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% Higgs Commands
% \newcommand{\mhpp}{\mbox{$M_{H^{\pm\pm}}$}}
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\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.
%


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%\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}

