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\pagestyle{empty}
\begin{titlepage}

\noindent
{Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000}


\vspace*{3cm}

\begin{center}
  \Large
  {\bf 
        A Search for Excited Neutrinos in \boldmath{$e^- p$} Collisions at
        HERA}\\

  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}


\begin{abstract}
We present a search for excited neutrinos using $e^- p$ data taken by
the H1 experiment with an integrated luminosity of 15 pb$^{-1}$.  No
evidence for excited neutrino production is found and mass dependent
exclusion limits on cross-sections and on the ratio of coupling
constants to the compositeness scale are derived.
\end{abstract}


\vfill
\begin{flushleft}
  {\bf Abstract: 956 } \\
  {\bf Parallel session: 11} \\
  {\bf Plenary talk: 07b} 
\end{flushleft}

\end{titlepage}

\pagestyle{plain}


%\section{Introduction}
Convincing evidence for a substructure of fermions
would be established by the discovery of excited quarks and leptons which are 
predicted by composite models.
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 an excited neutrino ($\nu^*$) through t-channel $W$ boson exchange.
  In this paper we present a search for $\nu^*$ production
  followed by the electroweak radiative decays 
  $\nu^* \rightarrow \nu \gamma$ and $\nu^* \rightarrow e W$.
  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.  
           At a $\nu^*$ mass of 200 GeV
           the expected $\nu^*$ cross-section for $e^- p$ collisions 
           is more than two orders of magnitudes larger than for
           $e^+ p$ collisions previously analysed~\cite{posidata}.


A full description of the  H1 detector can be found in reference~\cite{dete}. 
Here  the components used for this analysis are briefly described.
The forward direction ( $z >$ 0 ) is the proton beam direction and a direct referential ($z$, $\theta$, $\varphi$) is used later in this paper.   
The interaction region is surrounded by a system of drift and proportional
chambers covering the angular range $7^o < \theta < 176^o$. The tracking system is
placed inside a finely segmented liquid argon (LAr) calorimeter
covering the polar angular range 4$^o < \theta <$ 154$^o$.
The electromagnetic part is made of lead/argon  and the 
hadronic part of stainless steel/argon~\cite{lar}. 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{testcalo1,testcalo2}.

Production cross-section and decay of excited neutrinos can be
calculated using an effective Lagrangian~\cite{hagi}.  The
cross-section and the branching ratio depend then 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
$\nu^* \rightarrow \nu \gamma$ and $\nu^* \rightarrow e
W_{\hookrightarrow q \bar{q}} $ comprise more than 80\% of the
branching ratio of the excited neutrino under the hypothesis $f=-f'$. 
The channel $\nu^* \rightarrow eW_{\hookrightarrow q \bar{q}} $
dominates the decay mode for the hypothesis $f=+f'$ with more than
60\% branching ratio.

%\section{Data sample, particles identification algorithms and uncertainties}
%\subsection{Data sample}
%\section{The H1 detector}
 The selection of excited neutrino event candidates is based on the requirement of either missing
transverse energy (\etm) and at least one high transverse energy ($E_t$) electromagnetic cluster or 
two high $E_t$ hadronic jets and an electron.
%\subsection{Particle identification algorithms}
An electromagnetic cluster is defined as an energy deposit in the LAr with 
more than 95\% of its energy in the electromagnetic part of the calorimeter. If this electromagnetic cluster is linked to a track, then it is taken as an electron, else if there are no tracks in a radius of 12 cm around the cluster, this electromagnetic cluster is considered to be a photon. In the forward part of the LAr which is farther from the interaction point, the track-cluster link condition is relaxed to 24 cm. A cone algorithm adapted from the LUCELL scheme being part of the JETSET package~\cite{jets} is used to search for hadronic jets (later called jets  in this paper). 


%\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 vertex within 
$\pm 35$ cm of 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 calculation of SM expectation for NC DIS and CC DIS has been done using the event generator Django~\cite{djan} which includes QED first order radiative corrections based on HERACLES~\cite{hera}. In Django, QCD radiation, based on the Colour Dipole Model (CDM)~\cite{cdm}, is implemented using ARIADNE~\cite{aria}. Parton densities are taken from the MRST~\cite{mrst} parametrization  which includes constraints from DIS measurements at HERA up to squared momentum transfer $Q^2 =$ 5000 ${\rm GeV^2}$~\cite{mrst1,mrst2}. The hadronisation is performed in the Lund string fragmentation scheme by JETSET~\cite{jets}.
% It is important to note that DJANGO does not take fully into account QED radiation from the quark line. Direct and resolved photoproduction  processes ($\gamma$p), incuding prompt photon production, are simulated with PYTHIA~\cite{pyth}. 
A simulation of $\nu^*$ production using COMPOS~\cite{kohl}
          is performed to adjust discriminating cuts and to calculate 
          acceptances. All Monte Carlo generators are interfaced to a full simulation of the H1 detector response.


%\subsection{Uncertainties and systematics errors}

The systematic errors on the mean background expectation come from the
limited energy resolution on one hand and from theoretical modelling
on the other hand.  The uncertainties in the energy scale in the
electromagnetic part of the LAr ranges between 0.7\% in the central
part of the calorimeter up to 3\% in the forward region.  The
uncertainties in the energy scale in the hadronic parts of the
calorimeter was taken to be 4\%.  The uncertainty on the integrated
luminosity is 2.25\%.  For the $\nu^* \rightarrow \nu \gamma$ channel
an uncertainty of 40\% on the background was added to take into
account the lack of modelling of the QED radiation on the quark line
in DJANGO~\cite{djan}.  For the estimate of the \newqq background an
uncertainty of 15 \% was added.  That was determined by a comparison
to data of either a Monte Carlo with $O(\alpha_s)$ QCD matrix elements
which approximates the higher order emission of partons using the
concept of parton showers, or perturbative QCD calculations to order
$O(\alpha^2_s)$ which produces an exact leading order calculation of
the three parton final state~\cite{errjets}.




%\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 final state of an excited neutrino that decays in a neutrino and a
photon 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.  Photons with a transverse momentum ($P_t$)
of more than 16 GeV are searched in events with a missing momentum of
more than 16 GeV. To reject NC DIS background where the scattered
electron (sometimes mistaken as a photon) is preferably scattered
backward, photons are required to be in the forward part of the
calorimeter ($\theta < 1.8$ rad).  For missing transverse energies
greater than 30 GeV photons in the very forward region ($\theta < 1 $
rad) are also accepted if they are linked to a track and are
identified as an electron.  In that particular region the conversion
rate $\gamma \rightarrow ee$ and the number of fake linked photons due
to the high multiplicity of hadronic charged particles from jets are
expected to be high.  In order to reconstruct the primary vertex
position from charged particles, the recoil jet of the struck quark is
also required.  In order to 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 must 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 (by requiring $\Delta\varphi($jet,$\gamma) > 0.35$ rad).  These
selection criteria are summarised in table \ref{table:nnga_cuts}.  In
this channel 2 events have been found for an expected SM background
(mainly CC DIS) of 2.56 $\pm 0.17 \pm 1.20$ events (statistical error
is given first followed by the systematical one).  The SM expectation
corresponds to 2.24 CC DIS, 0.31 NC DIS and 0.01 $\gamma$p events. 
Efficiencies are given in figure \ref{fig:eff} as function of the
excited neutrino mass.



\begin{table}[htbp]
\begin{center}
\begin{tabular}{c||c|c||}
& Photon-like candidates & Electron-like candidates \\ 
\hline
\hline
\etm & $> 16 $ GeV & $> 30 $ GeV \\ 
\hline
$\theta$ & $< 1.8 $ rad & $ < 1 $ rad \\
\hline
$P_t$ & $ > 16 $ GeV & $ > 16 $ GeV \\
\hline
& + recoil jet & + recoil jet \\
\hline
 $\Delta\varphi($jet,$\gamma) $ & $ > 0.35$ rad & $ > 0.35$ rad \\
\hline
\hline
\end{tabular}
\caption{Selection cuts for the $\nu^* \rightarrow \nu \gamma$ channel.}
% Both photons and electrons passing the corresponding cuts are accepted.}
\label{table:nnga_cuts}
\end{center}
\end{table}

\begin{figure}[htbp]
\begin{center}
%\epsfxsize7.0cm
%\epsfysize16.0cm
\hspace*{-1.cm}\epsffile{H1prelim-00-063.fig1.eps}~
\end{center}
\caption{Acceptance of the selection cuts for both channels.}
\label{fig:eff}
\end{figure}


%\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 final state of an excited neutrino decaying into an electron and a $W$ boson
that itself decays into 2 quarks is characterised by an electron and 2
jets.  The main SM background originates from NC DIS events.  Photoproduction
becomes negligible as soon as an electron of high transverse momentum
 is required ($P_t^{ele}>$15~GeV). The electron must be found
in the forward part of the detector.  The exact limit on the polar
angle of the electron ($\theta^{ele}$) varies with the transverse
momentum of the electron (see table~\ref{table:newqq_cuts}).  More NC
DIS events can be rejected by requiring at least one jet of the event
to have a transverse energy $E_t$(jet1) greater than 32 GeV. For $W$
identification all dijet combinations of the event are considered and
the invariant masses are calculated.  A $W$ candidate is defined by
the two jets with the invariant mass closest and within 15 GeV to the
nominal $W$ boson mass.  NC DIS events are rejected by requiring a
third jet which is associated with the recoil of the excited neutrino. 
When $P_t^{ele}$ is greater than 65 GeV, there is almost no SM
background left and all other requirements are removed.  These cuts
are summarised in table~\ref{table:newqq_cuts}.  In this data sample,
4 events pass these selection cuts for an expected SM background of
7.74 $\pm 1.38 \pm 1.63 $ events (almost all expected to be NC DIS). 
Efficiencies are given in figure \ref{fig:eff}.


\begin{table}[htbp]
\begin{center}
\begin{tabular}{l||c|c||}
 $P_t^{ele}$ \small (GeV)  & $ 15 - 65 $ & $ > 65 $ \\
\hline
\hline
 $E_t$(jet1) \small (GeV) &  $ > 32 $ &  \\
\hline
 $\theta^{ele} $ \small (rad) & $ < (2 - ( P_t^{ele} - 15) *0.015) $  &  All cuts \\
\hline
dijet inv. Mass \small (GeV) & $ M_W \pm 15 $ & removed \\
\hline
& + recoil jet & \\
\hline
\hline
\end{tabular}
\caption{Selection cuts for the $\nu^* \rightarrow e W_{\hookrightarrow q \bar{q}} $ channel.}
\label{table:newqq_cuts}
\end{center}
\end{table}

%\newpage

%\section{ Upper Limits on Excited Neutrino production} 
In this analysis the number of observed events in the 2 channels and
the predictions of the SM are in good agreement.  Therefore upper
limits on the product of the $\nu^*$ production cross-section and the
decay channel branching ratio have been derived in a Bayesian way
following \cite{pdg} at $95 \%$ confidence level.  Background and its
uncertainties are included in these calculations and follows the
procedure of \cite{posidata}.  The inferred limits are shown in
figure~\ref{fig:limBrH1} as function of the $\nu^*$ mass.  These
results improve significantly earlier published H1 $e^-p$
results~\cite{oldfs} which are based on an integrated luminosity of
0.528 pb$^{-1}$.  Figure~\ref{fig:folH1} shows the limits on
$\frac{f}{\Lambda}$ obtained with the hypothesis $f=-f'$ (left) and
$f=+f'$ (right).  For $f=-f'$ both channels are combined using the
method described in~\cite{posidata} and taken into account in the
limit calculation.  For the hypothesis $f=+f'$ the \nnga decay is
forbidden, thus only the \newqq limit is shown.  At 220 GeV with the
coupling found here, the intrinsic decay width of the excited neutrino
is of the order of 20 GeV and thus the Narrow Width Approximation
(NWA) assumed by the generator becomes less accurate.  To take this
into account, a band reflecting the uncertainty due to the use of the
NWA has been added to the limit.  In figure~\ref{fig:folAll}, these
new limits are compared with the limits obtained by H1 from $e^+p$
data.  The LEP experiments~\cite{lep1,lep2,lep3} have also reported on
excited neutrino searches and the L3 results are shown on
figure~\ref{fig:folAll}.  Even with the lower luminosity the new H1
results improve the previous ones obtained from $e^+p$ data, as
expected.  Using the assumption $\frac{f}{\Lambda} =
\frac{1}{M_{\nu^*}}$, excited neutrino of masses between 50 and 150
GeV for $f=-f'$ and between 110 and 134 GeV for $f=+f'$ are excluded.


%\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 a signal was found.  Therefore new limits on $ f /
\Lambda$ for the production of excited neutrinos in high energy $ep$
interactions have been inferred which extend beyond the mass reach of
LEP experiments.  Results obtained by the LEP experiments for the
excited neutrino are more stringent but limited to excited neutrino
masses below 195 GeV. Assuming $\frac{f}{\Lambda} =
\frac{1}{M_{\nu^*}}$ and $f=-f'$ ($f=+f'$) excited neutrinos are
excluded in the mass range 50-150 GeV (resp.  110-134 GeV) at 95\%
confidence Level.

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%
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\end{thebibliography}

\newpage

\begin{figure}[h]
\begin{center}
\epsfxsize15.0cm
%\epsfysize8.0cm
%\hspace*{2cm} 
\epsffile{H1prelim-00-063.fig2.eps}~
\caption{Upper limits at the $95 \%$ confidence level
on the product of the excited neutrino cross-section and the decay branching fraction for the $\nu^* \rightarrow \nu\gamma$ (dashed line) and  $\nu^* \rightarrow e W_{\hookrightarrow q \bar{q}} $ (dotted line). The areas above the lines are excluded.}
\label{fig:limBrH1}
\end{center}
\end{figure}

\begin{figure}[h]
%\hspace*{2cm} 
\begin{center}
\begin{tabular}{cc}
\epsfxsize8.0cm
%\epsfysize8.0cm
\epsffile{H1prelim-00-063.fig3a.eps} &
\epsfxsize8.0cm
%\epsfysize8.0cm
\epsffile{H1prelim-00-063.fig3b.eps}
\end{tabular}
\caption{Exclusion limits on coupling constants at $95 \%$ confidence level
as a function of the mass
for excited excited neutrino production.
The assumptions $f=-f'$ (left) and $f=+f'$ (right) are made respectively. Exclusion limits are given for each channel:  $\nu^* \rightarrow \nu\gamma$ (dashed line) and  $\nu^* \rightarrow e W_{\hookrightarrow q \bar{q}} $ (dotted line) and for both channels combined (full line).
The areas above the lines are excluded. The hatched band reflects the uncertainty due to the use of the NWA.}
\label{fig:folH1}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\epsfxsize15.0cm
%\epsfysize8.0cm
%\hspace*{2cm} 
\epsffile{H1prelim-00-063.fig4.eps}~
\vspace*{-1.5cm}
\caption{Exclusion limits on coupling constants at $95 \%$ confidence level
as a function of the mass for excited excited neutrino production. The assumption $f=-f'$ is made. Exclusion limits are given for H1 $e^-p$ (full line) with an integrated luminosity of 15 pb$^{-1}$, H1 $e^+p$ data (dotted line) with an integrated luminosity of 37 pb$^{-1}$ and L3 (dashed line). The areas above the lines are excluded. The hatched band reflects the uncertainty due to the use of the NWA.}
\label{fig:folAll}
\end{center}
\end{figure}

\end{document}