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%%% My specific commands
\newcommand{\etm}{\ensuremath{E_t^{\mathrm{miss}}}}
\newcommand{\nnga}{$\nu^* \rightarrow \nu \gamma$~}
\newcommand{\newqq}{$\nu^* \rightarrow e W_{\hookrightarrow q \bar{q}} $~}
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\begin{titlepage}

\noindent
Date:      \today         \\
Version:   0.1         \\
Editors:  M.C Cousinou, N.Delerue \\
Referees:  A.Sch\"oning, S.Schmitt \\
EPS 2001 Abstract number: 823, Session 6 \\
LP 2001 Abstract number: 515, Session S11\\
\vspace{2cm}

\begin{center}
\begin{Large}
  {\bf 
	SEARCH FOR EXCITED NEUTRINOS AT HERA}\\

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
We present a  search for excited neutrinos
using $e^- p$ data taken by the H1 experiment at $\sqrt{s} = 318 $~GeV with an integrated luminosity of 15 pb$^{-1}$.
No evidence for excited neutrino production is found. Mass dependent exclusion limits are determined for the ratio of the coupling to the compositeness scale, $f/\Lambda$, independently of the relative values of the coupling constants $f$ and $f'$.
\end{abstract}

\vspace{1.5cm}


\end{titlepage}


\newpage



%\section{Introduction}

The discovery of excited quarks or leptons,
as predicted by composite models, would supply convincing evidence for a substructure of fermions.
Electron-proton interactions at very high energies provide ideal conditions
to look for excited states of  first generation fermions.  In particular the magnetic-transition coupling of the electron to a heavy fermion would
allow for single production of excited neutrinos ($\nu^*$) through t-channel $W$ boson exchange.
  In this paper we present a search for $\nu^*$ production
  followed by the electroweak radiative decays 
  $\nu^* \rightarrow \nu \gamma$, $\nu^* \rightarrow e W$ or $\nu^* \rightarrow \nu Z$.
  The analysis makes use of 15 pb$^{-1}$ of $e^- p$ data with an electron beam energy of 27.6 GeV and a proton beam energy of 920 GeV collected in  1998 and 1999 with the H1 experiment at HERA.  
Compared to previous H1 results from $e^-p$ collisions~\cite{Ahmed:1994yi} the analysis benefits from an increase in luminosity by a factor of 30 and in the center-of-mass energy from 300 GeV to 318 GeV. Furthermore, it also improves significantly on results derived from larger luminosity of $e^+p$ data at a center-of-mass energy of 300 GeV~\cite{Adloff:2000gv}, due to a much larger cross-section for $\nu^*$ production in $e^-p$ scattering as compared to the $e^+p$ case.
At a $\nu^*$ mass of 200 GeV the ratio of those cross-sections is of the order of 100.
Production cross-sections and decays of excited neutrinos can be calculated using an effective lagrangian~\cite{Hagiwara:1985wt,Baur:1990kv}. The cross-section and the branching ratio depend on 
coupling constants $f$ and $f'$ for the gauge groups $SU(2)$ and $U(1)$ and a
compositeness mass scale $\Lambda$.
The electroweak decay channels $\nu^* \rightarrow \nu \gamma$, $\nu^* \rightarrow e W $ and $\nu^* \rightarrow \nu Z $ cover all possible decay channels of the excited neutrino.
As shown in~\cite{Baur:1990kv}, the width of the $\nu^*$ is a function of $f$, $f'$ and $\Lambda$. For the coupling constants our analysis is sensitive to, the decay width of the $\nu^*$ can be larger than the detector resolution. This experimental resolution is of the order of 10~GeV, while the natural width of the $\nu^*$ can reach a few hundred GeV at high masses. 
Within the framework of this analysis the narrow width approximation (NWA) is valid for masses below 200 GeV.
In this approximation the production and decay of the $\nu^*$ are factorized, and we use the COMPOS~\cite{Kohler:1991yu} generator for our calculations. For larger masses, the full cross-section of $\nu^*$ production and the 3-body decay is evaluated with COMPHEP~\cite{Pukhov:1999gg} using the lagrangian~\cite{Baur:1990kv}. In the overlap region the compability of COMPOS and COMPHEP has been verified.




The data presented in this analysis have been collected with the H1 apparatus~\cite{Abt:1997hi}.
Here only the detector components most relevant for this analysis are described briefly.
The interaction region is surrounded by a system of drift and proportional
chambers covering the angular range $7^o < \theta < 176^o$\footnote{The forward direction ( $z >$ 0 ) is the proton beam direction and a direct frame ($z$, $\theta$, $\varphi$) is used later in this paper.}. The tracking system is
placed inside a finely segmented liquid argon (LAr) calorimeter
covering the polar angular range 4$^o < \theta <$ 154$^o$~\cite{Andrieu:1993kh}.
%The electromagnetic part is made of lead/argon  and the 
%hadronic part of stainless steel/argon~\cite{Andrieu:1993kh}.
Energy resolutions of
 $\sigma_E / E \simeq 12\% / \sqrt{E} \oplus 1\%$ for
 electrons and $ \sigma_E / E \simeq 50\% / \sqrt{E} \oplus 2\%$ for
 hadrons have been obtained in test beam measurements 
~\cite{Andrieu:1994xn,Andrieu:1994yn}. The tracking system and calorimeters are surrounded by a
 super-conducting solenoid and an iron yoke instrumented with streamer tubes.
Leakage of hadronic showers outside the calorimeter is measured by analogue 
charge sampling of the streamer tubes with a resolution~\cite{iron} of $\sigma_E / E \simeq 100\% / \sqrt{E}$.
%Muon tracks are identified from their hit pattern in the streamer tubes.



%\section{Data sample, particles identification algorithms and uncertainties}
%\subsection{Data sample}
The selection of $\nu^*$ events is based on photon or electron identification, missing
transverse energy (\etm), and the identification of jets, depending on the search channel. Electromagnetic clusters are identified with more than 95\% of the energy in the electromagnetic part of the calorimeter and certain 
isolation criteria~\cite{Schoening}. They are further differentiated into electron and photon candidates, depending 
on whether a charged track is pointing to the cluster center within a radius of 12 cm or not. In the forward region of the calorimeter this condition is relaxed to 24 cm. Jets are reconstructed from the hadronic final state using a cone algorithm, adapted from the LUCELL scheme in the JETSET package~\cite{Sjostrand:1995iq}.


%\section{ Monte Carlo generators}
Background not related to $e^- p$ collisions is rejected by requiring
that the event time coincides with the time of the bunch crossing,
by using topological filters, and by requiring a primary interaction vertex reconstructed within 
$\pm 35$ cm around the nominal vertex value.
The Standard Model (SM) backgrounds which could mimic the $\nu^*$ signatures
are Neutral Current Deep Inelastic Scattering (NC~DIS), Charged Current Deep Inelastic Scattering (CC~DIS) and photoproduction processes ($\gamma$p). 
The background expectation from NC~DIS and CC~DIS is calculated by the event generator Django~\cite{Schuler:1991yg}. It includes first order QED corrections based on HERACLES~\cite{Kwiatkowski:1992es}, and QCD radiation based on the Colour Dipole Model~\cite{Andersson:1989gp}. Parton densities are taken from the MRST~\cite{Martin:1998sq} parametrization  which includes constraints from DIS measurements at HERA up to squared momentum transfer $Q^2 = 5000 {\rm GeV^2}$~\cite{Aid:1996au,Adloff:1997mf,Derrick:1996ef,Derrick:1996hn}. The hadronisation process is simulated in the Lund string fragmentation scheme using JETSET.
% It is important to note that DJANGO does not take fully into account QED radiation from the quark line. 
Direct and resolved $\gamma$p processes, including prompt photon production, are simulated with PYTHIA~\cite{Sjostrand:1994yb}. 
All Monte Carlo samples are interfaced to a full simulation of the H1 detector response.




%\boldmath\section{Description of the event selections and comparison with Standard Model Expectation }\label{subsec:ana}\unboldmath 

%\subsection{Events with one electromagnetic cluster and missing transverse energy: the 
%$\nu^* \rightarrow \nu \gamma$ channel} \label{subsec:etnu}


The \nnga channel is characterised by missing transverse energy and an electromagnetic cluster in the LAr. The main SM background is expected to come from CC~DIS events.
Events are selected with an identified photon with a transverse momentum
($P_t$) greater than 16 GeV and a total missing transverse energy \etm greater than 16 GeV.
To reject NC~DIS background where the scattered electron (sometimes mistaken as a photon) is preferably scattered by small angles, photons are accepted in the forward region of the detector only ($\theta < 1.8$~rad). For \etm $> 30$~GeV photons in the
very forward region ($\theta < 1 $~rad) are also accepted if they                     are linked to a track and thus have been identified as an electron.
In that particular region the conversion rate $\gamma \rightarrow ee$ and the number of randomly assigned tracks is expected to be high due to the high multiplicity of hadronic charged particles from jets. 
In order to be able to reconstruct the event vertex position from charged particles, the event is required to contain a jet ($P_t^{jet}>$5~GeV). To further suppress background from events with hadronic energy fluctuations of jets resulting in a measured missing transverse momentum, the projection of the missing transverse energy on the plane perpendicular to the recoil jet is required to be greater than 8~GeV. 
To reduce the influence of photons coming from QED radiation on the quark line, the jet must be isolated from the photon in the $\varphi$ plane ($\Delta\varphi($jet,$\gamma) > .35$ rad). 
%These selection criteria are summarised in table \ref{table:nnga_cuts}.
In total, 2~events are found in this channel, for an expected background
of $ 3.0 \pm 0.2 \pm 1.2 $ events (statistical error is given first followed by the systematical one). The background is composed of 2.7 events from CC~DIS
and 0.3 events from NC~DIS with negligible contributions from $\gamma$p. 
The resulting selection efficiencies are shown in fig.~\ref{fig:eff}.



%\subsection{Events with 2 high $E_t$ jets and one electron: the $\nu^* \rightarrow e W_{\hookrightarrow q \bar{q}} $ channel} \label{subsec:je}

The \newqq channel is characterised by an electromagnetic cluster with an associated track and
two jets. The main SM background are NC DIS events. Photoproduction events
do not contribute significantly for electrons with high transverse
momentum. A cut $P_t^{ele} >$ 12.5~GeV is chosen.
At very high transverse momentum $P_t^{ele} >$ 85~GeV the background
from NC DIS is low and no further cuts are made. For a transverse momentum
65~GeV $< P_t^{ele} <$ 85~GeV two jets with an invariant mass $\md >$50~GeV are
required, consistent with the expectation  of a W decay. For a transverse momentum
12.5~GeV $< P_t^{ele} <$ 65~GeV three jets are required and cuts on the electron
polar angle and jet variables are made. The electron polar angle cut is $P_t^{ele}$ dependent and ranges from 1.20 to 2.25 rad. To reconstruct a
W candidate, the dijet-pair with invariant mass closest to the nominal W
boson mass is accepted with an invariant mass is in the range
65~GeV~$< \md <$~87~GeV. The third jet is assumed to be the recoil jet.
The two jets chosen as W candidate are ordered by their transverse
momentum such that $P_t^{jet1}>P_t^{jet2}$. As many background events have a second jet in the forward direction an additional requirement on its polar angle, $\theta^{jet2}>$ 0.2~rad, is made if the transverse momentum of the
second jet is lower than 30 GeV. 
%These cuts are summarised in table~\ref{table:newqq_cuts}.
After those cuts, 6 events survive in
the data. The expected background is $ 7.0 \pm 0.6 \pm 1.4 $ events mainly from NC DIS with negligible contribution from CC DIS and $\gamma$p. The resulting
efficiencies are depicted in fig.~\ref{fig:eff}.



%%% NNZQQ
The \nnzqq channel is characterised by two
jets and missing transverse energy  \etm . The main background are 
CC~DIS events and moderate contributions from $ \gamma $p, whereas the NC~DIS
contribution is significantly suppressed for large  \etm . A cut
$ $~\etm~$ > 10$~GeV is chosen. At $ $~\etm~$ > 40$~GeV only two jets are
required, while at lower \etm a third jet is required and events with
an electron or photon candidate are rejected. Similar to the
eW case a Z candidate is reconstructed from the dijet-pair with
invariant mass closest to the nominal Z boson mass. It is accepted if
$\md >$76 GeV. Again those two jets are ordered. To suppress
further the background from CC~DIS a cut on
the  polar angle $\theta^{jet2}>$ 0.15 rad is applied. In the region of
relatively low missing transverse momentum $ 10 $~GeV~$ < $~\etm~$ < 20 $~GeV
an additional requirement is made on the transverse momentum of jet 1
($P_t^{jet1}>$50 GeV).
% These cuts are summarised in table~\ref{table:nnzqq_cuts}.
With these criteria, 1 candidate event is found in the
data, for an expected background of $ 3.7 \pm 0.2 \pm 0.9 $ events. The background consists
mainly of CC DIS (2.3 events), and $\gamma$p (1.3 events). The
resulting signal efficiencies are given in fig.~\ref{fig:eff}.


\begin{figure}[htbp]
\begin{center}
\epsfxsize8.0cm
\epsfysize8.0cm
\vspace*{-1.cm}

\epsffile{H1prelim-01-162.fig1.eps}

\caption{Acceptance of the selection cuts for the 3 channels, with the hypothesis $f=-f'$.
%(top) and for wide $\nu^*$, using the width corresponding to the couplings of the limit set for $f=-f'$ (bottom left) and $f=+f'/2$ (bottom right).
}
\label{fig:eff}
\end{center}
\end{figure}

%\subsection{Uncertainties and systematics errors}
The main source of systematic uncertainties are the limited knowledge of
the absolute energy scale and missing higher order corrections in the
event generators which are used for the background estimation. The
uncertainties of the electromagnetic energy scale amount to 0.7\% in the
central part of the detector and up to 3\% in the forward region. For the
hadronic part an uncertainty of 4\% is assigned.
Due to the lack of QED radiation from the quark line in the DJANGO
generator, the background expectation is varied by $40\%$ in the \nnga
channel. For the \newqq and \nnzqq channels the 3-jet cross-section is varied by 15\%, to
account for differences observed between perturbative calculations of the
order $O(\alpha_s^2)$~\cite{Carli:1998zr,bate,tampere157} and the parton shower approach. The statistical error of the Monte Carlo generations is taken into account as systematic error on the efficiencies. Finally, the
limited precision of the luminosity measurement gives an additional
normalisation uncertainty of 2.25\%.


%\section{ Upper Limits on Excited Neutrino production} 

In all three search channels the number of observed and expected events are
in good agreement. Upper limits on the coupling $\frac{f}{\Lambda}$ have been derived 
as described in \cite{Adloff:2000gv}
following the Bayesian approach~\cite{Barnett:1996hr,Helene:1984ph}, at 95$\%$ confidence level.
Systematic uncertainties are taken into account~\cite{Adloff:2000gv}. The
resulting limits after combination of all decay channels,
are given as a function of the $\nu^*$ mass in fig.~\ref{fig:folH1fm}, for the hypothesis $f=-f'$ and $f=+f'$. Note that
the decay \nnga is forbidden for $f=+f'$.
These results improve significantly our limits published earlier in $e^-p$~\cite{Ahmed:1994yi}
and $e^+p$~\cite{Adloff:2000gv} collisions. The LEP experiments also have reported on
excited neutrino searches~\cite{Acciarri:2001kb,Abreu:1999jw,Abbiendi:2000sa}.
To illustrate their sensitivity, the L3
results~\cite{Acciarri:2001kb} are depicted in fig.~\ref{fig:folH1fm}. Using the
assumption $\frac{f}{\Lambda} = \frac{1}{M_{\nu^*}}$ excited neutrinos with masses between 50 GeV and
150 GeV (110 GeV and 123 GeV) are excluded by this analysis for the
assumption $f=-f'$ ($f=+f'$).

Less model-dependent limits can be derived if arbitrary ratios $f'/f$
are considered. Fig.~\ref{fig:folScan} illustrates how the limits depend on that ratio
for various $\nu^*$ mass hypothesis. By choosing the point with the
worst limit for each mass hypothesis, limit has been derived which do
not depend on the ratio $f'/f$ anymore. The result is shown in
fig.~\ref{fig:folIndep} for masses below 225~GeV and -5$< f'/f <$5. It deviates
from the limit obtained assuming $f=+f'$ only for high $\nu^*$ masses.
Limits on the single $\nu^*$ production independent of $f'/f$ also have been shown previously by the
OPAL collaboration~\cite{Abbiendi:2000sa}.



%------------------------------------------------------------------------------
%\section{ Summary} 
In summary, using $e^- p$ data taken from 1998 to 1999
a search for excited neutrinos production has been performed and no indication of any signal was found. Therefore
new limits on $ f / \Lambda$, independent of the ratio $f'/f$, have been inferred which extend beyond the mass reach
       of LEP experiments.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\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.



\begin{figure}[htbp]
\begin{center}

\vspace*{-3cm}

\hspace*{-0.18cm}\begin{tabular}{cc}
 
\epsfxsize=0.52\textwidth
 \epsffile{H1prelim-01-162.fig2a.eps} &
\epsfxsize=0.52\textwidth

\hspace*{-0.3cm}\epsffile{H1prelim-01-162.fig2b.eps} \\
\end{tabular}

\caption{Exclusion limits on coupling constants at $95 \%$ confidence level
as a function of the mass
for excited neutrino production with the assumptions ({\it a}) $f=-f'$
and ({\it b}) $f=+f'$ .
Exclusion limits are given for H1 $e^-p$ (full line) with an integrated luminosity of 15 pb$^{-1}$, H1 $e^+p$ data~\cite{Adloff:2000gv} (dashed line) with an integrated luminosity of 37 pb$^{-1}$ and L3~\cite{Acciarri:2001kb} (dotted line).}
\label{fig:folH1fm}

\end{center}
\end{figure}


\begin{figure}[htbp]
\begin{center}
 \begin{tabular}{p{0.4\textwidth}p{1.0\textwidth}}
% -> ci-dessus : 0.3 = taille horizontale pour la
%    caption (a gauche). 0.7 = taille pour la fig
    \vspace*{1.5cm}
% -> modifier le vspace ci-dessous pour monter/descendre
%    la caption
      \caption[]{ \label{fig:folScan}
{Exclusion limits on coupling constants at $95 \%$ confidence level
as a function of the value of $f'/f$ 
for excited neutrino production. Each curve corresponds to a different $\nu^*$ mass, the circles indicate the maximum (worst limit) of each curve.
The areas above the lines are excluded.}}      &
\vspace*{-1.5cm}
      \mbox{\epsfxsize=0.50\textwidth
       \epsffile{H1prelim-01-162.fig3.eps}}
\end{tabular}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
 \begin{tabular}{p{0.4\textwidth}p{1.0\textwidth}}
% -> ci-dessus : 0.3 = taille horizontale pour la
%    caption (a gauche). 0.7 = taille pour la fig
    \vspace*{-7.5cm}
% -> modifier le vspace ci-dessous pour monter/descendre
%    la caption
      \caption[]{ \label{fig:folIndep}
{Exclusion limits on coupling constants at $95 \%$ confidence level
as a function of the mass
for excited neutrino production. All $f'/f$ values have been considered in the interval 
$[-5;+5]$ (see figure~\ref{fig:folScan}), so this limit is independent of the relation between $f$ and $f'$ in that interval. 
The areas above the lines are excluded.}}      &
      \mbox{\epsfxsize=0.50\textwidth
       \epsffile{H1prelim-01-162.fig4.eps}}
\end{tabular}
\end{center}
\end{figure}
%------------------------------------------------------------------------------


\newpage

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

%\cite{Ahmed:1994yi}
\bibitem{Ahmed:1994yi}
T.~Ahmed {\it et al.}  [H1 Collaboration],
%``A Search for heavy leptons at HERA,''
Phys.\ Lett.\ B {\bf 340} (1994) 205.
%%CITATION = PHLTA,B340,205;%%

%\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{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:1990kv}
\bibitem{Baur:1990kv}
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{Kohler:1991yu}
\bibitem{Kohler:1991yu}
T.~Kohler,
%``Exotic processes at HERA: The Event generator COMPOS,''
{\it  In *Hamburg 1991, Proceedings, Physics at HERA, vol. 3* 1526-1541
% (see HIGH ENERGY PHYSICS INDEX 30 (1992) No. 12988)
}.

%\cite{Pukhov:1999gg}
\bibitem{Pukhov:1999gg}
A.~Pukhov {\it et al.},
%``CompHEP: A package for evaluation of Feynman diagrams and integration  over %multi-particle phase space. User's manual for version 33,''
hep-ph/9908288.
%%CITATION = HEP-PH 9908288;%%


%\cite{Abt:1997hi}
\bibitem{Abt:1997hi}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 detector at HERA,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310.
%%CITATION = NUIMA,A386,310;%%

%\cite{Andrieu:1993kh}
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%%CITATION = NUIMA,A336,460;%%

%\cite{Andrieu:1994xn}
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%%CITATION = NUIMA,A344,492;%%

%\cite{Andrieu:1994yn}
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%%CITATION = NUIMA,A350,57;%%


%\cite{Braunschweig:1988by}
\bibitem{iron}
W.~Braunschweig {\it et al.}  [H1 Collaboration],
%``Results From A Test Of An Iron Streamer Tube Calorimeter,''
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%%CITATION = NUIMA,A270,334;%%

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%\cite{Sjostrand:1995iq}
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%%CITATION = HEP-PH 9508391;%%

%\cite{Schuler:1991yg}
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G.~A.~Schuler and H.~Spiesberger,
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%(see HIGH ENERGY PHYSICS INDEX 30 (1992) No. 12988)
}.


%\cite{Kwiatkowski:1992es}
\bibitem{Kwiatkowski:1992es}
A.~Kwiatkowski, H.~Spiesberger and H.~J.~Mohring,
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%%CITATION = CPHCB,69,155;%%

%\cite{Andersson:1989gp}
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%%CITATION = ZEPYA,C43,625;%%


%\cite{Lonnblad:1992tz}
%\bibitem{Lonnblad:1992tz}
%L.~Lonnblad,
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%#%CITATION = CPHCB,71,15;%%

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\bibitem{Martin:1998sq}
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%%CITATION = HEP-PH 9803445;%%

%\cite{Aid:1996au,Adloff:1997mf,Derrick:1996ef,Derrick:1996hn}
%\cite{Aid:1996au}
\bibitem{Aid:1996au}
S.~Aid {\it et al.}  [H1 Collaboration],
%``A Measurement and QCD Analysis of the Proton Structure Function $F_2(x,Q~2)$ %at HERA,''
Nucl.\ Phys.\ B {\bf 470}, 3 (1996).
%[hep-ex/9603004].
%%CITATION = HEP-EX 9603004;%%

%\cite{Adloff:1997mf}
\bibitem{Adloff:1997mf}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``A measurement of the proton structure function F2(x,Q**2) at low x and  low %Q**2 at HERA,''
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%[hep-ex/9703012].
%%CITATION = HEP-EX 9703012;%%

%\cite{Derrick:1996ef}
\bibitem{Derrick:1996ef}
M.~Derrick {\it et al.}  [ZEUS Collaboration],
%``Measurement of the Proton Structure Function ${F_2}$ at low ${x}$ and low %${Q~2}$ at HERA,''
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%[hep-ex/9510009].
%%CITATION = HEP-EX 9510009;%%

%\cite{Derrick:1996hn}
\bibitem{Derrick:1996hn}
M.~Derrick {\it et al.}  [ZEUS Collaboration],
%``Measurement of the F2 structure function in deep inelastic e+ p  scattering %using 1994 data from the ZEUS detector at
%HERA,''
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%[hep-ex/9607002].
%%CITATION = HEP-EX 9607002;%%

%\cite{Sjostrand:1994yb}
\bibitem{Sjostrand:1994yb}
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%%CITATION = CPHCB,82,74;%%


%\cite{Carli:1998zr}
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T.~Carli,
%``Renormalisation scale dependencies in dijet production at HERA,''
hep-ph/9906541.
%%CITATION = HEP-PH 9906541;%%

\bibitem{bate}
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Thesis University of Manchester, 1999.
%%CITATION = NONE %%

\bibitem{tampere157}
H1 Collaboration,
% First Measurement of Three jet Cross Sections in DIS at HERA,
abstract 157, Tampere, HEP99 conference.
%%CITATION = NONE %%

%\cite{Barnett:1996hr}
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R.~M.~Barnett {\it et al.}  [Particle Data Group Collaboration],
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%%CITATION = PHRVA,D54,1;%%

%\cite{Helene:1984ph}
\bibitem{Helene:1984ph}
O.~Helene,
%``Errors In Experiments With Small Number Of Events,''
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%%CITATION = NUIMA,A228,120;%%

%\cite{Acciarri:2001kb}
\bibitem{Acciarri:2001kb}
M.~Acciarri {\it et al.}  [L3 Collaboration],
%``Search for excited leptons in e+ e- interactions at  s**(1/2) = 192-GeV - %202-GeV,''
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%[hep-ex/0011068].
%%CITATION = HEP-EX 0011068;%%

%\cite{Abreu:1999jw}
\bibitem{Abreu:1999jw}
P.~Abreu {\it et al.}  [DELPHI Collaboration],
%``Search for composite and exotic fermions at LEP2,''
Eur.\ Phys.\ J.\ C {\bf 8} (1999) 41.
%[hep-ex/9811005].
%%CITATION = HEP-EX 9811005;%%

%\cite{Abbiendi:2000sa}
\bibitem{Abbiendi:2000sa}
G.~Abbiendi {\it et al.}  [OPAL Collaboration],
%``Search for unstable heavy and excited leptons at LEP2,''
Eur.\ Phys.\ J.\ C {\bf 14} (2000) 73.
%[hep-ex/0001056].
%%CITATION = HEP-EX 0001056;%%

\end{thebibliography}


\end{document}




