal. For a given \hpp~mass $M_H$, we define $M_{ll}$ as the invariant mass of the two leptons (or, for ``3e'' events, the invariant dilepton mass which is closest to $M_H$). % For signal events where the Higgs decays into electrons (muons), % the width $\sigma$ of the $M_{ll}$ % distribution varies from $\sim 3$ ($\sim 4$)~GeV % to $\sim 5$ ($\sim 20$)~GeV in the $M_H$ range $80-150$~GeV. % % In the $M_H$ range $80-150$~GeV, the width of the $M_{ee}$ % distribution varies from $\sim 3$~GeV to $\sim 5$~GeV, while % the width $\sigma_{\mu \mu}$ of the $M_{\mu \mu}$ % distribution varies from $\sim 4$~GeV to $\sim 20$~GeV. % In the $M_H$ range $80-150$~GeV, the resolution for $M_{ee}$ varies from $\sim 3$~GeV to $\sim 5$~GeV, while the resolution $\sigma_{\mu \mu}$ for $M_{\mu \mu}$ varies from $\sim 4$~GeV to $\sim 20$~GeV. % The selection of Higgs candidates of mass $M_H$ further requires $M_{ll}$ to be within a mass window designed to maximize the signal significance, which is found to be $M_H \pm 10$~GeV ($M_H \pm 2 \sigma_{\mu \mu}$) for a Higgs decaying into electrons (muons). % This is achieved using Monte Carlo events, by finding the % mass window which yields the most stringent expected upper % limit on the signal cross-section. For the electron channel, the precise measurement of the electron transverse momenta is further exploited by applying an additional $M_H$-dependent cut on the sum of the $P_T$ of the two electrons assigned to the decay products of the Higgs candidate. %whose mass is $M_{ee}$. % The lower bound is chosen to keep $95\%$ of the signal and is optimized separately for the di- and tri-electron final states. It varies between $\sim 45$~GeV and $\sim 120$~GeV in the considered \mhpp~range. Finally, the charge measurement of the two leptons %whose mass is $M_{ll}$ assigned to the Higgs candidate is exploited. % In $e^+ p$ ($e^- p$) collision mode, where $H^{++}$ ($H^{--}$) bosons could be produced, events where at least one of the two leptons is reliably assigned a negative (positive) charge are rejected. % The charge assignment requires that the curvature $\kappa$ of the track associated to the lepton is measured with an error satisfying $\mid \kappa / \delta \kappa \mid > 2$. %-------------------------------------------------------------------- \begin{table}[htb] \begin{center} \begin{tabular}{||c|c||} \hline \hline {\bf{multi-electron}} & {\bf{di-muon}} \\ \hline \multicolumn{2}{||c||}{Preselection criteria} \\ \hline $P_T^{e_1} > 10$ GeV & $P_T^{\mu_1} > 2$ GeV \\ $P_T^{e_2} > 5$ GeV & $P_T^{\mu_2} > 1.75$ GeV \\ $ 20^\circ < \theta^{e_1,e_2} < 150^\circ $ & $20^\circ < \theta^{\mu_1, \mu_2} < 160^\circ $ \\ & $M_{\mu \mu} > 5$ GeV \\ \hline \multicolumn{2}{||c||}{Final selection cuts} \\ \hline $ \mid M_{ee} - M_H \mid < 10$ GeV & $ \mid M_{\mu \mu} - M_H \mid < 2 \sigma_{\mu \mu}$ \\ large $P_T^{e_1} + P_T^{e_2}$ & \\ \multicolumn{2}{||c||}{no ``wrong sign" lepton from $H^{\pm \pm}$ decay} \\ \hline \end{tabular} \caption[] {\small \label{tab:cuts} Selection criteria for the two Higgs decay channels analyzed. } \end{center} \end{table} %-------------------------------------------------------------------- Table~\ref{tab:cuts} summarizes the selection criteria for both the multi-electron and the di-muon analyses. After these requirements, the efficiency for selecting signal events varies from $\sim 50$ ($35$)$\%$ for an \hpp~mass of $80$~GeV to $\sim 30$ ($20$)$\%$ for an \hpp~mass of $150$~GeV in the electron (muon) analysis. For the electron channel, about half of the selected signal events are classified as di-electron in the full mass range considered. % The numbers of observed and expected events which satisfy all the above criteria are given in Table~\ref{tab:final} for some typical $M_H$ values, together with the final signal efficiencies. The three high mass events observed in the ``3e'' sample (see Fig.~\ref{invmass}) do not fulfill the criteria on the sum of the $P_T$ of the two leptons applied to select high mass Higgs candidates. Amongst the three high mass events observed in the ``2e'' sample, only one event (at $M_{ee}=113$~GeV) satisfies the required condition on the lepton charges. %-------------------------------------------------------------------- \begin{table}[htb] \begin{center} \begin{tabular}{||c||c|c|c|c||c|c|c|c||} \hline $M_H$ & \multicolumn{4}{c||}{\bf electron analysis (``2e" + ``3e")} & \multicolumn{4}{c||}{\bf muon analysis} \\ \cline{2-9} (GeV) & $N_{obs}$ & $N_{bckg}$ & $\varepsilon$ & $N_{signal}$ & $N_{obs}$ & $N_{bckg}$ & $\varepsilon$ & $N_{signal}$ \\ \hline 100 & 0 & 0.23 & 0.46 & 4.72 & 0 & 0.01 & 0.31 & 2.25\\ \hline 120 & 1 & 0.09 & 0.43 & 1.77 & 0 & 0.01 & 0.26 & 0.80\\ \hline 150 & 0 & 0.02 & 0.32 & 0.37 & 0 & 0.01 & 0.20 & 0.15\\ \hline \end{tabular} \caption[] {\small \label{tab:final} Number of observed events ($N_{obs}$) and number of events expected from the Standard Model prediction ($N_{bckg}$) which satisfy all criteria designed to select Higgs candidates of mass $M_H$. The signal selection efficiencies $\varepsilon$ are also shown, together with the number of signal events ($N_{signal}$) expected for a Yukawa coupling $h_{ee} = 0.3$. } \end{center} \end{table} %-------------------------------------------------------------------- % The most important sources of uncertainties on the signal are, % %Contributions to the systematic errors of the signal come from, % for the inelastic production processes, % due to the PDFs ($5\%$) and the $\mu$ scale choice dependance ($10\%$) % which is determined by varying $\mu$ from $Q_p^2/2$ to $2Q_p$, % where $Q_p$ is defined at the proton vertex. % For the elastic production processes an uncertainty of $15\%$ is assigned. % The Monte Carlo predictions for the multi-electron analysis % are attributed theoretical and experimental % systematic uncertainties~\cite{me}. % For the multi-electron analysis, the theoretical and experimental systematic uncertainties attributed to the Monte Carlo predictions are detailed in~\cite{me}. The main contribution to the experimental systematic error of the SM predictions is due to the tracker efficiency in the electron identification procedure, which is $90 \%$ on average with an uncertainty increasing with decreasing polar angle from $3 \%$ to $15 \%$. Systematic errors due to the uncertainty on the electromagnetic energy scale (known at the level of $0.7$ to $3\%$ in the central and forward regions of the detector, respectively), and to the trigger efficiency ($\sim 95 \% \pm 3 \%$) are also taken into account. % come from the uncertainty on the absolute energy scale of the calorimeter. % The electromagnetic energy scale is known to the level % of $0.7$ to $3\%$ from the central to the forward part % of the detector. % The hadronic energy scale is understood at the $2\%$ level when % comparing to the Monte Carlo expectations. % The trigger efficiency ($\sim 95\%$) is controlled with a precision of $3\%$. The total uncertainty of the SM expectation in the di-muon analysis is about $10\%$. The main contributions to this error are due to the trigger efficiency ($\sim 70 \%$ and $\sim 60 \%$ for inelastic and elastic events respectively, with an uncertainty of about $5.5\%$), and to the uncertainty of the muon identification which was found to be $5.8\%$. % Main sources contributing to this error are the error of the trigger % efficiency which is about $5.5\%$ and the uncertainty of the muon % identification which was found to be $5.8\%$. In both analyses the statistical error of the Monte Carlo samples is taken into account as an additional systematic error. Finally, the luminosity measurement leads to a normalization uncertainty of $1.5\%$. % ======================= \section{Interpretation} % ======================= After the final Higgs selection criteria no significant excess over the SM expectation remains in the data. Upper limits on the signal cross-section and on the doubly-charged Higgs couplings to electrons $h_{ee}$ are derived as a function of the \hpp~mass at $95\%$ confidence level following a Bayesian approach~\cite{cl} that takes statistical and systematic uncertainties into account. The limits at $95\%$ confidence level on the product of the \hpp~production cross-section and the decay branching ratio, $\sigma(e^{\pm}p \rightarrow e^{\mp}H^{\pm\pm}X) \times {\rm BR}(H^{\pm\pm} \rightarrow l^{\pm}l^{\pm})$, for the leptonic decays $H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}$ and $H^{\pm\pm} \rightarrow \mu^{\pm}\mu^{\pm}$ are shown in Fig.~\ref{sigmabr} as a function of the doubly-charged Higgs mass. The solid curves show the observed limits, while the dotted curves show the expected limits. % The difference between the observed and expected limits % for the electron channel is due to the presence % of remaining candidate events after the final selection. The cross-section limits vary from $0.06$ to $0.11$~pb for the electron channel and from $0.12 $ to $0.23$~pb for the muon channel. The bound on $\sigma(e^{\pm}p \rightarrow e^{\mp}H^{\pm\pm}X) \times {\rm BR}(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm})$ is interpreted in terms of mass-dependent upper limits on the coupling $h_{ee}$. The resulting constraints are shown in Fig.~\ref{electron} for two representative values of the branching ratio ${\rm BR}(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm})$. % % assuming either that $h_{ee}$ only is non-vanishing % $($BR$(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm})=1)$, % either a democratic coupling of the % doubly charged Higgs to leptons % $($BR$(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}) = 1/3)$. % % The limits for the electron decay channel % $H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}$ % on the coupling $h_{ee}$ % as a function of the doubly charged Higgs mass % are shown in Fig.~\ref{electron}, % assuming either that $h_{ee}$ only is non-vanishing % $($BR$(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm})=1)$, % either a democratic coupling of the % doubly charged Higgs to leptons % $($BR$(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}) = 1/3)$. % The results of this analysis are compared to indirect limits from Bhabha scattering~\cite{indlim1} and limits from a direct search by OPAL~\cite{opallep2}. % Assuming that the doubly charged Higgs only decay to electrons, % we set a lower limit of about 137 (119)~GeV % for a strength of the coupling equal to the % maximal allowed value from indirect limits % (equal to the electromagnetic strength). Assuming that the doubly-charged Higgs bosons only decay to electrons, we set a lower limit of about 131~GeV for $h_{ee} = 0.3$, corresponding to an interaction of the electromagnetic strength ($h^2_{ee} / 4 \pi \simeq \alpha_{em}$). The sensitivity of this analysis is better than that derived from Bhabha scattering measurements for masses up to $\sim 145$ GeV. % % Assuming a democratic coupling to leptons, % the lower limit is 106 (105)~GeV % for a maximum strength of the coupling % (for an electromagnetic strength). % % Assuming a democratic coupling to leptons, the lower limit % is 105~GeV for $h_{ee} = 0.3$. % Assuming that ${\rm BR}(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}) = 1/3$ the lower limit is $102$~GeV for $h_{ee} = 0.3$. % % The H1 limits extend the excluded region to masses that are beyond those reached in previous searches for pair production at LEP. % Assuming that BR$(H^{\pm\pm} \rightarrow l^{\pm}l^{\pm})=1/3$, % Assuming a democratic coupling of the doubly-charged Higgs to leptons, i.e. ${\rm BR}(H^{\pm\pm} \rightarrow l^{\pm}l^{\pm}) = 1/3$, the multi-electron analysis, the di-muon analysis, and the combination of both channels allow to set the mass-dependent upper limits on $h_{ee} = h_{\mu \mu} = h_{\tau \tau}$ shown in Fig.~\ref{combination}. % The results of this analysis are compared to indirect limits from Bhabha scattering and limits from a direct search at OPAL. The combination of the electron and muon channels enhances the limit set using the electron channel only from $102$~GeV to $108$~GeV. % for $h_{ee} = h_{\mu \mu} = 0.3$. % This analysis shows that the excess of events observed with % a large di-electron mass is unlikely to be due to % doubly-charged Higgs production. % Other possible interpretations of these events by % non-standard physics - e.g. single sneutrino production in R-parity % violating supersymmetry, single production of a (scalar or % vectorial, neutral or charged) bilepton coupling to an $e^+ e^-$ % pair - remain to be investigated. % ==================== \section{Conclusion} % ==================== We have presented a dedicated search for the single production of doubly-charged Higgs bosons, combining di- and tri-electron as well as di-muon final states. % In a previous model independent analysis, H1 has observed six events with a di-electron mass above 100~GeV, i.e. a region where the Standard Model expectation is small. % Out of the six events only one is compatible with the production of a doubly-charged Higgs boson, when kinematic cuts and lepton charges are taken into account. No di-muon event was found in the same mass domain. This analysis places new limits on the \hpp~mass and its Yukawa coupling to electrons. Assuming that the doubly-charged Higgs only decays to electrons, we set a lower limit of about 131~GeV for a coupling value $h_{ee} = 0.3$, corresponding to an interaction of the electromagnetic strength. % The data presented here restrict doubly charged Higgs to higher % mass values than has been possible previously % at LEP in searches for pair production. % ========================= \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. We are specially grateful to J. Maalampi and N. Romanenko for providing the doubly-charged Higgs Lagrangian implementation in CompHEP which was used in this analysis. We would like also to thank K.~Huitu, N.~Romanenko and E.~Boos for their help and valuable discussions. % \begin{thebibliography}{99} \bibitem{me} H1 Collaboration, C. Adloff {\it et al.}, ``Multi-electron Production at High Transverse Momentum in $ep$ collisions at HERA'', contributed paper 1019, ICHEP 2002, Amsterdam. % to be published in ICHEP 2002 Proceedings. % \bibitem{mm} H1 Collaboration, C. Adloff {\it et al.}, ``Muon Pair Production in $ep$ collisions at HERA'', contributed paper 1021, ICHEP 2002, Amsterdam. % to be published in ICHEP 2002 Proceedings. % \bibitem{HTM} G.B.~Gelmini and M.~Roncadelli, Phys. Lett. {\bf B99} (1981) 411. % \bibitem{pati} J.C. Pati and A. Salam, Phys. Rev. {\bf D10} (1974) 275; R.E. Marshak and R.N. Mohapatra, Phys. Lett. {\bf B91} (1980) 222. % \bibitem{moha1} R.N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. {\bf 44} (1980) 912. % % \bibitem{moha2} R.N. Mohapatra and J.D. Vergados, % Phys. Rev. Lett. {\bf 47} (1981) 1713. \bibitem{moha3} G.S. and R.N. Mohapatra, Phys. Rev. {\bf D12} (1975) 1502. \bibitem{moha4} R.N. Mohapatra and R.E. Marshak, Phys. Rev. Lett. {\bf 44} (1980) 1316. %\bibitem{aulakh} C.S. Aulakh, A. Melfo, A. Rasin and G. Senjanovic, %Phys. Rev. {\bf D58} (1998) 115007. % % \bibitem{rizzo} T.G. Rizzo, Phys. Rev. {\bf D} 25 (1982) 1355. % % \bibitem{gunion} J.F. Gunion, C. Loomis and K.T. Pitts, % Proceedings of the ``1996 DPF/DPB Summer Study % on New Directions for High Energy Physics'', Snowmass (1996) 603-607. % % \bibitem{huitu} K. Huitu, P.N. Pandita and K. Puolamaki, % Helsinki Institute of Physics Preprint 1999-16TH % (April 1999), hep-ex/9904388. % \bibitem{zeus} E. Accomando and S. Petrarca, Phys. Lett. {\bf B323} (1994) 212. % \bibitem{indlim1} M.L Swartz, Phys. Rev. {\bf D40} (1989) 1521. % \bibitem{indlim2} J.F. Gunion {\it et al.}, Phys. Rev. {\bf D40} (1989) 1546. % \bibitem{indlim3} M. Lusignoli and S. Petrarca, Phys. Lett. {\bf B226} (1989) 397. % \bibitem{indlim4} G. Barenboim {\it et al.}, Phys. Lett. {\bf B394} (1997) 132. % \bibitem{opallep1} OPAL Collaboration, P.D. Acton {\it et al.}, Phys. Lett. {\bf B295} (1992) 347. % \bibitem{opallep2} OPAL Collaboration, G. Abbiendi {\it et al.}, Phys. Lett. {\bf B526} (2002) 221. % \bibitem{delphi} DELPHI Collaboration, G. Gomez-Ceballos and F. Marrotas, Preprint DELPHI 2002-010 CONF 551 (March 2002). % % --- Signal Simmulation % % \bibitem{comphep} A. Pupkhov {\it et al.}, hep-ph/9908288. \bibitem{comphep} E.E.~Boos {\it et al.}, SNUTP-94-116, hep-ph/9503280; E.E.~Boos {\it et al.}, Proceedings of the Xth Int. Workshop on High Energy Physics and Quantum Field Theory, QFTHEP-95, (Moscow, 1995), Eds. B.~Levtchenko and V.~Savrin, p 101. % %\bibitem{RIZZO} T.G.~Rizzo, Phys. Rev. D {\bf 27} (1983) 657. % \bibitem{ROMANENKO} S.~Godfrey, P.~Kalyniak and N.~Romanenko, Phys. Rev. {\bf D65} (2002) 033009. % \bibitem{pythia} T. Sj\"ostrand, P. Eden, C. Friberg, L. Lonnblad, G. Miu, S. Mrenna and E. Norrbin, Computer Physics Commun. {\bf 135} (2001) 238. % \bibitem{VEGAS} G.P.~Lepage (Cornell U., LNS), CLNS-80/447 (1980). % \bibitem{cteq} H.L. Lai {\it et al.}, Phys. Rev. {\bf D55} (1997) 1280. % \bibitem{JETSET74} JETSET~7.4: T.~Sj\"ostrand, Lund Univ. preprint LU-TP-95-20 (August 1995) 321pp; {\it ibid.}, CERN preprint TH-7112-93 (February 1994) 305pp. % \bibitem{DGLAP} V.N. Gribov et L.N. Lipatov, Sov.\ Journ.\ Nucl.\ Phys.\ {\bf 15} (1972) 78;\\ G. Altarelli et G. Parisi, Nucl.\ Phys.\ {\bf B126} (1977) 298;\\ Y.L. Doskhitzer, JETP 46 (1977) 641. % \bibitem{JLAB} Jefferson Lab. Hall A Collaboration, O.~Gayou {\it et al.}., Phys. Rev. Lett. {\bf 88} (2002) 092301. % \bibitem{SLAC} R.C.~Walker {\it et al.}, Phys. Rev. {\bf D49} (1994) 5671. % %\bibitem{modelHTM} J. Maalampi and N. Romanenko, Phys. Lett. B {\bf 532} (2002) 202. %\bibitem{cteq} R. Brock {\it et al.}, Rev. Mod. Phys. {\bf 67} (1995) 157. % % % ----- SM Backgrounds % \bibitem{dy} N. Artego-Romero, C. Carimalo and P. Kessler, Zeit.f.Phys. {\bf C52} (1991) 289. % \bibitem{grape} T. Abe, Comp. Phys. Comm. {\bf 136} (2001) 126, { http://www.awa.tohoku.ac.jp/$\sim$tabe/grape}. % \bibitem{DIFFVM} B. List, Diploma Thesis, Technische Universit\"at Berlin, H1-10/93-319 (1993). % \bibitem{lpair1} S.P. Baranov, O. Dunger, H. Shooshtari and J.A. Vermaseren, Hamburg 1991, Proceedings, Physics at HERA, Vol. 3 pp. 1478-1482. \bibitem{lpair2} J.A. Vermaseren, Nucl. Phys. {\bf B229} (1983) 347. % \bibitem{aroma} G. Ingelman, J. Rathsman and G.A. Schuler, Comput. Phys. Commun. {\bf 101} (1997) 135. % \bibitem{django} DJANGO 2.1: G.A. Schuler and H. Spiesberger, Proceedings of the Workshop Physics at HERA, Vol 3 p. 1419. % \bibitem{wabgen} Ch. Berger and P. Kandel, ``A new Generator for Wide Angle Bremsstrahlung", Proc. of the Monte Carlo Generators for HERA Physics Workshop, DESY-PROC-1999-02, p. 596. % % % \bibitem{cl} Particle Data Group Collaboration, R.M. Barnett {\it et al.}, Phys. Rev. {\bf D54} (1996) 1. % \end{thebibliography} %\clearpage \vspace{3cm} % Feynman Diagrams \begin{figure}[p] \begin{center} \epsfig{file=H1prelim-02-162.fig1a.eps,width=8cm} \epsfig{file=H1prelim-02-162.fig1b.eps,width=8cm} \epsfig{file=H1prelim-02-162.fig1c.eps,width=8cm} \end{center} \caption{ Feynman diagrams for the single production of doubly-charged Higgs bosons in $e^{\pm}p$ collisions at HERA. The hadronic final state is denoted by $p$ ($X$) in the elastic (inelastic) case, where the initial proton remains intact (dissociates). } \label{feyn} \end{figure} % Invariant Mass \begin{figure}[p] \begin{center} \begin{picture}(10,60)(0,50) %\put(-80.,-50.){\epsfig{file=mass.electron.ichep.eps,bbllx=0,bblly=0,bburx=240,bbury=500,width=8cm,clip=}} \put(-80.,-50.){\epsfig{file=H1prelim-02-162.fig2a.ps,bbllx=85,bblly=280,bburx=320,bbury=800,width=7.5cm,clip=}} %\put(5.,-50.){\epsfig{file=mumu.v1.eps,bbllx=50,bblly=180,bburx=460,bbury=715,width=8cm,clip=}} %\put(5.,40.){\epsfig{file=masse.muon.nosignal.eps,bbllx=50,bblly=70,bburx=540,bbury=470,width=8cm,clip=}} \put(5.,37.){\epsfig{file=H1prelim-02-162.fig2b.ps,bbllx=110,bblly=490,bburx=520,bbury=750,width=12.3cm,clip=}} \end{picture} \end{center} \vspace*{10cm} \caption{ Invariant mass $M_{12}$ of the two highest $P_T$ electrons for events classified as di-electron (top left) and tri-electron (bottom left), and di-muon invariant mass $M_{\mu\mu}$ (right) in comparison with the Standard Model expectation. % The invariant mass distribution expected from a doubly charged Higgs % of 130~GeV is shown as dashed histograms (arbitrary normalization). } \label{invmass} \end{figure} % SigmaBR \begin{figure}[p] \begin{center} % \epsfig{file=doublyqichep3.eps,width=16cm} \epsfig{file=H1prelim-02-162.fig3.eps,width=16cm} \end{center} \caption{Upper limits at $95\%$ confidence level on $\sigma(e^{\pm}p \rightarrow e^{\mp}H^{\pm\pm}X) \times {\rm BR}(H^{\pm\pm} \rightarrow l^{\pm}l^{\pm})$ for the leptonic decays $H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}$ (lower set of curves) and $H^{\pm\pm} \rightarrow \mu^{\pm}\mu^{\pm}$ (upper set of curves), as a function of the doubly-charged Higgs mass. The solid (dashed) curves show the observed (expected) limits. %, while the dotted curves %show the expected limits for background only. } \label{sigmabr} \end{figure} % Limit, e-channel \begin{figure}[p] \begin{center} % \epsfig{file=doublyqichep1.eps,width=16cm} \epsfig{file=H1prelim-02-162.fig4.eps,width=16cm} \end{center} \caption{ Exclusion limits on the coupling $h_{ee}$ at $95\%$ confidence level as a function of the doubly-charged Higgs mass %for the decay $H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}$ from the multi-electron analysis assuming that (dashed curve) % a democratic coupling of the % doubly-charged Higgs to leptons BR$(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}) = 1/3$ or (full curve) BR$(H^{\pm\pm} \rightarrow e^{\pm}e^{\pm})=1$. % The solid curves show the observed limits, while the dotted curves % show the expected limits for background only. The results of this analysis are compared to indirect limits from Bhabha scattering and to limits from a direct search by OPAL. } \label{electron} \end{figure} % Limit, All Channels \begin{figure}[p] \begin{center} % \epsfig{file=doublyqichep2.eps,width=16cm} \epsfig{file=H1prelim-02-162.fig5.eps,width=16cm} \end{center} \caption{ Exclusion limits on the coupling $h_{ee} = h_{\mu \mu} = h_{\tau \tau}$ at $95\%$ confidence level as a function of the doubly-charged Higgs mass %for the decay channels $H^{\pm\pm} \rightarrow e^{\pm}e^{\pm}$ from the multi-electron analysis (dashed curve), %$H^{\pm\pm} \rightarrow \mu^{\pm}\mu^{\pm}$ the di-muon analysis (dotted curve), and from the combination of these channels (full curve), assuming a democratic coupling of the doubly-charged Higgs to leptons, i.e. BR$(H^{\pm\pm} \rightarrow l^{\pm}l^{\pm})=1/3$. The results of this analysis are compared to indirect limits from Bhabha scattering and to limits from a direct search by OPAL. } \label{combination} \end{figure} \end{document}