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% Higgs Commands
% \newcommand{\mhpp}{\mbox{$M_{H^{\pm\pm}}$}}
\newcommand{\mhpp}{\mbox{$M_H$}}
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\pagestyle{empty}
\begin{titlepage}

\noindent

\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline
%\epsfig{file=H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                XXII International Symposium on Lepton-Photon Interactions at High Energy},
                June~30,~2005,~Uppsala} \\
                 & Abstract:        & {\bf 418}    &\\
                 & Session: & {\bf Electroweak physics and beyond}   &\\ \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
$H^{\pm \pm}_{L,R}$
is performed in the framework of models
in which a Higgs triplet is coupled to leptons of the $i^{th}$ and $j^{th}$
generation via Yukawa couplings $h^{L,R}_{ij}$.
%
The signal is searched for via the decays of the doubly-charged Higgs to
like-sign electron, muon, or tau pairs or electron-muon pairs,
%including lepton flavor violating decays,
using a sample of $e^{\pm}p$ events 
corresponding to up to $118$~pb$^{-1}$ of data 
collected with 
the H1 detector at HERA
for the $ee$, $\mu\mu$, $\mu e$ channels and
$65$~pb$^{-1}$ for the $\tau\tau$ channel.
%
We observe no evidence for doubly-charged Higgs production
and derive limits on the $h_{ee}^{L,R}$ and $h_{e\mu}^{L,R}$
Yukawa couplings as a function of the $H^{\pm\pm}_{L,R}$ mass.
Assuming that the doubly-charged Higgs only decays to electrons,
we set a lower limit of about $139$~GeV on the $H^{\pm\pm}_{L,R}$ mass
for a value $h_{ee}^{L,R} = 0.3$ corresponding to a coupling of electromagnetic strength. 
Assuming that the doubly-charged Higgs only decays to electron-muon,
we set a lower limit of about $140$~GeV on the $H^{\pm\pm}_{L,R}$ mass
for a coupling value $h_{e\mu}^{L,R} = 0.3$.
%This is the first search for doubly-charged Higgs production at HERA.

\noindent
\end{abstract}


\end{titlepage}

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% from /h1/iww/ipublications/h1auts.tex 

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\newpage

% =======================
\section{Introduction}
% =======================

\noindent

The H1 Collaboration has observed~\cite{me,mm}
multi-electron and multi-muon production at high transverse
momentum in $ep$ collisions 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 are observed with a di-electron mass
above 100~GeV, a domain where the Standard Model (SM) prediction
is low. 
One di-muon event is found in the same mass region.

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,
is presented in this paper. 
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.
Other decay modes are considered to be either theoretically suppressed
or kinematically forbidden.
The signal is searched for in $ee$, $eee$, $\mu\mu$, $e\mu$, $e\mu\mu$
and $\tau\tau$  final states.
The  $ee$, $eee$, $\mu\mu$, $e\mu$, and $e\mu\mu$ analyses make use of all 
data collected from 1994 to 2000 corresponding to an
integrated luminosity up to $118$~pb$^{-1}$.
The  $\tau\tau$ analysis makes use of the 1999--2000 data
corresponding to an integrated luminosity of
$65$~pb$^{-1}$.
%
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 an $SU(2)_R$
triplet of scalar fields, whose neutral component acquires a
non-vanishing vacuum expectation value (vev).
The Higgs triplet or triplets may be coupled to matter fields
via Yukawa couplings.
Whereas all charged fermions acquire their masses via their
couplings to 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 extensions
of 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 $i,j = e, \mu, \tau$ are the 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 an $SU(2)_L$ 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 $SU(2)_R$ Higgs
triplet contain an $H^{--}$ 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 I are insensitive to the
chirality of the lepton fields\footnote{HERA I operated with longitudinally unpolarised beams.}, 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 $h_{ee}$ or $h_{e\l}$ the single production
of a doubly-charged Higgs boson is possible
in $e\gamma^*$ interactions
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 or off-diagonal products  $h_{ij}h_{ij}$  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 from PEP and PETRA which yield~\cite{indlim1}
$h_{ee} \le 3.1 \times 10^{-3} {\rm GeV}^{-1} M_{H}$,
using $e^+ e^-$ data taken at centre-of-mass energies of $\sim 30$~GeV.
OPAL sets significantly more stringent limits on $h_{ee}$ using data
at centre-of-mass energies of $183-209$~GeV~\cite{opal-singleprod}.
%
Search for muonium $(\mu^+e^-$) to
anti-muonium $(\mu^-e^+$) conversion~\cite{indlim1,indlim4} 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.
%$G_{\mu}$ measurements yield to $h_{e\nu_{\mu}}^L < 2.4 \times 10^{-4} {\rm GeV}^{-1} M_{H}$,
%which can interpreted as a limit on $h_{e\mu}^L$ assuming $h^L_{e\mu}= h^L_{e\nu_{\mu}}$.
%Less stringent limits come from $e\nu_e$ scattering.
% For a coupling of electromagnetic strength,
% $h_{ee}=e$ with $e= \sqrt{4\pi\alpha}$,
% doubly charged Higgs which 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 and Tevatron experiments.
For pair production in $e^+e^-$ collisions, the kinematic
reach is restricted to $\mhpp < \sqrt{s}/2$.
Masses below approximately $100$~GeV
have been excluded by the
DELPHI, L3, and OPAL experiments ~\cite{leppairprod}
in searches for \hpp~pair production
at centre-of-mass energies 
between $189$ and $209$ GeV
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.
CDF~\cite{cdf-pairprod} and D\O \cite{d0-pairprod}
performed searches for  $H^{\pm\pm}$ pair production 
and CDF sets lower mass limits on the doubly charged Higgs decaying with 
a $100\%$ branching fraction to $ee$ 
($100 < M_{H_L} < 133$~GeV and $101 < M_{H_R} < 109$~GeV excluded),
$\mu\mu$ ($M_{H_L} > 136$~GeV  and $M_{H_R} > 113$~GeV), or 
$e\mu$ ($M_{H_L} > 115$~GeV).
OPAL performed a search for the single production of doubly charged Higgs 
and sets limits on $h_{ee}$, $h_{\mu\mu}$ and $h_{\tau\tau}$ at the order
of $0.05$ or below for masses up to $160$~GeV~\cite{opal-singleprod}.


In this paper we consider scenarios with diagonal couplings and Higgs decays into
electrons, muons or taus through the process
$e^{\pm}p \rightarrow e^{\mp}\hpp X \rightarrow e^{\mp}l^{\pm}l^{\pm}X$
involving $h_{ee}$ at the Higgs production vertex and $h_{ll}$ at its decay vertex.
We also consider the scenario in which the off-diagonal coupling
$h_{e\mu}$ is involved at the production vertex and the decay of the Higgs
through the process 
$e^{\pm}p \rightarrow \mu^{\mp}\hpp X \rightarrow \mu^{\mp}e^{\pm}\mu^{\pm}X$.
This leads to final states with three leptons,
two of them being of like-sign and together having large invariant mass.
It should be noted that the final state lepton which does not come from
the Higgs decay is often scattered in the direction of the
incident proton 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} parameterization. They are
evaluated at the scale $\sqrt{Q^2}$, where $Q^2$ denotes
the negative squared momentum transfer at the hadronic vertex.
The inelastic cross-section is calculated in the range
$Q^2 > 4$~GeV$^2$
and the quasi-elastic contribution  in the range $1<Q^2<4$~GeV$^2$.
%
At the generator level, the parton shower 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 explicitly 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, quasi-elastic,
and inelastic contributions leads to a cross-section of
$\sim 0.39$ pb ($\sim 0.04$ pb) for a Higgs mass of
$100$ GeV ($150$ GeV). The quasi-elastic (inelastic) contribution is found
to be $\sim 1/2$ ($1/3$)
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.

Backgrounds from  NC-DIS and
photoproduction ($\gamma p$) contribute to tau-tau final states
if isolated hadrons with pencil-like jet topology are 
misidentified as tau candidates.
The $\gamma p$ background is simulated using the 
% extra reference for PYTHIA 6.1?
PYTHIA generator~\cite{pythia}.

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{Analysis of the \boldmath{$\hpp \rightarrow e^{\pm}e^{\pm}$}, 
\boldmath{$\mu^{\pm}\mu^{\pm}$} Decays}
% ========================

For the 
$e^{\pm}p \rightarrow e^{\mp}\hpp X \rightarrow e^{\mp}e^{\pm}e^{\pm}X$ 
($e^{\mp}\mu^{\pm}\mu^{\pm}X$) analysis
we use 
the full $e^{\pm}p$ dataset recorded by the H1
experiment in the period 1994--2000.
For the electron (muon) final states, the total integrated luminosity
of $115.2$ ($113.7$)~pb$^{-1}$ is shared
between $36.5$ ($42.8$)~pb$^{-1}$ and $65.1$ ($60.8$)~pb$^{-1}$
of $e^+p$ collisions recorded at centre-of-mass energies
$\sqrt{s}$ of $300$~GeV and $318$~GeV, respectively,
and $13.6$ ($10.1$)~pb$^{-1}$ of $e^-p$ collisions recorded 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
($20^{\circ} < \theta^{\mu} < 150^{\circ}$),
with the transverse momenta
$P_T^{\mu1} > 10$~GeV and $P_T^{\mu2} > 5$~GeV.
Additional electrons or muons are accepted.
%
After this selection, we observe $108$ ($17$) data events in the 
di-(tri-) electron final state, which is to be compared with $117.1 \pm 8.6$
($20.3\pm 2.1$) from SM expectation,
and $56$ data events in the di-muon and di-muon-electron final states which is to be compared with
$54.7\pm 5.7$ from SM expectation. 
No event with three or more muons or with two muons and more than one electron is observed.
%
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}.
Overall, good agreement is observed between data and the SM expectation.
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 expectation of $0.30 \pm 0.04$ and $0.23 \pm 0.04$, respectively. 
In the multi-muon analysis, one di-muon event is found with $M_{12} > 100$~GeV,
while $0.08 \pm 0.01$ are expected.

Further selection criteria are then applied, which are designed
to maximize the sensitivity of the analysis
to a possible \hpp~signal. 

The charge measurement of the two leptons 
assigned to the Higgs candidate
is exploited.
%
In $e^+ p$ ($e^- p$) collision mode, where $H^{++}$ ($H^{--}$) bosons 
could be produced,
events in which 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      
$\mid \kappa / \delta \kappa \mid > 2$.
%
The distribution of the invariant mass $M_{12}$
of the two highest $P_T$ electrons after requiring the charge assignment
is shown in Fig.\ref{invmass}.


For a given hypothetical \hpp~mass $M_H$, we define $M_{ll}$ to be the invariant
mass of the two leptons (or, for ``3e'' events, the 
invariant dilepton mass which is closest to $M_H$).
%
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 $M_H$
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).


Finally, 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.



%--------------------------------------------------------------------
\begin{table}[htb]
 \begin{center}
  \begin{tabular}{||c|c||}
   \hline \hline
    {\bf{multi-electron}}    &    {\bf{multi-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
 \multicolumn{2}{||c||}{no ``wrong sign" lepton from $H^{\pm \pm}$ decay} \\
  $ \mid M_{ee} - M_H \mid < 10$ GeV    &
       $ \mid M_{\mu \mu} - M_H  \mid  < 2 \sigma_{\mu \mu}$ \\
  large $P_T^{e_1} + P_T^{e_2}$      &    \\   
 \hline
  \end{tabular}
 \caption[]
          {\small \label{tab:cuts}
       Selection criteria for the multi-electron and multi-muon Higgs decay
      channels.
          }
 \end{center}
\end{table}
%--------------------------------------------------------------------

Table~\ref{tab:cuts} summarizes the selection criteria
for both the multi-electron and the multi-muon analyses.
After these requirements, the efficiency for selecting signal events
varies from $\sim 50$ ($35$)$\%$ for an \hpp~mass of $80$~GeV to
$\sim 35$ ($15$)$\%$ 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
mass range considered.
%
The numbers of observed and expected events which satisfy all
the above criteria are given in Table~\ref{tab:eemumu} for three
values of $M_H$, together with the 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 $M_{ee}=112.5\pm 2.4$~GeV)
satisfies the required condition
on the lepton charges.
The high mass di-muon event does not satisfy  the charge requirement.


%--------------------------------------------------------------------
\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   &   0.29          &   0.48   &  6.78        &    0    & 0.05       &  0.36   & 4.96\\
\hline
120    &  1  &    0.12         &    0.44   &  2.58        &     0   &  0.03      &   0.29   & 1.67\\
\hline
150    &  0  &    0.02         &    0.36   &  0.56        &     0   &  0.02      &   0.17   & 0.25\\
\hline
  \end{tabular}
 \caption[]
          {\small \label{tab:eemumu}
           Number of observed  ($N_{obs}$) and  expected ($N_{bckg}$) events
           from the multi-electron and multi-muon analyses 
           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 on the signal and 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
$0.5$ to $3\%$ level in the central and forward regions of the detector, respectively)
and to the trigger efficiency 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  dominant experimental systematic errors on the signal and SM expectation in the
multi-muon analysis are due to the trigger
efficiency ($\sim 70 \%$ and $\sim 80 \%$ for inelastic and
elastic signal events respectively, with an uncertainty of about $6\%$),
and to the uncertainty of the muon identification which was found
to be $6\%$.

% 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 $1.5\%$.
These theoretical and experimental systematic uncertainties added in quadrature lead to a
total signal systematic error of about $11\%$ ($13\%$) for the multi-electron(-muon) analysis.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% e-mu part
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Analysis of the \boldmath{$H^{\pm\pm} \rightarrow e^\pm \mu^\pm$} Decay}

The full $e^\pm p$ dataset of the run period 1994--2000 was used for the 
analysis
of the process $e^{\pm}p \rightarrow \mu^{\mp}\hpp X \rightarrow \mu^{\mp}e^{\pm}\mu^{\pm}X$,
and corresponds to a total integrated luminosity of 118 pb$^{-1}$.

The electron and muon identification criteria are the same as for the 
analysis
of the $e^\pm e^\pm$ and $\mu^\pm \mu^\pm$ channels and are described in 
\cite{me} and
\cite{mm}, respectively.
Electrons are identified in the polar angle range 20$^\circ$ $< \theta^e <$
140$^\circ$ and with a minimum transverse momentum of $P_T^e >$ 10 GeV, to
ensure a high trigger efficiency of the events.
Muons are required to have a momentum $P_T^\mu >$ 5 GeV and to be in the polar angle
range 10$^\circ$ $< \theta^e <$ 140$^\circ$. 
Events are selected with at least one electron and muon fulfilling the above criteria.
Moreover an isolation distance of 0.5 in $\eta-\phi$ space is required 
between
the two leptons.
After this selection, 35 data events are observed compared to a SM 
expectation
of 30.6 $\pm$ 2.8. The distribution of the invariant mass of the 
electron and
the muon $M_{e\mu}$ is presented in Fig.\ref{invmass}.
Good agreement is observed between data and the SM expectation and no data 
events
with $M_{e\mu} > $ 70 GeV are present.

Similar to the analysis of the $e^\pm e^\pm$ and $\mu^\pm \mu^\pm$ channels,
further selection criteria are applied in order to maximise the 
sensitivity to
an $H^{\pm\pm}$ signal.
Events in which at least one of the two leptons is reliably assigned a
negative
(positive for $e^{-}p$ data) charge are rejected.
For events with two identified muons and one electron, we define 
$M_{e\mu}$ to be
the electron-muon invariant mass which is closest to a given 
$H^{\pm\pm}$ mass
$M_H$. The resolution $\sigma_{e\mu}$ on $M_{e\mu}$ varies from $\sim$ 4 
GeV to
$\sim$ 8 GeV in the $M_H$ range 80--150 GeV.
The selection of Higgs candidates of mass $M_H$ further requires 
$M_{e\mu}$ to
be within a mass window of 2$\sigma_{e\mu}$.
The resulting signal efficiency varies from $\sim$ 55\% to  $\sim$ 45\% for
$M_H$ in the range 80--150 GeV.
The numbers of observed and expected events which satisfy all
the above criteria are given in Table~\ref{tab:emu} for three values of
$M_H$, together with the signal efficiencies.
The experimental systematic errors are similar to those given in the previous section.


%--------------------------------------------------------------------
\begin{table}[htb]
   \begin{center}
    \begin{tabular}{||c||c|c|c|c||}
   \hline
   $M_H$ & \multicolumn{4}{c||}{\bf electron-muon analysis}\\
\cline{2-5}
   (GeV)
   & $N_{obs}$  &  $N_{bckg}$  & $\varepsilon$  &  $N_{signal}$\\
   \hline
100    &  0   &   1.01          &   0.49   &  7.12  \\
\hline
120    &  0  &    0.65         &    0.47   &  2.82  \\
\hline
150    &  0  &    0.33         &    0.42   &  0.67  \\
\hline
    \end{tabular}
   \caption[]
            {\small \label{tab:emu}
             Number of observed ($N_{obs}$) and  
             expected events
             from the electron-muon analysis
             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 $h_{e\mu} = 
0.3$.
            }
   \end{center}
\end{table}



\section{Analysis of the \boldmath{$\hpp \rightarrow \tau^{\pm}\tau^{\pm}$} Decay}
For the 
$e^+p \rightarrow e^-H^{++} X \rightarrow e^-\tau^{+}\tau^{+}X$ 
analysis we use 
the $e^+p$ dataset recorded by the H1
experiment in the period 1999--2000 corresponding to a
total integrated luminosity of $65.4$~pb$^{-1}$  at 
centre-of-mass energy of $\sqrt{s}=318$~GeV.

The selection of $\tau \tau$ final states requires two high $P_T$ 
tau candidates in the central region of the detector 
$20^{\circ} < \theta^\tau < 160^{\circ}$.
The tau identification is based on charged tracks measured in the 
central jet chamber with a transverse momentum
$P_T^{\tau 1}>10$~GeV and $P_T^{\tau 2}>5$~GeV.
They have to be separated in
the pseudorapidity-azimuth~\footnote{
$R=\sqrt{\Delta \eta^2 + \Delta \varphi^2}$,
with $\Delta \eta$ being the distance in pseudorapidity} plane by $R>2.5$.

Candidate events are selected by requiring the longitudinal position of
the primary interaction to be within $35$~cm around the nominal interaction point
and by applying topological filters to remove background induced by 
cosmic showers and other non-$ep$ sources.
The large background from NC-DIS at low $Q^2$ is reduced by rejecting
events with an electromagnetic energy deposition in the backward 
SpaCal calorimeter of more than $5$~GeV.

The leptonic tau decays $\tau \rightarrow e \nu \nu$ and 
$\tau \rightarrow \mu \nu \nu$ are reconstructed by identifying the
decay electron in the LAr calorimeter or the muon in the central muon detector,
respectively. 
Remaining tau candidates are reconstructed as hadronic tau decay if 
at least 40\% of the charged track momentum is reconstructed in
the LAr calorimeter. 
After this preselection about 24000 events are found compared to 
26000, mainly expected from NC-DIS.
These events are classified in 
$e \mu$, $e j$, $\mu j$ and $jj$ candidate classes for further analysis. 


Further selection criteria are applied to reduce mainly background due 
to misidentification of taus in $\gamma p$ and NC-DIS.
Tau candidates are required to be isolated from other tracks in the event
in a cone $0.15<R<1.5$ for hadronic decays and  $R<1.5$ for leptonic decays.
In order to suppress background from NC-DIS which is peaked at small
scattering angles, the polar angle of electrons is required to be below 120$^\circ$.
For the $ej$ class, which suffers large backgrounds from NC-DIS,
energy and longitudinal momentum invariance ($\sum_i E^i - P_z^i = 2 E_e = 55$~GeV for all particles) measured from all visible particles
is required to be smaller than 45~GeV to account for the missing tau neutrinos in the event. 
To reduce remaining background from $\gamma p$ and NC-DIS  
with large activity in the forward region of the calorimeter,
no significant energy deposition is allowed in the $jj$ and $ej$ classes  with 
$\eta>2.8$.

Finally, the invariant mass of the tau-tau system $M_{\tau\tau}$ is fitted by
imposing $\sum_i E^i - P_z^i \equiv 2 E_e$, by assuming the missing neutrinos 
to be in the direction of the tau tracks and by minimising the missing transverse 
momentum in the event. The mass resolution of this fit is about 4~GeV in the
Higgs mass range 80~to 150~GeV.
The results after the $\tau\tau$ selection and for $M_{\tau\tau}>65$~GeV 
are shown in
Table~\ref{tab:tau_cutflow}. One event  
%--------------------------------------------------------------------
\begin{table}[htb]
 \begin{center}
\begin{tabular}{|c||c|cc||c|cc|cc|}
   \hline
   Decay            & \multicolumn{3}{|c||}{\bf $\tau\tau$ preselection }
               & \multicolumn{3}{|c|}{\bf $H^{\pm\pm}$ final selection}
               & \multicolumn{2}{|c|}{
        \bf \boldmath{Eff.$ \times {\rm BR}$}} \\ \cline{2-9}
Topology & obs. & SM bg & ($\tau\tau$) & obs. & SM bg & ($\tau\tau$) & elastic & quasi-elastic \\ \hline \hline
   $e \mu$     & 0    & 0.29$\pm$ 0.03 & (0.11) & 0 & 0.09$\pm$ 0.01 & (0.00) & 2.9\% & 2.6\% \\ \hline
   $e j$       & 0    & 1.20$\pm$ 0.24 & (0.31) & 0 & 0.78$\pm$ 0.16 & (0.03) & 6.9\% & 2.8\% \\ \hline
   $\mu j$     & 0    & 0.25$\pm$ 0.05 & (0.16) & 0 & 0.03$\pm$ 0.01 & (0.03) & 6.4\% & 5.5\% \\ \hline
   $jj$        & 1    & 0.38$\pm$ 0.10 & (0.16) & 0 & 0.13$\pm$ 0.08 & (0.00) & 8.0\% & 2.9\% \\ \hline \hline
   total     & 1    & 2.12$\pm$ 0.32 & (0.74) & 0 & 1.03$\pm$ 0.19 & (0.06) & 24.2\% & 13.8\% \\ \hline
\end{tabular} 
 \caption[]
          {\small \label{tab:tau_cutflow}
            Number of observed and expected 
            tau tau candidates after $\tau\tau$ selection and 
            after the {\hpp} selection requiring like-sign charges.
            The expectation is given for all SM processes 
            and for the process $\gamma \gamma \rightarrow \tau\tau$.
            The efficiencies including the branching ratio of 
            $\tau \tau \rightarrow {\rm class}_{ij}$, where $i,j$ stands 
            for $e,\mu,j$, are given after final selection for the elastic and  
             quasi-elastic production process for $\mhpp=100$~GeV.
          }
 \end{center}
\end{table}
is selected with oppositely charged tracks and with a reconstructed
invariant mass of 85~GeV in the $jj$ class compared to 
a total SM expectation of 2.1 events (dominated by NC-DIS) 
and 0.7 events from $\gamma \gamma \rightarrow \tau^+ \tau^-$.

In a final step, both charges of the $\tau$ candidates are required
to be like-sign as expected for doubly charged Higgs bosons. 
This cut is only applied if both $\tau$~candidates have 
a 1-prong signature.
It removes almost completely background from $\gamma \gamma \rightarrow \tau^+ \tau^-$
and increases
the purity in the $e\mu$ and $ej$ classes where in some cases the
scattered electron is wrongly selected as $\tau$ candidate.

The signal efficiencies depend only weakly on \mhpp. 
They are summarized for the elastic and quasi-elastic production process in
Table~\ref{tab:tau_cutflow} after applying the 
like-sign charge cut for a {\hpp} mass of $\mhpp=100$~GeV 
and include the branching ratios for the different
decay classes. 
The main experimental systematic uncertainty of 6\% is due to the
track reconstruction efficiency. 
All systematic errors including uncertainties from the luminosity measurement,
lepton and jet identification are added in quadrature and result in a total 
uncertainty of 10\% for all classes. 

%The uncertainties on the SM background prediction 
%are dominated by the model uncertainties of the
%NC-DIS background (10\%) and 
%$\gamma p$ background (20\%), and track reconstruction uncertainties (6\%). 
%An additional error of about 15\% comes from the hadronic
%energy scale uncertainty in the reconstruction of {\mhpp} at low {\hpp} masses
%in the $ej$ and $jj$ class. 
%The total SM background uncertainties are about
%26\% for the $jj$ class and 17\% for the other classes.
Because of the smallness of the background expectation after applying all cuts,
remaining background is ignored in the following statistical interpretation and
no background subtraction is performed.



% =======================
\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
$h_{ee}^{L,R}$ and $h_{e\mu}^{L,R}$ are derived as a function of the \hpp~mass
at the $95\%$ 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,
$\sigma(e^{\pm}p \rightarrow e^{\mp}H^{\pm\pm}X)
\times {\rm BR}(H^{\pm\pm} \rightarrow l^{\pm}l^{\prime\pm})$,
for the leptonic decays $H^{\pm\pm} \rightarrow  e^{\pm}e^{\pm}$,
$\mu^{\pm}\mu^{\pm}$, $\tau^{\pm}\tau^{\pm}$ and $e^{\pm}\mu^{\pm}$
are shown in Fig.\ref{fig: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 $0.25$ to $0.3$~pb for the $\tau\tau$ channel
and from $0.05$ to $0.15$~pb for the channels 
with decays into electrons and muons.

The bounds on $\sigma(e^{\pm}p \rightarrow e^{\mp}H^{\pm\pm}X)
\times {\rm BR}(H^{\pm\pm} \rightarrow l^{\pm}l^{\pm})$
are interpreted in terms of mass-dependent upper limits
on the couplings $h_{ee}^{L,R}$, $h_{\mu\mu}^{L,R}$, and $h_{\tau\tau}^{L,R}$. 
%
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 electron, muon, and tau channels and the 
combination of these three  channels allow a mass-dependent
upper limit on $h_{ee}^{L,R} = h_{\mu \mu}^{L,R} = h_{\tau \tau}^{L,R}$ 
shown in Fig.\ref{fig:democratic}.
%
We set a lower limit on $M_{H_{L,R}}$ of about 108 (109)~GeV in the electron (muon) channel 
for $h_{ll}^{L,R} = 0.3$,
corresponding to an interaction of electromagnetic strength
($h^2_{ee} / 4 \pi \simeq \alpha_{em}$). The combination of the 
electron, muon and tau channels gives a lower limit on  $M_{H_{L,R}}$  of 119~GeV 
for $h_{ll}^{L,R} = 0.3$.
%
%
%---
%

The resulting constraints
are also shown in Fig.\ref{electron} 
assuming that the doubly-charged Higgs bosons only decay to electrons,
i.e. ${\rm BR}(H^{\pm\pm} \rightarrow  e^{\pm}e^{\pm}) = 1$.
We set a lower limit on $M_{H_{L,R}}$ of about 139~GeV for $h_{ee}^{L,R} = 0.3$.
%
The result is compared to indirect limits 
from Bhabha scattering from OPAL~\cite{opal-singleprod}, 
to limits from direct searches 
for single production of doubly-charged Higgs from OPAL~\cite{opal-singleprod},
and from pair production from  CDF~\cite{cdf-pairprod}
and the LEP experiments~\cite{leppairprod}.
%
%
%

From the  $e^{\pm}p \rightarrow \mu^{\mp}\hpp X \rightarrow \mu^{\mp}e^{\pm}\mu^{\pm}X$
analysis we set upper limits on $h_{e\mu}^{L,R}$.
Assuming that the doubly-charged Higgs bosons only decay to electron-muon,
i.e. ${\rm BR}(H^{\pm\pm} \rightarrow  e^{\pm}\mu^{\pm}) = 1$,
we set a lower limit on $M_{H_{L,R}}$ of about 140~GeV for $h_{e\mu}^{L,R} = 0.3$.
%
The results of this analysis are shown in Fig.\ref{emu} and compared to limits from direct searches 
for pair production of doubly-charged Higgs from CDF~\cite{cdf-pairprod}
and the LEP experiments~\cite{leppairprod}.
The H1 limits extend the excluded region in the electron-muon channel
to masses that are beyond those reached in previous searches
for pair production at LEP and the Tevatron.




% 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
$ee$, $eee$, $\mu\mu$, $e\mu$, $e\mu\mu$
and $\tau\tau$  final states. 
%
In a previous model independent analysis, H1 observed
six events with a di-electron mass above 100~GeV,
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 multi-muon, multi-tau, nor electron-muon event is found in this  mass domain
compatible with the production of a doubly-charged Higgs boson.

This analysis places new limits on the \hpp~mass
and its Yukawa coupling to electrons and muons.
Assuming that the doubly-charged Higgs only decays to electrons, 
we set a lower limit on $M_{H_{L,R}}$  of about 139~GeV 
for a coupling value $h_{ee}^{L,R} = 0.3$, corresponding
to an interaction of electromagnetic strength.
Assuming that the doubly-charged Higgs only decays to electron-muon,
we set a lower limit on  $M_{H_{L,R}}$ of about 140~GeV 
for a coupling value $h_{e\mu}^{L,R} = 0.3$.

% 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 this experiment possible. 
We thank
the engineers and technicians for their work in constructing and
maintaining the H1 detector, our funding agencies for 
financial support, the
DESY technical staff for continual assistance
and the DESY directorate for support and 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.
%


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%\clearpage
\vspace{3cm}


% Feynman Diagrams
\begin{figure}[p] 
%  \begin{center}
  \epsfig{file=H1prelim-04-161.fig1a.eps,width=8cm}
  \epsfig{file=H1prelim-04-161.fig1b.eps,width=8cm}
  \epsfig{file=H1prelim-04-161.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 involving the $h_{ee}$ coupling
at the production vertex and the decay of the Higgs.
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.,26.){\epsfig{file=H1prelim-04-161.fig2a.eps,bbllx=15,bblly=15,bburx=380,bbury=370,width=7.5cm,clip=}}
\put(-83.,-49.){\epsfig{file=H1prelim-04-161.fig2b.eps,bbllx=15,bblly=0,bburx=560,bbury=475,width=7.9cm,clip=}}
\put(5.,26.){\epsfig{file=H1prelim-04-161.fig2c.eps,bbllx=15,bblly=0,bburx=560,bbury=475,width=7.9cm,clip=}}
%\put(5.,-46.){\epsfig{file=H1prelim-04-161.fig2d.eps,bbllx=5,bblly=20,bburx=540,bbury=550,width=7.7cm,height=7cm,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 
and tri-electron (top left), di-muon  invariant mass
$M_{\mu\mu}$ (top right), and electron-muon invariant mass (bottom left), 
%tau-tau candidates invariant mass $M_{\tau\tau}$ (bottom right),
compared 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} 

% tau tau Event
%\begin{figure}[p] 
%  \begin{center}
%  \epsfig{file=event_tautau.eps,width=16cm}
%  \end{center}
%  \caption{
%}
%\label{fig:event_tautau}
%\end{figure} 


% SigmaBR
%\begin{figure}[p] 
%  \begin{center}
%  \epsfig{file=doublyQichep3.feb04.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} 

% tau tau Event
\begin{figure}[p] 
  \begin{center}
  \epsfig{file=H1prelim-04-161.fig3.eps,width=16cm}
  \end{center}
  \caption{
Upper limits at $95\%$ confidence level on 
$\sigma(e^{\pm} p \rightarrow e^{\mp} H^{\pm\pm}X)
\times {\rm BR}(H^{\pm\pm} \rightarrow l^{\pm}l^{\prime\pm})$
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{fig:sigmabr}
\end{figure} 

% Limit, All Channels
\begin{figure}[p] 
  \begin{center}
  \epsfig{file=H1prelim-04-161.fig4.eps,width=16cm}
  \end{center}
  \caption{
Exclusion limits on the coupling 
$h_{ee}^{L,R}$ at $95\%$ confidence level
as a function of the doubly-charged Higgs mass
for the decay channels $H^{\pm\pm} \rightarrow  e^{\pm}e^{\pm},
\mu^{\pm}\mu^{\pm}, \tau^{\pm} \tau^{\pm}$ 
and the combination of these channels (full curve),
assuming  a democratic coupling of the doubly-charged
Higgs to leptons, i.e. BR$(H^{\pm\pm} \rightarrow  l^{\pm}l^{\pm})=1/3$.
}
  \label{fig:democratic}
\end{figure} 




% Limit, h_ee
\begin{figure}[p] 
  \begin{center}
  \epsfig{file=H1prelim-04-161.fig5.eps,width=16cm}
  \end{center}
  \caption{
Exclusion limits on the coupling $h_{ee}^{L,R}$ at $95\%$ confidence level
as a function of the doubly-charged Higgs mass
for the decay $H^{\pm\pm} \rightarrow  e^{\pm}e^{\pm}$
assuming BR$(H^{\pm\pm} \rightarrow  e^{\pm}e^{\pm})=1$.
The results of this analysis are compared to indirect limits 
from Bhabha scattering from OPAL, to limits from direct searches
for single production of doubly-charged Higgs from OPAL, and for 
pair production from the LEP experiments and CDF.
}
  \label{electron}
\end{figure} 



% Limit, h_emu
\begin{figure}[p] 
  \begin{center}
  \epsfig{file=H1prelim-04-161.fig6.eps,width=16cm}
  \end{center}
  \caption{
Exclusion limits on the coupling $h_{e\mu}^{L,R}$ at $95\%$ confidence level
as a function of the doubly-charged Higgs mass
for the decay $H^{\pm\pm} \rightarrow  e^{\pm}\mu^{\pm}$
assuming BR$(H^{\pm\pm} \rightarrow  e^{\pm}\mu^{\pm})=1$.
The results of this analysis are compared to limits from direct searches
for pair production of doubly-charged Higgs from the LEP experiments and CDF.
}
  \label{emu}
\end{figure} 




\end{document}

