%================================================================
% LaTeX file with prefered layout for H1 paper drafts
% use: dvips -D600 file-name
%================================================================
\documentclass[12pt]{article}
\usepackage{epsfig}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{hhline}
\usepackage{amssymb}
\usepackage{times}
\usepackage{cite}
\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}
\newlength{\dinwidth}
\newlength{\dinmargin}
\setlength{\dinwidth}{21.0cm}
\textheight23.5cm \textwidth16.0cm
\setlength{\dinmargin}{\dinwidth}
\setlength{\unitlength}{1mm}
\addtolength{\dinmargin}{-\textwidth}
\setlength{\dinmargin}{0.5\dinmargin}
\oddsidemargin -1.0in
\addtolength{\oddsidemargin}{\dinmargin}
\setlength{\evensidemargin}{\oddsidemargin}
\setlength{\marginparwidth}{0.9\dinmargin}
\marginparsep 8pt \marginparpush 5pt
\topmargin -42pt
\headheight 12pt
\headsep 30pt \footskip 24pt
\parskip 3mm plus 2mm minus 2mm
%===============================title page=============================
\begin{document}  
% The rest
\newcommand{\pom}{{I\!\!P}}
\newcommand{\reg}{{I\!\!R}}
\newcommand{\slowpi}{\pi_{\mathit{slow}}}
%\newcommand{\gevsq}{\mathrm{GeV}^2}
\newcommand{\fiidiii}{F_2^{D(3)}}
\newcommand{\fiidiiiarg}{\fiidiii\,(\beta,\,Q^2,\,x)}
\newcommand{\n}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)}
\newcommand{\nz}{1.30\pm 0.08 (stat.)^{+0.08}_{-0.14} (syst.)}
\newcommand{\fiidiiiful}{F_2^{D(4)}\,(\beta,\,Q^2,\,x,\,t)}
\newcommand{\fiipom}{\tilde F_2^D}
\newcommand{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)}
\newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (syst.)}
\newcommand{\fiipomarg}{\fiipom\,(\beta,\,Q^2)}
\newcommand{\pomflux}{f_{\pom / p}}
\newcommand{\nxpom}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)}
\newcommand {\gapprox}
   {\raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim}$}}
\newcommand {\lapprox}
   {\raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim}$}}
\def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex%
\raise 0.55ex\hbox{$\scriptstyle >$}\,}
\def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex%
\raise 0.55ex\hbox{$\scriptstyle <$}\,}
\newcommand{\pomfluxarg}{f_{\pom / p}\,(x_\pom)}
\newcommand{\dsf}{\mbox{$F_2^{D(3)}$}}
\newcommand{\dsfva}{\mbox{$F_2^{D(3)}(\beta,Q^2,x_{I\!\!P})$}}
\newcommand{\dsfvb}{\mbox{$F_2^{D(3)}(\beta,Q^2,x)$}}
\newcommand{\dsfpom}{$F_2^{I\!\!P}$}
\newcommand{\gap}{\stackrel{>}{\sim}}
\newcommand{\lap}{\stackrel{<}{\sim}}
\newcommand{\fem}{$F_2^{em}$}
\newcommand{\tsnmp}{$\tilde{\sigma}_{NC}(e^{\mp})$}
\newcommand{\tsnm}{$\tilde{\sigma}_{NC}(e^-)$}
\newcommand{\tsnp}{$\tilde{\sigma}_{NC}(e^+)$}
\newcommand{\st}{$\star$}
\newcommand{\sst}{$\star \star$}
\newcommand{\ssst}{$\star \star \star$}
\newcommand{\sssst}{$\star \star \star \star$}
\newcommand{\tw}{\theta_W}
\newcommand{\sw}{\sin{\theta_W}}
\newcommand{\cw}{\cos{\theta_W}}
\newcommand{\sww}{\sin^2{\theta_W}}
\newcommand{\cww}{\cos^2{\theta_W}}
\newcommand{\trm}{m_{\perp}}
\newcommand{\trp}{p_{\perp}}
\newcommand{\trmm}{m_{\perp}^2}
\newcommand{\trpp}{p_{\perp}^2}
\newcommand{\alp}{\alpha_s}

\newcommand{\alps}{\alpha_s}
\newcommand{\sqrts}{$\sqrt{s}$}
\newcommand{\LO}{$O(\alpha_s^0)$}
\newcommand{\Oa}{$O(\alpha_s)$}
\newcommand{\Oaa}{$O(\alpha_s^2)$}
\newcommand{\PT}{p_{\perp}}
\newcommand{\JPSI}{J/\psi}
\newcommand{\sh}{\hat{s}}
%\newcommand{\th}{\hat{t}}
\newcommand{\uh}{\hat{u}}
\newcommand{\MP}{m_{J/\psi}}
%\newcommand{\PO}{\mbox{l}\!\mbox{P}}
\newcommand{\PO}{I\!\!P}
\newcommand{\xbj}{x}
\newcommand{\xpom}{x_{\PO}}
\newcommand{\ttbs}{\char'134}
\newcommand{\xpomlo}{3\times10^{-4}}  
\newcommand{\xpomup}{0.05}  
\newcommand{\dgr}{^\circ}
\newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}}
\newcommand{\gev}{\,\mbox{GeV}}
\newcommand{\WBoson}{\mbox{$W$}}
\newcommand{\fbarn}{\,\mbox{{\rm fb}}}
\newcommand{\fbarnt}{\,\mbox{{\rm fb$^{-1}$}}}
%
% Some useful tex commands
%
\newcommand{\qsq}{\ensuremath{Q^2} }
\newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} }
\newcommand{\et}{\ensuremath{E_t^*} }
\newcommand{\rap}{\ensuremath{\eta^*} }
\newcommand{\gp}{\ensuremath{\gamma^*}p }
\newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} }
\newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} }
% Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4}
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
\def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}}
\def\NPB{{\em Nucl. Phys.}   {\bf B}}
\def\PLB{{\em Phys. Lett.}   {\bf B}}
\def\PRL{\em Phys. Rev. Lett.}
\def\PRD{{\em Phys. Rev.}    {\bf D}}
\def\ZPC{{\em Z. Phys.}      {\bf C}}
\def\EJC{{\em Eur. Phys. J.} {\bf C}}
\def\CPC{\em Comp. Phys. Commun.}

%%%%%%%%%%%%% my new commands %%%%%%%%%%%%%%%%
\newcommand{\be}{\begin{equation}} 
\newcommand{\ee}{\end{equation}} 
\newcommand{\ba}{\begin{eqnarray}} 
\newcommand{\ea}{\end{eqnarray}} 

\begin{titlepage}

\begin{center}
%{\it {\large version 1.08 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
\epsfig{file=H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                XV International Workshop on Deep-Inelastic Scattering and Related Subjects,}}\\
\multicolumn{4}{l}{{ DIS 2007 April~16-20,~2007,~Munich}} \\
%                 & Abstract:        &     &\\
%                 & Parallel Session: &    &\\ 
\hline
 & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}

% \noindent
% Date:               \\
% Version:            \\
% Editors:            \\
% Referees:           \\
% Comments by         
%\begin{flushright}
%H1prelim-04-063\\
%July 28, 2004
%\end{flushright}
\vspace{2cm}

\begin{center}
\begin{Large}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\bf \boldmath A search for excited electrons at HERA}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{1cm}

\begin{abstract}
\noindent

We present a search for excited electrons  using all data collected by the H1 experiment at HERA at a center-of-mass energy of $320$ GeV with an integrated luminosity of $435$~pb$^{-1}$. The electroweak decay of excited electrons, ${e}^{*}\rightarrow{e}{\gamma}$, ${e}^{*}\rightarrow{e}Z$, ${e}^{*}{\rightarrow}{\nu}W$ are considered and possible final states resulting from the $Z$ or $W$ hadronic decays are taken into account. No evidence for excited electron production is found. Mass dependent exclusion limits are determined for the ratio of the coupling to the compositeness scale, $f/{\Lambda}$. These limits extend the excluded region to higher masses than has been possible in previous searches.


\end{abstract}


\vspace{1.5cm}

\end{titlepage}

\newpage

\pagestyle{plain}

                                                                                                                                                                  


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

The discovery of excited states of quarks or leptons as predicted by compositness models~\cite{Harari:1982xy,Boudjema:1992em} would provide a convincing evidence for a new substructure of matter. 
Electron\footnote{the term ``electron'' is used generically to refer to both electrons and positrons.}-proton interactions at very high energies provide an excellent environement to look for excited states of first generation fermions. 
In particular, these excited electrons ($e^*$) could be singly produced throught $t$-channel $\gamma$ or $Z$ boson exchange.

In this paper we present a search for excited electrons using all HERA collider data of the H1 experiment. The data collected at electron and proton beam energies of $27.6$ GeV and $920$~GeV respectively corresponds to an integrated luminosity of $435$ pb$^{-1}$. The excited electrons are searched for through all their electroweak decays into a fermion and a gauge boson ($\gamma$, $W$ and $Z$). Only hadronic decays of the $W$ and $Z$ bosons are considered.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Phenomenology}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Compositeness models~\cite{Harari:1982xy,Boudjema:1992em,Hagiwara:1985wt,Baur:1989kv} attempt to explain the hierarchy of masses in the Standard Model by the existence of a substructure within the fermions. Several of these models predict excited states of the known leptons. Excited leptons are assumed to have the same electroweak SU(2) and U(1) gauge couplings, $g$ and $g'$, to the vector bosons, but are expected to be grouped into both left- and right-handed weak isodoublets with vector couplings. The existence of the right-handed doublets is required.

In $ep$ collisions, excited leptons could be produced via the process $ep{\rightarrow}F^{*}X$ (here X represents the proton remnant or proton in the case of elastic $e^*$ production), as a result of the F*FV couplings. Depending on the details of these couplings, excited leptons could be detected in the photonic, charged current, or neutral current channels.

The branching ratio of the excited leptons into the different vector bosons are determined by the strength of the three F*FV couplings. We use the effective Lagrangian: 
\be
L_{F^{*}F} = \frac{1}{2\Lambda}{\bar{F^{*}_{R}}}{{\sigma}^{\mu\nu}}[gf\frac{\vec{\tau}}{2}{\partial}_{\mu}{\vec{W_{\nu}}}+g'f'\frac{Y}{2}{\partial}_{\mu}B_{\nu}]{F_{L}} + h.c.
\ee
which describes the generalised magnetic de-excitation of the excited states. The matrix ${{\sigma}^{\mu\nu}}$ is the covariant bilinear tensor, $\tau$ are the Pauli matrices, $W_{{\mu}{\nu}}$ and $B_{{\mu}{\nu}}$ represent the fully gauge invariant field tensors, and Y is the weak hypercharge. The parameter $\Lambda$ has units of energy and can be regarded as the compositeness scale, while $f$ and $f'$ are the weight associated with the different gauge groups.

The relative values of $f$ and $f'$ also affect the size of the single-production cross-sections and their detection efficiencies. Depending on their relative values, either the photonic decay, the CC decay, or the NC decay will have the largest branching ratio, depending on the respective couplings:
$$
f_{\gamma} = e_{f}f' + I_{3L}(f-f') , f_{W} = \frac{f}{{\sqrt{2}}s_{\omega}} , f_{Z} = \frac{4I_{3L}(c_{\omega}^{2}f+s_{\omega}^{2}f')-4e_{f}s_{\omega}^{2}f'}{4s_{\omega}c_{\omega}}
$$
where $e_{f}$ is the excited fermion charge, $I_{3L}$ is the weak isospin, and $s_{\omega}(c_{\omega})$ are the sine (cosine) of the Weinberg angle ${\theta}_{\omega}$.

The following results for excited electrons will be interpreted using the conventional coupling assignments, $f = +f'$. 




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Standard Model processes and their simulation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Final states of events selection in this analysis contain either missing transverse momentum or an high energy electron (or photon) and a photon or jets with high tranverse energy. The main backgrounds from Standard Model (SM) processes which could mimic such signatures are mostly neutral current (NC)  and charged current (CC) deep-inelastic scattering (DIS) or photoproduction processes.
The Born, QCD Compton and Boson Gluon Fusion matrix elements are used in 
the RAPGAP~\cite{Jung:1993gf} event generator to model NC DIS and CC DIS events. The QED radiative effects arising from real photon emission from both the 
incoming and outgoing electrons are simulated using the 
HERACLES~\cite{Kwiatkowski:1990es} generator. 
To simulate the direct and resolved photoproduction of jets, prompt photon production  and the resolved photoproduction of photon pairs, the PYTHIA $6.1$ event generator~\cite{Sjostrand:2000wi} is used. Light and heavy flavoured jets 
are generated. The simulation contains the Born level hard scattering
matrix elements and radiative QED corrections. 
Processes with the production of three or more jets are accounted for using leading logarithmic parton showers as a representation of higher order QCD radiation. Hadronisation is modelled using Lund string fragmentation~\cite{Sjostrand:2000wi}.
The prediction of processes with two or more high transverse momentum jets is scaled by a factor of $1.2$ to normalise the leading order Monte Carlos to next-to-leading order QCD calculations~\cite{Adloff:2002au}. 
Contributions from elastic and quasi-elastic QED-Compton scattering are simulated with the WABGEN~\cite{Berger:kp} generator. 
Possible contributions arising from the production of $W$ bosons or multi-lepton events are also considered and modelled using the EPVEC~\cite{Baur:1991pp} and GRAPE~\cite{Abe:2000cv} event generators, respectively.

All generated events are passed through the full GEANT~\cite{Brun:1987ma} based simulation of the H1 apparatus, which takes into account the running conditions of the different data taking
periods.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The H1 Detector}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

A detailed description of the H1 experiment can be found in \cite{Abt:h1}.
Only the H1 detector components relevant to the
present analysis are briefly described here.
Jets and electrons are measured with the Liquid
Argon (LAr) calorimeter~\cite{Andrieu:1993kh}, which covers the polar angle\footnote{ 
  The origin of the H1 
  coordinate system is the nominal $ep$ interaction point, with 
  the direction of the proton beam defining the positive 
  $z$-axis (forward region). The transverse momenta are measured 
  in the $xy$ plane. 
  The 
  pseudorapidity $\eta$ is related to the polar 
  angle $\theta$ by $\eta = -\ln \, \tan (\theta/2)$.} range
$4^\circ < \theta < 154^\circ$ with full azimuthal acceptance.
Electromagnetic shower energies are measured with a precision of
$\sigma (E)/E = 12\%/ \sqrt{E/\mbox{GeV}} \oplus 1\%$ and hadronic energies
with $\sigma (E)/E = 50\%/\sqrt{E/\mbox{GeV}} \oplus 2\%$, as measured in test beams.
In the backward region, energy measurements are provided by a lead/scintillating-fiber (SpaCal) calorimeter~\cite{Appuhn:1996na} covering the range $155^\circ < \theta < 178^\circ$.
The central and forward tracking detectors are used to
measure charged particle trajectories, to reconstruct the interaction
vertex and to supplement the measurement of the hadronic energy.
The LAr and inner tracking detectors are enclosed in a super-conducting magnetic
coil with a strength of $1.15$~T.
% The return yoke of the coil is the outermost part of the detector and is
% equipped with streamer tubes forming the central muon detector
% ($4^\circ < \theta < 171^\circ$).
% In the forward region of the detector ($3^\circ < \theta < 17^\circ$) a set of
% drift chamber layers (the forward muon system) detects muons and, together with an
% iron toroidal magnet, allows a momentum measurement.
The luminosity measurement is based on the Bethe-Heitler process  $ep \rightarrow ep \gamma$,
where the photon is detected in a calorimeter located
downstream of the interaction point.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Data Analysis}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



Events are first selected by requiring that the event vertex be reconstructed within $35$ cm in $z$ of the nominal interaction point. In addition topological filters and timing vetoes are applied to remove background events  induced by cosmic showers and other non-$ep$ sources.
The main trigger of the events is provided by the LAr calorimeter.
The trigger efficiency is close 
to $100\%$ for events having an electromagnetic deposit in the LAr
(electron or photon) with an energy greater than 
$10$~GeV~\cite{Adloff:2003uh}. For events with missing transverse momentum above $20$ GeV, the trigger efficiency is $\sim$ $90$~\%.

The identification of electrons or photons is first based on the measurement of a compact and isolated electromagnetic shower in the LAr calorimeter. In addition, the electromagnetic cluster is required to be be isolated from jets by a distance $R > 0.5$ to the jet axis in pseudorapidity-azimuth.
Energy deposits in the calorimeter and tracks in the inner tracking system are used to form combined cluster-track objects, from which the hadronic energy is reconstructed.
Jets are defined using an inclusive $k_T$ algorithm \cite{Ellis:1993tq,Catani:1993hr} with a minimum transverse momentum of $3$ GeV.
The missing transverse momentum  $P_T^{miss}$ of the event is derived from all identified particles and energy deposits in the event.



\subsection{$e\gamma$ Resonance Search}


The signature of this channel consist of two isolated electromagnetic cluster with an high transverse momentum. The principal SM background arise from elastic and inelastic Compton events.
Two isolated electromagnetic clusters in the  polar angle $5^\circ < \theta_{e1,e2} < 130^\circ$ are first required, with a transverse momentum larger than $20$ and $15$ GeV, respectively.
To further suppress contributions from Compton events, the sum of the energies of the two electromagnetic clusters has to be greater than $100$ GeV and the sum of their total transverse momentum should be larger than $75$ GeV. 
Finally, $112$ events survives the selection criteria. The expected SM contribution is $125$~$\pm$~$19$ events and is dominated by Compton events. The resulting selection efficiency varies from $60$\% to $70$\% for excited electrons of mass $100$ GeV and $250$ GeV, respectively.



\subsection{$\nu{q}{\bar{q}}$  Resonance Search}

For this search, the dominant SM background consists of multi-jet CC DIS events with a moderate contribution from photoproduction.
The presence of a neutrino is inferred from substantial missing momentum $P_{T}^{miss} > 20$~GeV. 
We use a subsample of events with at least two jets, each having a transverse momentum larger than $20$ and $15$ GeV, respectively, and a polar angle between $5^{\circ}$ and $130^{\circ}$. 
The ratio $V_{ap}/V_{p}$ of transverse energy flow anti-parallel and parallel to the hadronic final state~\cite{Adloff:2003uh} is used to suppress photoproduction events. Events with $V_{ap}/V_{p} > 0.3$ are rejected.
The $W$ candidate is reconstructed from the combination of two jets with an invariant mass closest to the nominal $W$ boson mass. The reconstructed mass is required to be above $50$ GeV and above $65$ GeV for events whose missing energy $E^{miss}$ is below $65$ GeV.
After these cuts, $172$ events are found compared to an expected SM contribution of $175$~$\pm$~$39$ events. No significant excess is observed. 
The acceptance for $e^*$ events in this final state is approximately $40$~\% for $M_{e^*} > $ $150$ GeV.
 

\subsection{e$q{\bar{q}}$ Resonance Search} 

In this channel multi-jet NC DIS events constitute the main contribution from SM processes.
Events are selected by the presence of an electron in the LAr ($5^\circ< \theta^e < 130^\circ$) with  $Q^2_e > 2500$~GeV$^2$ or a tranverse momentum $P_T^e$ greater than 25 GeV. The restriction on the electron polar angle to the forward region of the LAr removes a large part of the NC DIS contribution.
The presence of at least two high $P_T$ jets with $P_{T}^{jet1,\; jet2} > 20, 15$~GeV and  $5^{\circ} < \theta^{jet1,\; jet2} < 130^{\circ}$ is required.
Then, a $Z$ candidate is reconstructed in those events from the combination of two jets with an invariant mass closest to the nominal $Z$ boson mass. 
The reconstructed mass of the $Z$ candidate $M_{jj}$ is required to be larger than $61$ GeV.
To increase the separation power between NC DIS events and a $\nu^*$ signal we demand that the polar angle of the highest $P_T$ jet associated to the $Z$ candidate be lower than $80^\circ$ and that $M_{jj} > 76$ GeV for the events with $P_T^e <$ $65$ GeV.
After the selection, $351$ events are observed while $318$ $\pm$ $64$ are expected from the SM background.
The efficiency for selecting $e^*$ events is of the order of $45$~\% in this decay channel.


\section{Interpretation}


The event yields observed in each decay channel are summarised in table~\ref{tab:estaryields}. The observed event yields are in good agreement with SM expectations, which are dominated by NC DIS for $e{q}{\bar{q}}$ resonance search, by CC DIS events in the $\nu{q}{\bar{q}}$ decay cahnenl, and by Compton events for the   $e\gamma$ resonance search. 
The distributions of the invariant mass of the data events and of expected SM background are compared in figure~\ref{fig:Mass} for the three channels. 
Both data and SM are in good agreement and no additional resonance is seen in the data.
No data events is observed in channels corresponding to leptonic decays of $W$ or $Z$ bosons in agreement with SM expectations below one in those classes.

Since there is no evidence for excited electrons, an upper limit on the coupling $f/{\Lambda}$ as a function of the mass of the excited electron is derived. 
The limit is presented at the 95~\% confidence level and is obtained using a modified frequentist approach \cite{Junk:1999kv} which takes statistical and systematical uncertainties into account.

The resulting limit after combination of the three decay channels is presented in figure~\ref{fig:LimitCoupling}, for the conventional assumptions  $f = + f'$. 
This new result improve significantly the bounds previously obtained by H1~\cite{Adloff:2002dy} using $120$~pb$^{-1}$ of HERA I data.
Considering the assumption $f/\Lambda = 1/M_{e^*}$ excited electrons with masses up to $273$ GeV are excluded.  


For comparisons, combined direct and indirect limits obtained in $e^+ e^-$ collisions at LEP are also shown on figure~\ref{fig:LimitCoupling}, as well as the result from the CDF experiment \cite{Acosta:2004ri} at the Tevatron.
The limits from the present analysis are more stringent at high masses and extend beyond the kinematic reach of previous searches.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Summary}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

In summary, using all data collected by the H1 experiment at a center-of-mass energy of $320$ GeV with an integrated luminosity of $435$~pb$^{-1}$ a search for the production of excited electrons has been performed. 
The excited electron decay channels ${e}^{*} {\rightarrow} {e}{\gamma}$,  ${e}^{*} {\rightarrow} {e}{Z}$ and ${e}^{*} {\rightarrow} {\nu}{W}$ with subsequent hadronic decays of the $W$ and $Z$ bosons have been considered and no indication of a signal was found.
New limits on the coupling $f/\Lambda$ as a function of the excited electron masses have been established, using the specific relation between the couplings $f = + f'$.
Assuming $f = + f'$ and $f/\Lambda=1/M_{e^*}$ excited electrons with a mass lower than $273$ GeV are excluded at $95$\% confidence level.
The present results greatly extend previous searched domains at HERA and is complementary to searches for excited electrons performed at other colliders.



\newpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}

%%%%%%%%%%%%%%%  excited fermion pheno %%%%%%%%%%%%%%%%%%%%%
% \bibitem{Harrari:1979}
% S.~Weinberg,Phys.\ Rev. {\bf D 20} (1976); ibid Phys.\ Rev. {\bf D 19} (1979) 1277
% H.~Harrari, Phys.\ Lett. {\bf B 98} (1981) 269.


% \bibitem{Derrick:1995}
% ZEUS Collaboration, M.~Derrick {\it et al.}, Z.\ Phys.\ J.~{\bf C 65} (1995) 627.


%\cite{Harari:1982xy}
\bibitem{Harari:1982xy}
  H.~Harari,
  %``Composite Models For Quarks And Leptons,''
  Phys.\ Rept.\  {\bf 104} (1984) 159.
  %%CITATION = PRPLC,104,159;%%

%\cite{Boudjema:1992em}
\bibitem{Boudjema:1992em}
  F.~Boudjema, A.~Djouadi and J.~L.~Kneur,
  %``Excited fermions at e+ e- and e P colliders,''
  Z.\ Phys.\ C {\bf 57} (1993) 425.
  %%CITATION = ZEPYA,C57,425;%%

%\cite{Hagiwara:1985wt}
\bibitem{Hagiwara:1985wt}
  K.~Hagiwara, D.~Zeppenfeld and S.~Komamiya,
  %``Excited Lepton Production At Lep And Hera,''
  Z.\ Phys.\ C {\bf 29} (1985) 115.
  %%CITATION = ZEPYA,C29,115;%%

%\cite{Baur:1989kv}
\bibitem{Baur:1989kv}
  U.~Baur, M.~Spira and P.~M.~Zerwas,
  %``Excited Quark And Lepton Production At Hadron Colliders,''
  Phys.\ Rev.\ D {\bf 42} (1990) 815.
  %%CITATION = PHRVA,D42,815;%%


% %\cite{Adloff:2000gv}
% \bibitem{Adloff:2000gv}
%   C.~Adloff {\it et al.}  [H1 Collaboration],
%   %``A search for excited fermions at HERA,''
%   Eur.\ Phys.\ J.\ C {\bf 17} (2000) 567, [hep-ex/0007035].
%   %%CITATION = HEP-EX 0007035;%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\cite{Jung:1993gf}
\bibitem{Jung:1993gf}
H.~Jung,
%``Hard diffractive scattering in high-energy e p collisions and the Monte Carlo generation RAPGAP,''
Comput.\ Phys.\ Commun.\  {\bf 86} (1995) 147.
%%CITATION = CPHCB,86,147;%%

%\cite{Sjostrand:2000wi}
\bibitem{Sjostrand:2000wi}
T.~Sjostrand, P.~Eden, C.~Friberg, L.~Lonnblad, G.~Miu, S.~Mrenna and E.~Norrbin,
%``High-energy-physics event generation with PYTHIA 6.1,''
Comput.\ Phys.\ Commun.\  {\bf 135} (2001) 238,
[hep-ph/0010017].
%%CITATION = HEP-PH 0010017;%%

%\cite{Kwiatkowski:1990es}
\bibitem{Kwiatkowski:1990es}
A.~Kwiatkowski, H.~Spiesberger and H.~J.~Mohring,
%``Heracles: An Event Generator For E P Interactions At Hera Energies Including Radiative Processes: Version 1.0,''
Comput.\ Phys.\ Commun.\  {\bf 69} (1992) 155.
%%CITATION = CPHCB,69,155;%%

%\cite{Adloff:2002au}
\bibitem{Adloff:2002au}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of dijet cross sections in photoproduction at HERA,''
Eur.\ Phys.\ J.\ C {\bf 25} (2002) 13,
[hep-ex/0201006].
%%CITATION = HEP-EX 0201006;%%

%\cite{Berger:kp}
\bibitem{Berger:kp}
C.~Berger and P.~Kandel,
%``A New Generator For Wide Angle Bremsstrahlung,''
%\href{http://www.slac.stanford.edu/spires/find/hep/www?irn=4270703}{SPIRES entry}
Prepared for Workshop on Monte Carlo Generators for HERA Physics Hamburg, Germany, 27-30 Apr 1998.

%\cite{Baur:1991pp}
\bibitem{Baur:1991pp}
U.~Baur, J.~A.~Vermaseren and D.~Zeppenfeld,
%``Electroweak vector boson production in high-energy e p collisions,''
Nucl.\ Phys.\ B {\bf 375} (1992) 3.
%%CITATION = NUPHA,B375,3;%%

%\cite{Abe:2000cv}
\bibitem{Abe:2000cv}
T.~Abe,
%``GRAPE-Dilepton (Version 1.1): A generator for dilepton production in e  p collisions,''
Comput.\ Phys.\ Commun.\  {\bf 136} (2001) 126,
[hep-ph/0012029].
%%CITATION = HEP-PH 0012029;%%


%%%% NLO W rewaight
% %\cite{Diener:2003df}
% \bibitem{Diener:2003df}
% K.~P.~Diener, C.~Schwanenberger and M.~Spira,
% %``Photoproduction of W bosons at HERA: Reweighting method for  implementing QCD corrections in Monte Carlo programs,''
% hep-ex/0302040.
% %%CITATION = HEP-EX 0302040;%%
  
  %\cite{Brun:1987ma}
\bibitem{Brun:1987ma}
R.~Brun, F.~Bruyant, M.~Maire, A.~C.~McPherson and P.~Zanarini,
%``Geant3,''
CERN-DD/EE/84-1.

%%%%%%%%%%%%%%%%%%%%%%% H1 detector %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\bibitem{Abt:h1}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 Detector At Hera,''
%``The Tracking, calorimeter and muon detectors of the H1 experiment at HERA ,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310 and 348.
%%CITATION = NUIMA,A386,310;%%
 

%\cite{Andrieu:1993kh}
\bibitem{Andrieu:1993kh}
B.~Andrieu {\it et al.}  [H1 Calorimeter Group Collaboration],
%``The H1 liquid argon calorimeter system,''
Nucl.\ Instrum.\ Meth.\ A {\bf 336} (1993) 460.
%%CITATION = NUIMA,A336,460;%%
 
%\cite{Appuhn:1996na}
\bibitem{Appuhn:1996na}
R.~D.~Appuhn {\it et al.}  [H1 SPACAL Group Collaboration],
%``The H1 lead/scintillating-fibre calorimeter,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 397.
%%CITATION = NUIMA,A386,397;%%




%%%%%%%%%%%%%%%% trigger efficiencies %%%%%%%%%%%%%%%%%%%
%\cite{Adloff:2003uh}
\bibitem{Adloff:2003uh}
C.~Adloff {\it et al.}  [H1 Collaboration],
 %``Measurement and QCD analysis of neutral and charged current cross  sections
%at HERA,''
Eur.\ Phys.\ J.\ C {\bf 30}, 1 (2003), [hep-ex/0304003].
%%CITATION = HEP-EX 0304003;%%





%%%%%%%%%%%%%%%% kT jets %%%%%%%%%%%%%%%%%%%
%\cite{Ellis:1993tq}
\bibitem{Ellis:1993tq}
S.~D.~Ellis and D.~E.~Soper,
%``Successive combination jet algorithm for hadron collisions,''
Phys.\ Rev.\ D {\bf 48} (1993) 3160
[hep-ph/9305266].
%%CITATION = HEP-PH 9305266;%%
 
%\cite{Catani:1993hr}
\bibitem{Catani:1993hr}
S.~Catani, Y.~L.~Dokshitzer, M.~H.~Seymour and B.~R.~Webber,
%``Longitudinally invariant K(t) clustering algorithms for hadron-hadron collisions,''
Nucl.\ Phys.\ B {\bf 406} (1993) 187.
%%CITATION = NUPHA,B406,187;%%



%%%%%%%%%%%% limits %%%%%%%%%%%%%%
%\cite{Junk:1999kv}
\bibitem{Junk:1999kv}
  T.~Junk,
  %``Confidence level computation for combining searches with small
  %statistics,''
  Nucl.\ Instrum.\ Meth.\  A {\bf 434} (1999) 435,
  [hep-ex/9902006].
  %%CITATION = NUIMA,A434,435;%%

%%%%%%%%%%% other nustar results %%%%%%%%%%%%%%%%%
% \bibitem{Nico:2003}
% N.~Delerue. {\it Recherche de leptons excit\'es dans les donn\'ees de l'exp\'erience H1 aupr\`es du collisionneur HERA}. Thesis University of M\'editerran\'ee, 2003, http://www-h1.desy.de/publications/theseslist.html


%\cite{Adloff:2002dy}
\bibitem{Adloff:2002dy}
  C.~Adloff {\it et al.}  [H1 Collaboration],
  %``Search for excited electrons at HERA,''
  Phys.\ Lett.\  B {\bf 548} (2002) 35
  [arXiv:hep-ex/0207038].
  %%CITATION = PHLTA,B548,35;%%

%\cite{Acosta:2004ri}
\bibitem{Acosta:2004ri}
  D.~Acosta {\it et al.}  [CDF Collaboration],
  %``Search for excited and exotic electrons in the $e \gamma$ decay channel in
  %$p \bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV,''
  Phys.\ Rev.\ Lett.\  {\bf 94} (2005) 101802,
  [hep-ex/0410013].
  %%CITATION = PRLTA,94,101802;%%
\end{thebibliography}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newpage


% \begin{table}[]
% \begin{center}
% \begin{tabular}{|c||c|c||c|c|c|c|}
% \multicolumn{7}{c}{Search for e$^*$ HERA I+II ($\sqrt s = 920$ GeV, $435$ pb$^{-1}$, preliminary)}\\
% \hline
% Selection & Data & SM & CC DIS & NC DIS+Comptons & ~~${\gamma}p$~~ & $l$-pair \\
% 
% \hline
% ${e}^{*} {\rightarrow} {\nu}{W_{{\hookrightarrow}qq}}$ & $172$ & $175~{\pm}~39$ & $151$ & $1$ & $22$ & $1$ \\
% \hline
% ${e}^{*} {\rightarrow} {e}{Z_{{\hookrightarrow}qq}}$ & $351$ & $318~{\pm}~64$ & --- & $310$ & $4$ & $4$ \\
% \hline                                        
% ${e}^{*} {\rightarrow} {e}{\gamma}$ & $112$ & $125~{\pm}~19$ & --- & $117$ & --- & $8$ \\ 
% \hline
% \end{tabular}
% \end{center}
% \caption{Observed and predicted event yields for the $\nu\gamma$, ${\nu}{Z_{{\hookrightarrow}q\bar{q}}}$, ${e}{W_{{\hookrightarrow}q\bar{q}}}$  event classes.
%   The analysed data sample corresponds to an integrated luminosity of 114 pb$^{-1}$.
%   The errors on the prediction include model uncertainties and experimental systematic errors added in quadrature.}
% \label{tab:nustaryields}
% \end{table}
% 
\begin{table}[]
\begin{center}
\begin{tabular}{|c||c|c||c|}
\multicolumn{4}{c}{Search for e$^*$ HERA I+II ($\sqrt s = 320$ GeV, $435$ pb$^{-1}$, preliminary)}\\
\hline
Selection & ~~Data~~ & ~~~~~~~SM~~~~~~~ & Efficiency $\times$ BR \\

\hline
${e}^{*} {\rightarrow} {\nu}{W_{{\hookrightarrow}qq}}$ & $172$ & $175~{\pm}~39$ & $\sim 40$ \% \\
\hline
${e}^{*} {\rightarrow} {e}{Z_{{\hookrightarrow}qq}}$ & $351$ & $318~{\pm}~64$ & $\sim 45$ \%\\
\hline                                        
${e}^{*} {\rightarrow} {e}{\gamma}$ & $112$ & $125~{\pm}~19$ & $60$--$70$ \%\\ 
\hline
\end{tabular}
\end{center}
\caption{Observed and predicted event yields for the studied decay channels.
  The analysed data sample corresponds to an integrated luminosity of $435$ pb$^{-1}$.
  The errors on the prediction include model uncertainties and experimental systematic errors added in quadrature.}
\label{tab:estaryields}
\end{table}


\begin{figure}[htbp] 
  \begin{center}
    \includegraphics[width=.5\textwidth]{H1prelim-07-065.fig1.eps}\put(-10,37) {{\bf (a)}}
    \includegraphics[width=.5\textwidth]{H1prelim-07-065.fig2.eps}\put(-10,37) {{\bf (b)}}\\ 
    \includegraphics[width=.5\textwidth]{H1prelim-07-065.fig3.eps}\put(-10,37) {{\bf (c)}}
  \end{center}
  \caption{Invariant mass distribution of the $e^*$ candidates for the (a) ${e}^{*} {\rightarrow} {e}{\gamma}$, (b) ${e}^{*} {\rightarrow} {e}{Z_{{\hookrightarrow}q\bar{q}}}$ and (c) ${e}^{*} {\rightarrow} {\nu}{W_{{\hookrightarrow}q\bar{q}}}$ searches. The points corresponds to the observed data events in the final selections and the histogram to the total SM prediction. The error bands on the SM prediction include model uncertainties and experimental systematic errors added in quadrature.}
\label{fig:Mass}  
\end{figure} 

\begin{figure}[htbp] 
  \begin{center}
    \includegraphics[width=12cm]{H1prelim-07-065.fig4.eps}
  \end{center}
  \caption{Exclusion limits on the coupling $f/\Lambda$ at 95\% C.L. as a function of the mass of the excited electron with the assumption $f = +f'$. 
The observed limits from this analysis using $435$ pb$^{-1}$ of H1 data is represented by the yellow area.
Values of the couplings above the curves are excluded.
The orange-dark area corresponds to the exclusion domain published by the H1 experiment \protect{\cite{Adloff:2002dy}} using HERA~I data. The combined exclusion limit from LEP experiments is represented by the violet line, for direct (plain line) and indirect searches (dashed line) for excited electrons. The result from the CDF experiment \protect{\cite{Acosta:2004ri}} are also shown (blue line).}
\label{fig:LimitCoupling}  
\end{figure} 


\end{document}

