\subsection{Search for Physics Beyond the Standard Model}
\subsubsection{Supersymmetric Particles}
%
Supersymmetry (SUSY) is the theoretically favoured 
model for physics beyond the Standard Model. 
The new symmetry uniting fermions and bosons predicts for each Standard Model
particle a new supersymmetric partner with spin quantum number differing by $1/2$.
Supersymmetry provides a natural explanation for Higgs boson masses near the electroweak
scale. In addition, the lightest stable supersymmetric particle is a good candidate for 
dark matter. Another theoretical problems which can be solved by SUSY is the unification of the fundamental 
forces. 

If the mass scale of the SUSY particles is
accessible at LHC, the squarks and gluinos (the superpartners of quarks and gluons with spin 0 and $1/2$, respectively)
will be copiously produced in $pp$ collisions.
In order to suppress the processes violating the barionic and leptonic quantum numbers, R-parity is introduced.  
The consequences of R-parity are that supersymmetric particles must be produced in pairs and each will decay
to weakly interacting lightest supersymmetric particle via decay chains involving production of quarks and leptons. 
Therefore, the SUSY events at LHC are characterized by the large transverse missing  energy, high energetic hadronic jets and leptons.

Supersymmetry requires equal mass for the particle and its superpartner.
As the supersymmetric partners of Standard Model particles are not observed so far, SUSY must be a broken symmetry. 
A model with SUSY breaking mediated by gravitational interaction is called mSUGRA and is described by the common boson mass and common
fermion mass at energy scale above $10^{15}$ GeV, where the electroweak and strong interactions are unified (GUT scale).

The searches for SUSY signatures with R-parity conservation in ATLAS are performed by searching an excess of events in various
channels. These channels explore a large variety of possible signals, e.g. different jet and lepton multiplicities. 
Fig.~\ref{atlas_reach} shows 5-$\sigma$ discovery reach for the mSUGRA model for the 4 jet 0 lepton, the 4 jet 1 lepton and the 
2 jet 2 lepton channels
in the parameter space of mSUGRA model defined by common mass of fermion $m_{1/2}$ and common mass of bosons $m_{0}$ at the GUT scale.  

\begin{figure}
\figimage{1.05}{MSUGRA10_contourLines_summary}
\labelcaption{atlas_reach}{
ATLAS 5-$\sigma$ discovery reach for the the mSUGRA model for the channels with various jet and lepton multiplicity in 
the parameter space of mSUGRA model defined by common mass of fermion $m_{1/2}$ and common mass of bosons $m_{0}$ at the GUT scale. 
The discovery reach is estimated for the center-of-mass energy is 10 GeV and the integrated luminosity is 200~$pb^{-1}$.}
\end{figure}

The Standard Model processes with similar signature are top quarks ($t\bar{t}$)  and gauge bosons ($W$ and $Z$)  production.
In these processes the large transverse missing energy
is originated from weakly interacting neutrino. These processes constitute the main background to SUSY searches at LHC.
Jet production from QCD process with ``fake'' transverse missing energy originated from jet energy mis-measurement
is another important source of the background. It is expected that at LHC the Monte Carlo prediction will not be sufficient
to achieve the good understanding and the control of the background to SUSY searches. 
Our studies are concentrated on the data-driven estimation of the backgrounds
to SUSY searches, which is a key point of early discovery of SUSY by ATLAS detector. 

With Monte Carlo simulations we have studied methods for determining the $t\bar t$
background from data~\cite{ATLAS_Analysis_susybg_CSC}.
The background estimation is performed by selecting the SUSY-free ``control sample'' from which the prediction of background is derived.
The $t\bar{t}$ production with top quark decays involving the $\tau$ leptons and non-reconstructed electrons or muons 
is estimated from similar events with identified
muons and electron. The ``control sample'' composed mainly by events where both top quarks decayed to b-quark, neutrino and lepton (electron or muon)
is selected by applying the set of kinematic constrains particular to this process. The resulting variable, denoting the
number of b-jet pairs passing the kinematic constrains is used to separate the signal region into SUSY-dominated region and $t\bar{t}$-dominated
region.


\begin{figure}
\figimage{1.05}{susy12figure7a}
\labelcaption{fig:nJetPairs}{Number of b-jet pairs $N_{b-jet pairs}$ passing the kinematic 
requirements of $t\bar{t}$} process with both t-quarks decayed
to b-quark, neutrino and lepton (electron or muon). The $N_{b-jet pairs}>0$ region is mainly populated by $t\bar{t}$. This region is used as a 
``control sample'' for the estimations of $t\bar{t}$ background with $\tau$-lepton and non-identified electrons and muons in SUSY searches
with one lepton.
The bin $N_{b-jet pairs}=0$ is filled by the gauge boson production processes and by the SUSY events simulated by two typical models 
labeled SU1 and SU3.}
\end{figure}

Similar strategy is used for isolation of the control sample with $t\bar{t}$ events with one top quark decayed to jet, neutrino and lepton (electron
or muon), and the other top quark decayed to b-quark and two light quarks~\cite{ATL-PHYS-PUB-2009-083}. 
In this case the discriminating variable is the invariant mass
of three close hadron jets, which is close to mass of the top quark for $t\bar{t}$ events.

\begin{figure}
\figimage{1.05}{ATL_PHYS_PUB_2009_083_FIG_6}
\labelcaption{fig:mTopHad}{Distribution of invariant mass of tree nearby jets. This variable used for the selection of the ``control sample'' of
$t \bar{t}$ events with one top quark decayed to jet, neutrino and lepton (electron
or muon), and the other top quark decayed to b-quark and two light quarks. 
This ``control sample'' is used to derive the data-driven production of $t\bar{t}$ background in SUSY searches with no-lepton signatures.
The arrows show the chosen window for this variable. 
The Standard Model contributions are
shown by the stacked hatched histograms. The SUSY contribution for two typical SUSY mSUGRA models labeled as SU3 and SU4 are overlaid.}
\end{figure}

The $t\bar{t}$ events with tau leptons produced in top-quark decay are reproduced by the events of the ``control sample'' by replacing 
the electron or muon with a tau lepton and simulating the tau lepton decay. Similar, the contribution with non-identified electron or muon is 
reproduced by treating the lepton as if it had not been identified.   

\begin{figure}
\figimage{1.05}{ATL_PHYS_PUB_2009_083_FIG_7}
\labelcaption{fig:mTopHad}{Distribution of transverse missing energy in $t\bar{t}$ events. The solid line shows the Monte Carlo estimate,
circles show the result of data-driven estimation. The shaded histograms show the increase of data-driven estimates in the presence of SUSY signal 
(represented by SU3 and SU4 models) in the ``control sample''
and the dashed lines shows the SUSY signals stacked on the top of $t\bar{t}$ background.}
\end{figure}

We analyzed a set of the most important kinematic variables for the first 70 nb$^{-1}$ of data collected by ATLAS experiment 
during the period March-July 2010 \cite{ICHEP_0_lepton}. We find good
agreement between data and Monte Carlo simulation indicating that the Standard Model backgrounds to SUSY searches is under good control.

\begin{figure}
\figimage{1.05}{hEtmiss_2jet}
\labelcaption{fig:}{
Distribution of missing transverse energy for events with two jets.
Black points shows the  first 70 nb$^{-1}$ of data collected by 
ATLAS experiment during the period March-July 2010. Shaded histograms shows the contribution of gauge boson and top quark production
processes. The open red histogram shows the QCD di-jet production process. The prediction of low-mass mSUGRA model SU4 (enhanced by factor 10) 
is shown by black dashed line. }
\end{figure}
 



\subsubsection{Other Extensions of the Standard Model}

Since the discovery of the neutrino flavour oscillations it is known that the lepton flavour is not conserved in particle interactions.
One of the lepton flavour violating process accessible at LHC is a neutrinoless decay of a tau lepton $\tau\rightarrow \mu\mu\mu$.
Although the Standard Model predicts very small branching ratio for this decay, 
$$B(\tau\rightarrow \mu\mu\mu)\le 10^{-14},$$
some extensions of the Standard Model, such as SUSY and models with double charged Higgs Boson, predicts sizable value for it. Therefore, the 
measurement of branching ratio of   $\tau\rightarrow \mu\mu\mu$ will put stringent limits on the parameters of these models. 

During one year of data-taking at the low luminosity phase ATLAS will collect $10^{12}$ $\tau$ lepton decays. Due to severe background 
only fraction of these decays can be observed in ATLAS, namely decays of $\tau$ lepton produced via W and Z bosons. We studied the
sensitivity of the ATLAS detector to the   $\tau\rightarrow \mu\mu\mu$ decay, where the tau lepton is produced by decay of W boson 
\cite{joerg_thesis}. 
This process is characterized by large transverse missing energy produced by non-detectable neutrino, and by three nearby muon tracks. The main
background processes are production of charmed and beauty mesons, with following decay to muons.  

\begin{figure}
\figimage{1.05}{mass3mu}
\labelcaption{fig:mass3mu}{
Invariant  mass distribution of tree nearby muons produced by $\tau\rightarrow \mu\mu\mu$ decay with tau lepton produced via W boson (green)
and by the background processed, including decay of charmed and beauty mesons. All selection cuts except of the cut on the shown variable 
are applied to the Monte Carlo data, normalised to the integrated luminosity of 10 fb$^{-1}$. Non-shaded area shows the cut on the  
invariant mass of tree muons.
}

The study with the simulated data shows that the upper limit of $B(\tau\rightarrow \mu\mu\mu)\le 5.9^{-7}$ can be achieved with 10 fb$^{-1}$ of 
collected data. With the expected sensitivity, an integrated luminosity of 100 fb$^{-1}$ has to be collected by ATLAS experiment to reach the
current best upper limit of $B(\tau\rightarrow \mu\mu\mu)\le 3.2^{-8}$ (90\% CL) of the BELLE experiment.
\end{figure}

In addition, we pursue searches for non-Standard Model heavy neutral gauge boson $Z'$ predicted by some extensions of Standard Model which 
address the problems of mass hierarchy and number of generations of lepton and quarks.
