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\begin{document}

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\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 118} & 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 General Search for New Phenomena in $ep$ scattering at HERA}


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

\begin{abstract}
A model-independent search for 
deviations from the Standard Model prediction has been performed 
in $e^+ p$ and $e^- p$ collisions at HERA using H1 data
corresponding to an integrated luminosity of $115$ $\mbox{pb}^{-1}$. 
All experimentally measurable event topologies
involving electrons, photons, muons, neutrinos and jets with 
high transverse momenta have been investigated. 
Events are classified into exclusive event classes according to their
final state. 
A new algorithm has been developed to look for 
regions with large
deviations from the Standard Model in the invariant mass and sum of 
transverse momenta distributions and to quantify the 
significance of the fluctuations observed.
A good agreement with the Standard Model prediction is found in most 
of the event classes.
The largest deviation was found in \mujnp topologies 
where deviations have been previously observed. 
About $2\%$ of hypothetical Monte Carlo experiments would produce
deviations more significant than the
one observed in the corresponding sum of transverse momenta distribution.

 

\end{abstract}


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\section{Introduction}
% \noindent
At HERA electrons\footnote
{In this paper "electron" refers to both electrons and positrons, if
not otherwise stated.}
and protons collide with a centre-of-mass
energy of $319$~GeV.
The high centre-of-mass energy and the unique 
types of colliding particles provide an ideal
testing ground for the Standard Model (SM).
The H1 experiment at HERA has accumulated more 
than $100$~$\mbox{pb}^{-1}$ of integrated luminosity in 
the first period of HERA running (HERA I) at a centre-of-mass energy
of $319$ and $301$~GeV. 
These data 
 can in particular be used for the search for signals of new physics. Various 
tests of 
possible extensions of the 
SM have already been performed and upper
limits on cross-sections of new processes have been derived.
All these exotic models lead to different final state event topologies.
These analyses have been optimised to detect the anticipated 
experimental signatures of these extensions.

A complementary approach is described in this paper consisting in a
broad-range search for deviations from the SM 
prediction at large transverse momentum.
The analysis covers phase space regions 
where the SM prediction is sufficiently precise to detect anomalies
and does not rely on special models for physics beyond the 
SM.
A prior related 
strategy for such a model-independent search was presented by the
D0 collaboration ~\cite{Abbott:2000fb,Abbott:2001ke,Abazov:2001ny}.

In this work all final states are analysed having at least two objects 
with a transverse momentum ($P_T$) above $20$~GeV and in the 
polar angle range $10^\circ < \theta < 140^\circ$. 
The considered objects are electron ($e$), muon ($\mu$), 
photon ($\gamma$), jet ($j$) and neutrino ($\nu$) (or 
non-interacting particles). 
Moreover the objects are required to be isolated versus each other 
by a minimum distance $R=\sqrt{(\Delta \eta)^2+(\Delta \phi)^2}$
of $1$ unit in the pseudorapidity-azimuth ($\eta-\phi$) 
plane\footnote{The origin of the H1 coordinate system is the nominal $ep$ interaction point, while the direction of the proton beam defines the positive $z$-axis (forward region). The transverse momenta are measured in the $xy$ plane. The polar $\theta$ and azimuthal $\phi$ angles are measured with respect to the reference system. The pseudorapidity is a function of the polar angle: $\eta = -\mbox{log}(\mbox{tan}(\theta/2))$.}.
In order to avoid bias, the object phase space 
requirements have been defined a priori and no additional
cuts (except topological background finding)
on the event classes are applied. The object quality criteria are 
defined according to our knowledge of SM processes and detector
performances.
The complete HERA I data sample (1994-2000) has been used corresponding to an integrated luminosity of $115.3$~pb$^{-1}$.
All selected events are then classified into exclusive event classes 
(e.g.  \ej, \jj, \jnp) 
according to the number and types of objects detected in the final state. 
Exclusive event classes ensure a good
separation of final states and an 
unambiguous statistical interpretation. 

In a first step the global yields of all measurable 
event classes are compared to the SM expectation. Efficiencies and
purities are derived for all classes with a sizeable SM prediction. 
These efficiencies
can further be used to derive limits on signals from processes beyond the SM.

In a second step the invariant mass $\Mall$ and the scalar 
sum of transverse momenta $\sum P_T$ of high $P_T$ final state 
objects are considered.
A new algorithm is presented to search for the 
largest deviation from the SM prediction in these distributions. 
Finally the likelihood to find the deviation with 
the algorithm in a given event
class and in all studied event classes is derived. 


\section{SM processes and their Monte Carlo generation}
A search for deviations from the SM requires
a precise and reliable 
estimate of all relevant processes.
Hence several Monte Carlo generators are used to generate a large 
number of events
in all event classes carefully avoiding double-counting of processes. 
All 
events are passed through 
a full detector
simulation~\cite{Brun:1987ma}. All processes are generated with a luminosity
at least $20$ times higher than the one of the data.

% The Monte Carlo events give the Standard Model expectations, are
% used to determine systematic uncertainties, efficiencies and purities of 
% the event classes. 

The main contributions to the SM prediction at high transverse momentum are 
due the photoproduction
of jets and neutral current (NC) deep-inelastic scattering (DIS).

To simulate the 
direct and resolved photoproduction of jets ($ep \rightarrow jj X$)
and prompt photon production ($ep \rightarrow \gamma  j X$)
the PYTHIA 6.1 event generator~\cite{Sjostrand:2000wi} is used. 
The abbreviation $X$ stands for a
not specified low $P_T$ system of the reaction products. 
%Consequently a
%scattered electron with $P_T<20$~GeV is included in this low $P_T$ system. 
Light and heavy flavours are generated.
The simulation contains the Born level QCD hard scattering
matrix elements and radiative QED corrections. 

The order $\alpha_s$
matrix elements are used in 
the RAPGAP event generator to 
model NC DIS events. The QED radiative effects arising from
real photon emission from both incoming and outcoming lepton are simulated
using the HERACLES~\cite{Kwiatkowski:1990es} generator.
Hence the NC DIS prediction contains the 
processes $ep \rightarrow e j X$, $ ep \rightarrow e j j X$ and 
$ep \rightarrow e \gamma j X$. In the case the electron is undetected
RAPGAP contributes to $ep \rightarrow j j X$ and
$ep \rightarrow \gamma j X$.

Charged current (CC) deep-inelastic scattering events are calculated
using the DJANGO
\cite{Schuler:yg} program, which includes first order QED
corrections based on HERACLES.
Parton cascades are generated using the colour-dipole model in ARIADNE
~\cite{Lonnblad:1992tz}. 
This prediction contains the processes $ep \rightarrow \nu j X$,
$ep \rightarrow \nu j j X$
and processes with an additional photon radiation.

Multi-lepton events are generated with the GRAPE~\cite{Abe:2000cv} 
generator, which includes 
all exact electroweak
matrix elements at tree level. The multi-lepton production via $\gamma \gamma$,
$\gamma Z$, $ZZ$ collisions, internal photon conversion and via the
decay of virtual or real $Z$ bosons is considered. 
Initial and final state QED radiation is included.
The complete
hadronic final state is obtained via interfaces to 
PYTHIA (SOPHIA) ~\cite{Mucke:1999yb} for the inelastic (quasi-elastic) regime.
Consequently GRAPE predicts $ep \rightarrow \mu \mu X$ and
$ep \rightarrow e e X$ as well as additional jet production.

Elastic and quasi-elastic Compton processes ($ep \rightarrow e \gamma X$)
are simulated with the WABGEN~\cite{Berger:kp}
generator. The inelastic contribution is already included in the used
NC DIS RAPGAP prediction.

The production of $W$ bosons ($ep \rightarrow W X$ and $ep \rightarrow W j X$)
is modelled using the EPVEC~\cite{Baur:1991pp}
Monte Carlo generator.
QCD 
corrections ~\cite{Diener:2002if} 
to these processes are taken into account by reweighting the 
events 
as a function of transverse momentum and rapidity of the $W$ boson.

Processes with additional jets (e.g. $ep \rightarrow jjjX$ or 
$ep \rightarrow jjjjX$) are accounted for
in all models using leading
logarithmic parton showers as representation of
higher order QCD radiation.
The prediction of processes with two or more high transverse momentum jets  
(e.g. $ep \rightarrow jj$) was scaled by a factor of $1.2$ 
to re-weight the normalisation of the leading
order Monte Carlos to that of next-to-leading order QCD calculations
\cite{Adloff:2002au}.



\section{Experimental Technique}
\subsection{The H1 detector}
The H1 detector 
components relevant to the present analysis 
%in which
%the final state contains at least one measured object with high transverse momentum 
are briefly described here.
The Liquid
Argon (LAr )~\cite{Andrieu:1993kh} and SpaCal~\cite{Appuhn:1996na}
calorimeters are used
to trigger events and to measure the energy of the final state.
The LAr calorimeter is used to identify jets, photons and electrons 
and covers the polar angle range $4^\circ < \theta <
154^\circ$ with full azimuthal acceptance. 
The energy calibration uncertainty for jets with high transverse momentum
is determined to be $2\%$ and varies between $0.7\%$ and $3\%$ for electrons 
and photons.
% The angular region
% \mbox{$153^\circ < \theta < 177.8^\circ$} is covered by the SpaCal, a
% lead/scintillating-fibre calorimeter.
% It has an hadronic energy scale
% uncertainty of 8\%.
The central and forward tracking detectors are used to
measure charged particles' trajectories, to
reconstruct the interaction vertex and to supplement the measurement
of the hadronic energy flow.
%The CJC consists of two concentric cylindrical drift chambers, coaxial
%with the beam-line, with a polar angle coverage of $15^\circ <
%\theta < 165^\circ$. 
Two concentric drift chambers (CIP and COP) complement 
the vertex measurement.  Since the CIP is the 
innermost proportional chamber it is used to veto charged particles for
the photon identification.  The CIP angular
coverage is $7^\circ <\theta < 175^\circ$.
The core of the detector is enclosed by a superconducting magnetic coil
with a strength of $1.15$~T. The iron return yoke builds 
the outermost part of the detector and is equipped with streamer
tubes forming the central muon detector ($4^\circ < \theta < 171^\circ$).

The luminosity determination is based on the measurement of the 
Bethe-Heitler process  $ep \rightarrow ep \gamma$, where the electron and
photon are detected in calorimeters located
downstream of the interaction point.


The main trigger for events with high transverse momentum 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 transverse momentum greater than $20$~GeV. 
Events triggered only by jets have a trigger efficiency above 
$90\%$ for $P_T>20$~GeV and nearly $100\%$ for $P_T>25$~GeV.
For events with high missing transverse momentum, determined from an 
imbalance in transverse momentum measured in the calorimeter 
$P_T^{\mbox{\footnotesize{calo}}}$, the trigger efficiency is 
$\sim$ $90\%$ for $P_T^{\mbox{\footnotesize{calo}}} > $ $20$~GeV.
Events only triggered by muons have a trigger efficiency  
above $70\%$~\cite{mmuon}.


\subsection{Event Selection}
The event sample studied consists of the full 1994-2000 HERA I data set.
The data selection requires at least an isolated
electromagnetic cluster, muon or jet  to be found anywhere in
the used detector components. To reduce several kinds of background events
it is demanded that the event vertex is reconstructed within $35$~cm of the
nominal $z$ position of the vertex\footnote{This is not required for
the event classes containing only photons.}
and that $\sum_i E_i-P_{z,i}< 75$~GeV,
where $E_i$ is the energy and $P_{z,i}$ is the $z$ component of the particle
momentum.
The index $i$ runs over all hadronic objects,
electromagnetic clusters
and muons found in the event. Due to energy-momentum conservation a 
typical HERA event is expected to have a value of $\sum_i E_i-P_{z,i}=55$~GeV
if the complete final state has been detected, or if only longitudinal
momentum along the proton direction has been undetected. 
The non-$ep$ background is rejected as described in \cite{NCCCpaper} 
by searching for event topologies 
typical for cosmic ray and beam-induced background.
Moreover the event timing is required to be consistent with the HERA clock.

Identification criteria for each type of particle are widely based on 
previous analyses performed on specific 
final states \cite{NCCCpaper,Andreev:2003pm,multielectron,mmuon}. 
Additional 
requirements have 
been chosen to ensure an unambiguous identification of particles, still 
keeping 
high efficiencies. 
The following paragraphs describe the object identification criteria.
 

\paragraph{Electron identification}

The electron identification is based on the measurement 
of a compact and isolated electromagnetic shower in the LAr calorimeter. 
The hadronic energy within $0.75$ units in the $\eta - \phi$ plane around the 
electron is required to be below $2.5\%$ of the electron energy.
This calorimetric electron identification is complemented by 
tracking conditions.
It is required that a high quality 
track geometrically matches the electromagnetic cluster within a 
distance of closest approach ($DCA_{cl}^{tk}$) to the cluster 
center-of-gravity of $12$~cm. No other good track is allowed within 
0.5 units in the $\eta-\phi$ plane around the electron 
direction. 
In the region $20^\circ < \theta <  140^\circ$
the starting radius of the measured track, defined as the 
distance between the first measured point in the central drift chambers and 
the beam axis, is required to be below $30$~cm in order to reject photons 
that convert late in the central tracker material. In addition, the 
transverse 
momentum measured from the associated track $P_T^{e_{tk}}$ is required 
to match the calorimetric measurement $P_T^e$ with 
$1/P_T^{e_{tk}} - 1/P_T^e < 0.02$~GeV$^{-1}$. 
Due to higher material density in the forward 
region, the electrons are more likely to shower and therefore some  
conditions depend
on the polar angle of the electron candidate.
In the region not fully covered by the central drift chambers 
($10^\circ < \theta <  37^\circ$) a tighter calorimetric isolation 
cone of 1 unit in the $\eta - \phi$ 
plane is required to reduce the contribution of fake electrons from hadrons. 
The identification is then complemented by the requirement of hits 
in the central inner proportional chamber (CIP) within a distance $\Delta z_{\mbox{\tiny{CIP}}}<10$~cm
to the extrapolated $z$-impact of the electromagnetic cluster to the CIP surface.
The resulting electron finding efficiency 
is $\approx 85$\% in the central region and $70\%$ in the forward region.

%In the region where the central drift chambers have full acceptance 
%($10^\circ < \theta <  140^\circ$) 

% To further reduce the fraction of misidentified photons 
% and hadrons a track assigned 
% with an extrapolated distance of closest approach
% to the electron cluster of less than 12 cm is demanded. 
% To ensure well
% measured tracks several quality conditions 
% are applied on the track reconstruction. Due to the bad
% performance of the forward tracking device not all of these 
% criteria can be applied in the region
% of small polar angles, where the acceptance of the central tracker 
% is limited ($\theta_e<37^\circ$).
% Therefore a higher calorimetric isolation of the cluster and activity in
% the layers of the CIP is required
% for electron candidates in this region. 
% The efficiency, the background rejection and the Monte Carlo description
% of the applied criteria 
% are studied in a DIS, di-electron and Compton sample and are found to 
% maximise both the efficiency and background rejection in all event classes.
% Events with electron objects are triggered with an efficiency of nearly
% 1.

\paragraph{Photon identification}

The photon identification relies on the same measurement of an 
electromagnetic shower and the same calorimetric 
isolation criteria against hadrons as the electron identification. 
%Calorimetric 
%isolation criteria against hadrons depending on the cluster polar 
%angle similar to the electron are required. 
In addition no jet with a $P_T>5$~GeV in 
the vicinity of the photon candidate, i.e. within a distance 
below $1$ unit in the $\eta- \phi$ plane, should be present. 
%All preselected
%jets with a $P_T>5$~GeV are considered for the isolation. 
Vetoes on any charged track pointing to the electromagnetic cluster 
are applied.
No track with a $DCA_{cl}^{tk}$ below $24$~cm or 
within $0.5$ units in the $\eta-\phi$ plane should be present. 
To account for possible inefficiencies of the inner tracking system 
an additional veto on any hits in the CIP
is applied, i.e. $\Delta z_{\mbox{\tiny{CIP}}}>10$~cm.



\paragraph{Muon identification}
The muon identification is based on a track in the forward muon
system or a charged track in the inner tracking systems associated with
a track segment or an energy deposit in the instrumented 
iron~\cite{Andreev:2003pm}.
The muon momentum is measured from the track curvature in the toroidal or 
solenoidal magnetic field. A muon candidate should have no more than 
$8$~GeV deposited in the LAr calorimeter in a cylinder of radius $0.5$ 
in the $\eta-\phi$ plane, centered on the muon direction
associated with its track.
Cosmic background is rejected by applying several cuts.
A cut on the track opening 
angle and polar angle sum of muon pairs is intended
to discard events with muons coming from cosmic rays.
The event timing condition for muon events is more restricted and
  the cut on the track timing difference 
rejects the cosmic muons residing at high values of this quantity.
Beam halo events are rejected by requiring 
that the muons originate from the vertex.
Finally misidentified  hadrons are almost 
completely suppressed by requiring that the  muon candidate is seperated
from the closest jet by at least one unit in the  $\eta-\phi$ plane.
The efficiency to identify muons is established to be greater than $90\%$~\cite{Andreev:2003pm}.

% Events only triggered by the muon have a trigger efficiency of 
% above 70\%.

\paragraph{Jet identification}
Jets are defined using the 
inclusive $k_{\bot}$ algorithm
as proposed in \cite{Ellis:1993tq,Catani:1993hr}. 
It is applied in the laboratory frame with the separation parameter
set to $1$ and using
a $P_T$ weighted recombination scheme in which the jets are
treated as massless. 
Energy deposits in the calorimeters and tracks
in the inner tracking system  are combined to reconstruct the hadronic energy of
events. The jet algorithm is run on all energy deposits, not previously 
identified as a electron or a photon candidate.
Due to inefficiencies of the electron finder, especially in detector 
regions where the amount of dead material is important, the scattered 
electron may 
fake or be part of a jet.
This effect is important for multi-jet events, especially 
at high transverse momenta of the jets.
To reject these fake jets, jets are required to have a radial energy moment 
greater than $0.02$ and the quantity $M^{\mbox{\footnotesize{Jet}}}/P_T^{\mbox{\footnotesize{Jet}}}$ above 0.1. 
 Here $P_T^{\mbox{\footnotesize{Jet}}}$
denotes the transverse momentum of the jet and its invariant 
mass $M^{\mbox{\footnotesize{Jet}}}$ 
is derived using the four-momenta of the objects belonging to
the jet. If the fraction of the jet energy contained in the 
electromagnetic part of the LAr calorimeter is greater than $0.9$, the above
criteria are tightened to $0.04$ and $0.15$, respectively.
About $80\%$ of the non-genuine jets and $1\%$ of the genuine
jets are rejected by these requirements.



\paragraph{Neutrino identification}
A neutrino candidate is defined in events with a missing transverse momentum
above $20$~GeV. The missing momentum is derived from all identified particles and
energy deposits in the event. A neutrino candidate is only assigned to the
event if $\sum_i E_i-P_{z,i}<48$~GeV. 
%  For an event where only momentum
% in the proton direction is undetected due to beam pipe losses 
% $\sum_i E_i-P_{Z,i}=55$~GeV. 
%The neutrino phase space is only defined
%by the $P_T$ and $\sum_i E_i-P_{z,i}$ requirements.
Missing transverse momentum may arise due to
mismeasurement of an identified object. This effect is reduced
by isolating the four-vector of the neutrino against all identified objects
with a transverse momentum above $20$~GeV.
However an additional criteria is applied to reduce NC and lepton pair
background events
where one particle's energy is mismeasured. These events typically
have values of $\Delta \phi(l-X_{tot})$ of $180^\circ$. $\Delta \phi(l-X_{tot})$ is 
the azimuthal angle difference between the charged lepton and the direction of 
the system $X_{tot}$ build of all energies 
measured in the calorimeters.
If one electron or muon is found in the event a neutrino candidate is 
only assigned
to the event if $\Delta \phi(l-X_{tot})<170^\circ$. 
%This criteria reduced the background in the corresponding event
%^classes by 99\% percent, while discarding about 5-15\% of genuine 
%SM neutrino events.
 
 
The common phase space of electron, photons, muons and jets is defined 
by $10^\circ<\theta<140^\circ$ and $P_T > 20$~GeV. The  neutrino
phase space  is  defined by
the missing
transverse momentum above $20$~GeV and  $\sum_i E_i-P_{z,i}<48$~GeV. 
All particles with $P_T > 20$~GeV, 
including 
the neutrino defined by its reconstructed four-vector, are required 
to be isolated versus each other by a minimum distance of 1 unit in the 
$\eta-\phi$ plane. 
Based on these object definitions the events are subdivided, according 
to the number and types of objects, into
exclusive event classes.
Events with
a compact isolated 
object in the considered phase space which is 
not identified as photon, electron or jet are discarded from
the analysis in order to minimise wrong classifications of events.  

Purities and efficiencies resulting from these identification 
criteria are
derived as a function of the 
sum of transverse momenta $\sum P_T$ and as a function of the invariant
mass $\Mall$ of the objects. Mean values are given
 in Table~\ref{tab:effpur} for all event 
classes with a sizeable SM expectation. Most purities 
and efficiencies are found to be above $60\%$.
The highest efficiencies are found to be above $90\%$ 
for the \jj and \jjj  event classes.  



\subsection{Systematic Uncertainties}
This section describes the sources of experimental and theoretical systematic uncertainties that are considered.

 \begin{table}[b]
 \begin{center}
    \begin{tabular}{|l|c|c|c|c|c|}
      \hline
Object & Energy Scale & $\theta$ unc.& $\phi$ unc. & Identification & Trigger \\
       & unc.         &    (mrad)    &    (mrad) & efficiency unc. & efficiency unc.\\ 
\hline                                        
Jet &  2\%            &  5-10        &  --   &  -- & 3\% \\ 
Electron & 0.7-3\%    &  1-3         &  1    &  2-7\%(Tracking)+0.5\%(CIP) & -- \\    
Photon & 0.7-3\%      &  1-3         &  1    &  2-7\%(Tracking)+0.5\%(CIP) & -- \\ 
Muon &  5\%           &  3           &  1      &  5\% & 5\% \\ 
\hline
    \end{tabular}

    \caption{The uncertainties attributed to the particle measurements.}
    \label{tab:objectunc}
 \end{center}  
\end{table}
  
Experimental systematic uncertainties arising from the measurement of the objects are 
presented in Table~\ref{tab:objectunc}.
The energy scale, the polar angle $\theta$  and the azimuthal angle $\phi$ are varied by the 
specified numbers for all measured objects.
\begin{itemize}
\item  
The electromagnetic energy scale uncertainty is determined to be 1\% if the 
$z$ position of
the electromagnetic particle's impact 
on the LAr calorimeter
 is in the backward part ($z\,<\,-145$ cm), 
$0.7\%$ in the central part
($-145\,<\,z\,<\,20$ cm),
  $1.5\%$ for $20\,<\,z\,<\,100$~cm and 
$3\%$ in the forward part ($z\,>\,100$~cm) \cite{NCCCpaper}. 
The angular uncertainty of collimated electromagnetic clusters varies $\theta$
dependent between
$1$ and $3$~mrad~\cite{NCCCpaper}.
The identification
efficiency arises from uncertainties in the Monte Carlo description
of tracks and of hits in the CIP. The measured tracking efficiency is described
by the simulation to a precision ranging from $2\%$ for polar angles above $37^\circ$
to $7\%$ in the forward region. 
 The number of electron or
photon candidates with associated
CIP hits or tracks is
varied by the specified percent numbers.
\item
The hadronic energy scale of the LAr 
calorimeter is varied by $2\%$. The uncertainty on the jet polar angle
determination is $5$ mrad for $\theta<30^\circ$ and $10$ mrad for
$\theta>30^\circ$.
\item
The muon energy scale uncertainty amounts to $5\%$. 
The uncertainty on the polar angle determination is $3$~mrad.
\item
The trigger uncertainties are taken into account according to 
the object with the highest trigger efficiency.
\item
The uncertainty in the integrated luminosity results in an
  overall normalisation error of $1.5\%$.
\end{itemize}

Depending on the dominant production process 
different theoretical uncertainties are used.
 They are
listed in Table~\ref{tab:modelunc}. An additional theoretical uncertainty of 
$20\%$ is applied for each jet dominantly 
produced by parton shower processes (e.g. \jjj event class).
A model uncertainty of $50\%$ is added to 
NC DIS events with missing transverse momentum above $20$~GeV and a high $P_T$
electron. This uncertainty is estimated by a comparison 
of low $P_T$ NC DIS events with the SM prediction.
%\end{itemize}

All systematic errors are added in quadrature.
The resulting total uncertainty ranged, e.g. for the \ej event
class between $10\%$ and $35\%$ and for the \jj event class between 
$20\%$ and $60\%$ increasing with $P_T$.

 \begin{table}[h]
 \begin{center}
    \begin{tabular}{|l|c|}
      \hline
      Process(es) &Uncertainty\\
      \hline
      $ep\rightarrow jj X$ and $ep \rightarrow j\gamma X$ &15\%\\
      $ep\rightarrow j\nu X$ and $ep \rightarrow jeX$  & 10\%\\
      $ep \rightarrow jj\nu X$ and $ep \rightarrow jjeX$  & 15\%\\
      $ep \rightarrow \mu\mu$ and $ep \rightarrow ee$ & 3\%\\
      $ep \rightarrow W X$ and $ep \rightarrow WjX$ & 15\%\\
      $ep \rightarrow e\gamma X$ and $ep \rightarrow e\gamma j$& 10\% \\
      $ep \rightarrow e\gamma p$ & 5\% \\
      \hline
    \end{tabular}
    \caption{The uncertainties attributed to the different processes of the SM expectation. }
    \label{tab:modelunc}
  \end{center}
  \end{table}




\section{Results}

All possible event classes have been investigated. Among them only those 
experimentally measurable and having observed data events or a SM expectation 
greater than $0.1$ events will be considered in the following discussion. The $\mu-\nu$ event class 
was found to be overwhelmed by background from low 
$P_T$ photoproduction and was unmeasurable. It
was discarded from the analysis procedure.

The event yields subdivided in event classes are presented 
for the data and SM expectation
in Figure~\ref{fig:summaryplot}. 
A good overall agreement between data and SM 
expectation is observed for most of the event classes. 
%$e^+p$ and $e^-p$ data samples have been added together. 
%It is verified that the same level of agreement is present 
%in both $e^+p$ and $e^-p$ samples separately.
The predominant processes at HERA, i.e.  photoproduction, NC and CC
DIS processes, can be found in the \jj, \ej and \jnp event class, respectively.

The data event yields in these 
event classes are in good agreement with the SM expectation.
Likewise the  \ejj, \ejjj, \jjj and \jjnp event classes 
correspond to the same dominant processes with the 
inclusion of additional jet production due to higher order QCD processes.
The event yields of these event classes are also 
well described by the SM prediction. 
Event classes containing a radiative 
photon are \ejpho, \jjpho and \nppho, and correspond, respectively, to 
NC DIS, photoproduction and CC DIS processes with the radiation of a photon. 
These event classes are found to agree with the expectation. 
The \epho event class is dominated by QED Compton scattering 
processes ($94\%$) and again a good agreement is observed.
No radiative CC DIS event 
is observed in the \jnppho event class for $1.0 \pm 0.2$ expected.
The \jpho event class is
well described by the prediction, but, due to the still high 
NC DIS background in this event class, the purity is low ($20-40\%$). 

A discrepancy between data and SM expectation is observed 
in the \mujnp event class where $4$ events are observed for 
an expectation of $0.7\pm 0.2$.
This event class corresponds to typical 
event topologies arising from $W$ production. The 
deviation was already investigated in Ref.~\cite{Andreev:2003pm} and 
will be further discussed in Section 5.
Similarly, the event classes \enp, \ejnp are also populated 
by events arising from $W$ production.
In the \enp event class a slight deficit of $8$ data events 
compared to an expectation of 
$19.9 \pm 8.0$ is observed. This event class is 
dominated by background events from NC DIS, where possible 
fluctuations in the hadronic energy measurement or 
limited detector acceptance can produce missing transverse momentum. 
% The number of predicted events in the \ejnp event class is below the number
% of data events. 
In the \ejnp event class $2$ data events are observed for an expectation of 
$0.9 \pm 0.2$. 
Most of the interesting \ejnp events mentioned in~\cite{Andreev:2003pm} have 
an electron with a transverse momentum 
below $20$~GeV and are therefore not selected in the present analysis.

Another discrepancy to the SM expectation has been 
reported by H1 in multi-electron 
events from lepton pair production~\cite{multielectron}. 
In the present analysis the \ee event class is populated at 
about $85\%$ by electron pair 
production with $8$ measured data events for an expectation of $10.7 \pm 1.1$. 
All di-electron events mentioned in the dedicated multi-electron search
and available 
in the phase space of this analysis are selected; no 
tri-electron event is identified due to the requirement of 
high transverse momentum.
In the region $\Mall>100$~GeV 3 events are observed and 
$1.15\pm 0.25  $ are expected. The higher SM prediction compared to 
Ref.~\cite{multielectron} is due to background coming
from fake electrons with $\theta <20^\circ$ and a higher $ep\rightarrow eeX$
selection efficiency due to the increased phase space.

The event classes \emu and \mumu are dominated by muon pair 
production ($\approx 95\%$ and $100\%$, respectively). 
The \emu event class is populated when the scattered electron 
and only one of the muons is selected.
In the \emu and \mumu event classes 
$4$ and $5$ events are observed 
compared to an expectation of $4.9 \pm 0.6$  and  $2.6 \pm 0.6$, 
respectively.
Muon pair production processes also contribute to $\approx 85\%$ in
the \muj event class, where again a good agreement is found. 

Some discrepancies on the total event yields can 
be observed in the \jjjj and \ejjjj event classes between data and 
SM expectation. 
For the \ejjjj event class a low SM expectation 
of $\approx 0.05$ is estimated.
Events with four high $P_T$ jets are investigated for the first time at HERA.
Since these spectacular 
events can --- in the current Monte Carlo programs --- only 
be produced via parton shower, it can not be ensured that the 
prediction is reliable. No events are found in 
all other event classes in good agreement with the SM expectation.
The expectation of $\approx 1$ event 
in the \phopho event class is dominated by the 
$ep \rightarrow e \gamma X$ process, where the electron is misidentified
because of tracking inefficiency. Contributions of 
higher order QED processes, which could lead to two high transverse momentum ($P_T$) 
photons, are negligible.


\section{Search for deviations from the Standard Model}
\subsection{Search algorithm}

In order to quantitatively determine the level of agreement 
between the measured data and the SM expectation and 
to identify regions of possible 
deviations, a new search algorithm has been developed. The 
calculation of the global significance per event class was inspired by
Ref. \cite{Abbott:2000fb}.

Quantities sensitive to new physics signals and
easy to measure are the sum of transverse momenta and the invariant mass 
of all objects.
Detailed studies have shown that both quantities 
have a large finding potential by mixing 
various signals of new physics in data and Monte Carlo distributions. 
The algorithm
described in the following was run on these pseudo data samples and was 
successful in finding the signals.
Hence the invariant mass $\Mall$ and the scalar sum of transverse momenta 
$\sum P_T$ of all particles have been investigated, considering that 
signals of new physics are likely to manifest themselves at certain transverse 
momentum or invariant mass. It turned out that both quantities complement
each other in the search for these signals.
  
The basic design of the search algorithm is very simple:
\paragraph{Definition of regions}
All possible connected regions in a given distribution (a 
histogram) which have at least the size of twice the
resolution are considered. 
The data $N_{obs}$ and SM expectation $N_b+\delta N_b$
 of a region are defined as the sum of all 
entries found in the bins of the histogram which is to be tested.
\paragraph{Estimation of the probability for each region}
A statistical estimator $p$ is defined to judge which region is of 
most interest.
This estimator is 
derived from the convolution of the
Poisson probability density function (pdf) to account for statistical 
errors with a Gaussian pdf, $G(b;N_b,\delta N_b)$, to include the effect of 
non negligible systematics uncertainties. 

\begin{equation*}
 p  = \left\{ \begin{array}{ll}
      A \int\limits_0^{\infty} db  \, G(b;N_b,\delta N_b) \, \sum\limits_{i=\Nobs}^{\infty} \frac{e^{-b}
b^i} {i!} & \textrm{ if } \Nobs \ge N_b \\
      A \int\limits_0^{\infty} db  \, G(b;N_b,\delta N_b) \,\,\,\, \sum\limits_{i=0}^{\Nobs} \frac{e^{-b}
b^i} {i!} & \textrm{ if } \Nobs < N_b 
    \end{array} \right.
\end{equation*}

Here $N_b$ denotes the mean of the Gaussian pdf and $\delta N_b$
the corresponding width. $A$ is a normalisation factor to ensure that the
pdf is normalised to $1$.
Hence $p$ gives an estimate of the
probability that the SM expectation fluctuates upwards or downwards to 
the data.

\paragraph{Determination of the most interesting region}
A possible sign of new physics
is found (in our ansatz) if the expectation significantly
disagrees with the data.
This disagreement is quantified with the estimator $p$.
The region of greatest interest (of greatest deviation) is the
region having the smallest $p$-value, $\pmin$. 
This method 
finds narrow resonances, single outstanding events as well as signals spread over large regions of phase space.

\paragraph{Global significance per event class}
The fact that somewhere in the studied
distribution a fluctuation
with a value $\pmin$ occurs is taken into account.
$\hat{P}$ is defined as
the probability to observe a deviation with a $p$-value
$\pmin$
with this algorithm
in the investigated distribution
(similar to: at any position in the distribution).
$\hat{P}$ is a measure of the significance of the found deviation.
To determine $\hat{P}$ hypothetical data
histograms are produced by dicing in each bin 
a random event number according to the
pdfs of the expectation
(again a convolution of Poisson and Gaussian pdfs).
For each hypothetical data histogram the algorithm is run to find the region
of greatest deviation and to calculate $\pmin$.
The  probability $\hat{P}$ 
can then be defined as the fraction of hypothetical data histograms 
with a $\pmin$-value smaller than $p_{\mbox{\footnotesize{min,\,data}}}$. 
This fraction, $\hat{P}$, can be used
to combine results of different event classes, if the event classes are independent.
An event class with small $\hat{P}$ is of more interest
than an event class with
large $\hat{P}$. Consequently the event class of most interest
for a search is the one with the smallest $\hat{P}$ value.

% All $\hat{P}$ values differ only by less than 20\%
% if the bin size is decreased to 2 or 1 GeV. 
% 

To compare the obtained $\hat{P}$ values with an expectation, the data distributions
are replaced by distributions from 
Monte Carlo experiments. These Monte Carlo (MC) distributions are again 
hypothetical data distributions. 
The complete algorithm is applied on these independent sets of MC 
experiments. 
In the case that 
deviations from the SM arise only from statistical or systematical 
fluctuations 
the distribution of $\hat{P}$ values obtained in data events are  
compatible with the distribution of $\hat{P}$ arising from these MC
experiments.

\subsection{Search Results}

The final $\hat{P}$ values obtained for all event classes are summarised in Table~\ref{tab:phatmass} ($\Mall$) and 
Table~\ref{tab:phatet} ($\sum P_T$). The $\hat{P}$ values of the event 
classes with no data event and a SM expectation
$\lesssim 1$ are $1$.
Distributions of the 
invariant mass $\Mall$ and the sum of transverse momenta $\sum P_T$ together
with the regions selected by the algorithm
are presented in Figure 4-7.
The \jjjj and \ejjjj event classes
 are not considered in this statistical 
analysis as their SM prediction is less reliable. The 
values are compared to the distribution of $\hat{P}$ values 
obtained in MC experiments in Figure~\ref{fig:Massscan} 
for the invariant mass distributions and in Figure~\ref{fig:ptscan} for
the $\sum P_T$ distributions. The negative 
decade logarithm of the $\hat{P}$ values, $-\log{\hat{P}}$ 
is presented. Most  $\hat{P}$
values range from $0.01$ to $0.99$, corresponding to event classes
where no significant discrepancy 
between data and the SM expectation is observed. 
%neither in the $\sum P_T$ distributions nor in the invariant mass 
%distributions.
These results are in agreement with the expectation from MC experiments.

%A deficit is observed in the \ej event class in the $\sum P_T$ distribution at
%$180 < \sum P_T < 210$~GeV.
%For a SM expectation of $31.2\pm 5.0$ only 12 data events are measured. 
%The derived $\hat{P}$ value is  $0.015$.

%A $\hat{P}$ value of $0.10$ is found in the \ee event class in the region at 
%high invariant mass $110<\Mall<120$~GeV where 3 events are observed 
%for an expectation of $0.3\pm0.08$. The deviation is more prominent at 
%high transverse momenta where $3$ events are observed in the region of 
%$100<\sum P_T<110$~GeV and only $0.08\pm 0.03$ are expected. Consequently 
%the second 
%smallest  $\hat{P}$ value ($0.0015$) obtained by the $\sum P_T$ scans is observed in
%this class. 
%This corresponds to an 
%excess of data events also identified in Ref.~\cite{multielectron}

The largest deviation of the analysis is located in the
\mujnp event class, where $\hat{P}$ values of $0.010$ and $0.0008$ are found  
corresponding to the high invariant mass and high $\sum P_T$ region, respectively. The mass region
contains two data events for an expectation of $0.05\pm 0.02$. In the chosen 
$\sum P_T$ region three data events are found while only $0.07\pm 0.03$ are expected.
This discrepancy was studied in Ref.~\cite{Andreev:2003pm}.

This analysis
studies a large number of event classes. Thus there is some chance
that small $\hat{P}$ values may occur.
The likeliness can be calculated
 that the smallest probability found in the investigated 
$\Mall$ or $\sum P_T$ distributions may occur. This is the 
fraction
of MC experiments with a smaller $\hat{P}$ value than 
the smallest found in 
the data $\hat{P}_{\mbox{\footnotesize{data}}}$.
This value is found to be $\approx 0.25$ for the 
set of $\Mall$ distributions and about $0.02$ for 
the $\sum P_T$ distributions. 


\section{Conclusions}
The data collected with the H1 experiment during the years 
1994-2000 (HERA I) has been searched for deviations from the SM prediction
at high transverse momentum.
All possible event topologies have been investigated in a coherent and model 
independent way. Many event classes are analysed 
herein for the first time at HERA.
A good agreement between data and SM expectation has been found 
in most event classes. The invariant mass and sum of transverse momenta 
distributions of the event classes have been systematically searched for 
deviations with a
novel algorithm. 
%The results of this analysis are found to be consistent
%with all previously observed deviations.
The most significant deviation is found in the 
\mujnp event class, a topology where deviations have also been previously
observed.
About $2\%$ of hypothetical Monte Carlo experiments would produce
deviations more significant than the
one observed in the corresponding sum of transverse momenta distribution.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgements}

We are grateful to the HERA machine group whose outstanding
efforts have made this experiment possible. 
We thank
the engineers and technicians for their work in constructing and now
maintaining the H1 detector, our funding agencies for 
financial support, the
DESY technical staff for continual assistance
and the DESY directorate for support and for the
hospitality which they extend to the non DESY 
members of the collaboration. We
wish to thank B.~Knuteson for useful
discussions.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Figures 


% \begin{figure}[p]
% \center
% \epsfig{file=class9400_style.eps,width=1.1\textwidth}
% \caption{The data and SM expectation for all 3-object event classes. Event Classes
% with data events are also shown.}
% \label{fig:summaryplot}
% \end{figure}

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig1.eps,angle=270,width=0.9\textwidth}
\caption{The data and SM expectation for all event classes with data events or with a SM expectation
greater than $0.1$ events.
The \jjjj and \ejjjj event classes (grey area) 
is less reliable and not passed through the
 statistical analysis.
}
\label{fig:summaryplot}
\end{figure}

\clearpage

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig2.eps,width=0.9\textwidth}
\caption{The $-\log{\hat{P}}$  values for the data event classes and the 
expected distribution from MC experiments. 
The $\Mall$ distributions are tested with the search algorithm. All event 
classes
with a SM expectation greater than $0.1$ events, except the 
\jjjj and the \ejjjj event class, are presented.} 
\label{fig:Massscan}
\end{figure}

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig3.eps,width=0.9\textwidth}
\caption{The $-\log{\hat{P}}$  values for the data event classes and the 
expected distribution from MC experiments.
The $\sum P_T$ distributions are tested with the search algorithm. All 
event classes
with a SM expectation greater than $0.1$ events, except 
the \jjjj and the \ejjjj event class, are presented.} 
\label{fig:ptscan}
\end{figure}

\clearpage

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig4a.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4b.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4c.eps ,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4d.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4e.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4f.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4g.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4h.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4i.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4j.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4k.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig4l.eps,width=0.33\textwidth}
\caption{The number of data events
and the SM expectation for various event classes as a
function of $\sum P_T$ and of $\Mall$. The shaded 
region shows the regions of greatest deviation chosen by the 
search algorithm.}
\label{fig:1}
\end{figure}

\clearpage

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig5a.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5b.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5c.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5d.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5e.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5f.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5g.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5h.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5i.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5j.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5k.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig5l.eps,width=0.33\textwidth}
\caption{The number of data events and the 
SM expectation for various event classes as a
function of $\sum P_T$ and of $\Mall$. The shaded 
region shows the regions of greatest deviation chosen by the search algorithm.}
\label{fig:2}
\end{figure}

\clearpage

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig6a.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6b.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6c.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6d.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6e.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6f.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6g.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6h.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6i.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6j.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6k.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig6l.eps,width=0.33\textwidth}
\caption{The number of data events and the 
SM expectation for various event classes as a
function of $\sum P_T$ and of $\Mall$. The shaded 
region shows the regions of greatest deviation chosen by the search algorithm.}
\label{fig:3}
\end{figure}

\begin{figure}[p]
\center
\epsfig{file=H1prelim-03-063.fig7a.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig7b.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig7c.eps,width=0.33\textwidth}
\epsfig{file=H1prelim-03-063.fig7d.eps,width=0.33\textwidth}
\caption{The number of data events and the 
SM expectation for various event classes as a
function of $\sum P_T$ and of $\Mall$. The shaded 
region shows the regions of greatest deviation chosen by the search algorithm.}
\label{fig:4}
\end{figure}



%%%%%%%%%% Proposition for a table .....

\begin{table}[p]
\begin{center} 
\begin{tabular}{|c||l|r|rcr|c|} 
\hline
Event class & $\hat{P}$ & $N_{\mbox{\footnotesize{obs}}}$ & 
$N_{\mbox{\footnotesize{exp}}}$ & $\pm$ & $\delta 
N_{\mbox{\footnotesize{exp}}}$ & $p$ \\
\hline
\jj & 0.25 &        1&0.025 & $\pm$ & 0.014 &0.026 \\
\ej & 0.97 &       11& 7.2 & $\pm$ & 1.7 &0.15 \\
\muj & 0.68 &        3&1.10 &$\pm$& 0.27 &0.11 \\
\jnp & 0.51 &       84&114.7 &$\pm$& 14.3 &0.041 \\
\enp & 0.39 &        1& 9.9 &$\pm$& 5.2  & 0.044 \\
\ee & 0.28  &        3&0.52 &$\pm$& 0.11 &0.017 \\
\emu & 0.20 &        4&0.95 &$\pm$& 0.12 &0.017 \\
\mumu &0.05 &        2&0.12 &$\pm$& 0.04 &0.007 \\
\jpho &0.62 &        4&11.9 &$\pm$& 3.8 &0.062 \\
\epho &0.41 &        9&19.0 &$\pm$& 2.0 &0.015 \\
\nppho & 1. &        0&0.96 &$\pm$& 0.37 &0.406 \\
\jjj & 0.38  &        12 & 5.8 &$\pm$& 2.0 & 0.047 \\
\ejj & 0.57 &        11& 5.7 &$\pm$& 1.3   &0.053 \\
\jjnp & 0.66 &        5&1.86 &$\pm$& 0.45   &0.050 \\
\ejnp & 0.10 &         2& 0.18 &$\pm$& 0.04 &0.014 \\
\mujnp & 0.01 &      2& 0.046 &$\pm$& 0.02 & 0.0012 \\
\jjpho & 0.39 &     1& 0.12 &$\pm$& 0.07 &0.112 \\
\ejpho & 0.43 &    1& 5.76 &$\pm$& 1.6 & 0.049 \\
\ejjj & 0.91 &    4&2.10  &$\pm$& 0.9 & 0.19 \\
\jjjnp & 0.40 &     1& 0.08 &$\pm$& 0.07 & 0.091 \\
\hline
\end{tabular} 
\end{center} 
\caption{The $\hat{P}$ values, data events $N_{\mbox{\footnotesize{obs}}}$ and the 
SM expectation $N_{\mbox{\footnotesize{exp}}}$ of the region  
derived by the search algorithm using the $\Mall$ distributions 
for various event classes. }
\label{tab:phatmass}
\end{table}


\begin{table}[p]
\begin{center} 
\begin{tabular}{|c||l|r|rcr|c|c|} 
\hline
Event class & $\hat{P}$ & $N_{\mbox{\footnotesize{obs}}}$ & 
$N_{\mbox{\footnotesize{exp}}}$ & $\pm$ & $\delta 
N_{\mbox{\footnotesize{exp}}}$ & $p$ \\
\hline
\jj &0.065 &  1& 0.010&$\pm$&0.005 &0.010 \\
\ej &0.02 &  12& 30.4 &$\pm$& 5.0 & 0.0032  \\
\muj & 0.29 &  3& 0.70 &$\pm$&0.20 &0.038 \\
\jnp & 0.17 & 19& 36.6 &$\pm$& 6.4 & 0.020 \\
\enp & 0.38& 6& 18.0 &$\pm$& 7.4 & 0.073 \\   
\ee & 0.02 &  3&0.20 &$\pm$& 0.08 &0.0015 \\ 
\emu &0.51 & 0 & 2.70 &$\pm$& 0.4 &0.07 \\
\mumu &0.02 &  2&0.074 &$\pm$& 0.03 & 0.0031 \\  
\jpho &0.52& 2& 0.41&$\pm$&0.2&0.071 \\ 
\epho &0.76 & 8 &15.3&$\pm$& 2.3 &0.056 \\
\nppho &0.76 & 0&1.51&$\pm$& 0.53&0.252 \\
\jjj &0.35 &  7& 3.01&$\pm$& 0.96 &0.055 \\
\ejj & 0.49 &  9& 18.4&$\pm$& 3.4 & 0.040 \\
\jjnp &0.56& 5& 1.86&$\pm$& 0.55 & 0.054  \\
\ejnp &0.16&  2& 0.28&$\pm$& 0.07&0.035 \\
\mujnp & 0.0008 &  3& 0.07 &$\pm$& 0.03 & 0.00007 \\  
\jjpho &0.31 &  1&0.10 &$\pm$& 0.07 &0.104 \\
\ejpho & 0.37 &  1&5.64&$\pm$&1.50 &0.050 \\
\ejjj &0.75 &  1 & 0.14&$\pm$& 0.08&0.135 \\
\jjjnp &0.22& 2& 0.28&$\pm$&0.20 &0.048 \\
\hline
\end{tabular} 
\end{center} 
\caption{The $\hat{P}$ values, data events $N_{\mbox{\footnotesize{obs}}}$ and the 
SM expectation $N_{\mbox{\footnotesize{exp}}}$ of the region  
derived by the search algorithm using the $\sum P_T$ distributions 
of various event classes. }
\label{tab:phatet}
\end{table}

\begin{table}[htbp]
  \begin{center}
    \begin{tabular}{|c||c|c|}
      \hline
      Event class &  \makebox[3.cm]{Purity $\cal P\;(\%)$} & \makebox[3.cm]{Efficiency $\cal E\;(\%)$}  \\
      \hline
      \hline
      \jj        & 80-100  & 80-100 \\
      \ej        & 90-100  & 70 \\
      \muj       & 80-90  & 50-55 \\
      \jnp       & 85-95  & 75-90 \\
      \enp       & 50-80  & 40-50 \\
      \ee        & 30-70  & 40-50 \\
      \emu       & 90     & 40-50 \\
      \mumu      & 95-100 & 25-30 \\
                                %        \munp      & ---    & ---   \\
      \jpho      & 20-40  & 30-50 \\
      \epho      & 70     & 50-60 \\
                                %        \mupho     & ---    & ---   \\
      \nppho     & 70-80  & 20-40 \\
                                %        \phopho    & ---    & ---   \\
      \jjj       & 70-80  & 80-95 \\
      \ejj       & 70-90  & 60    \\
                                %        \mujj      & ---    & ---   \\
      \jjnp      & 60-80  & 60-85 \\
      \eej       & 40-70  & 20    \\
                                %        \eenp      & ---    & ---   \\
      \eee       & 30-70  & 20-70 \\
                                %        \eemu      & ---    & ---   \\
                                %        \mumumu    & ---    & ---   \\
      \jmumu     & 50-90  & 20-50 \\
      \emumu     & 60-70  & 20-40 \\
                                %        \mumunp    & ---    & ---   \\
      \emuj      & 30-50  & 20-40 \\
      \ejnp      & 50-70  & 40-50 \\
      \mujnp     & 65     & 40-50 \\
                                %        \emunu     & ---    & ---   \\
      \jjpho     & 5-25   & 10-20 \\
      \ejpho     & 40-60  & 30-45 \\
                                %        \mujpho    & ---    & ---   \\
      \jnppho    & 70-100 & 30-50 \\
                                %        \jphopho   & ---    & ---   \\
                                %        \eepho     & ---    & ---   \\
                                %        \emupho    & ---    & ---   \\
                                %        \enppho    & ---    & ---   \\
                                %        \ephopho   & ---    & ---   \\
                                %        \mumupho   & ---    & ---   \\
                                %        \munppho   & ---    & ---   \\
                                %        \muphopho  & ---    & ---   \\
                                %        \phophopho & ---    & ---   \\
      \jjjj      & 70-90  & 60-80 \\
      \ejjj      & 50-80  & 30-70 \\
      \jjjnp     & 30-90  & 30-80 \\
      \ejjjj     & 100    & 20\\
      \hline
    \end{tabular}
     \caption{The mean values of the efficiencies $\cal{E}$ and purities $\cal{P}$ in the $M_{all}$ and $\sum P_T$ distributions for some
event classes.}
     \label{tab:effpur}
  \end{center}
\end{table}
\end{document}




