.2\cdot 10^{6}$ events and taking into account the $e^+ e^-$
energy resolution.

To estimate the systematic error on the masses due to the luminosity spectrum,
the mass fit is performed 38 times. Prior to each fit the effective luminosity spectrum 
$L_{Eff}(\sqrt{s},\overrightarrow{p})$
is computed; one parameter $p_i$ is changed to $p_i + \tfrac{ \sigma_{p_{i}}} {2}$ or $p_i - \tfrac{ \sigma_{p_{i}}} {2}$
and all other parameters are kept to their nominal value.

\noindent The error on the mass from the luminosity is:
\begin{eqnarray}
\sigma_m= \sqrt{\sum_{i,j}\delta_i C_{ij} \delta_j }
\end{eqnarray}
$C_{ij}$ is the correlation matrix obtained from the luminosity spectrum fit and:
\begin{eqnarray}
\delta_i = m(L_{Eff}(\sqrt{s}, \overrightarrow{p} +\overrightarrow{e}_{i} \frac{ \sigma_{p_i} } {2}))
-m(L_{Eff}(\sqrt{s},\overrightarrow{p} -\overrightarrow{e}_{i} \frac{\sigma_{p_i}}{2})).
\end{eqnarray}
where \textit{m} is the the result of the mass fit described in section 5.

Table~\ref{tab:syste3tev} shows the values of the slepton and gaugino masses, the corresponding statistical 
uncertainty, and the systematic errors from the knowledge of the shape of the luminosity spectrum.
For 2 $\mathrm{ab^{-1}}$ of integrated luminosity, the statistical errors are dominant.

\begin{table} [htbp]
\centering
\resizebox{\textwidth}{!} {
\begin{tabular}{ l c c c c c c }
\hline
Process &$m_{\tilde \ell}$ &$\sigma_m$ & $\sigma_m$  &$m_{\neutralino{1}}$ or $m_{\chargino{\pm}}$ &$\sigma_m$ &$\sigma_m$   \\
        &GeV               &(stat)\% &(lumi)\%  &GeV &(stat)\% &(lumi)\%            \\ \hline
$\ee \rightarrow \tilde\mu_R^+ \tilde\mu_R^-$  &1011.5  &0.45 &0.02  &341.7 &2.8 &0.06  \\
$\ee \rightarrow  \tilde e_R^+ \tilde e_R^-    $  &1011.8  &0.15 &0.02  &341.2 &0.80 &0.06 \\
$\ee \rightarrow  \tilde \nu_e \tilde \nu_e    $  &1093.6  &0.19 &0.02 &643.6 &0.54 &0.03  \\
\hline
\end{tabular}
}
\caption{Slepton and gaugino masses, statistical and systematic uncertainties, from the knowledge of the shape
of the luminosity spectrum (lumi), at  $\sqrt{s}=$ 3 TeV.
}
\label{tab:syste3tev}
\end{table}

\section{Polarization}
Beam polarization is very helpful in the
study of SUSY processes both to improve the signal-to-background ratio and as an
analyzer~\cite{MoortgatPick:2005cw}, in particular to establish
the chirality of the sleptons.
Table~\ref{tab:cross_polar} shows the signal cross sections for
different electron and positron beam polarization conditions.
Running with left polarized electron beam would establish the
chirality of the selectron which decays into two leptons and of the selectron and sneutrinos
which decay into two leptons and four jets.
Running with right polarized electron beam would increase the cross sections of the
$\tilde \ell_R$ processes and reduce some of the backgrounds.


\begin{table} [htbp]
\caption{Signal processes cross sections ($\sigma$), for different electron, positron beam
polarization conditions, at  \mbox{$\sqrt{s}=$ 3 TeV}. }
\label{tab:cross_polar}
\centering
\begin{tabular}{ l c c c c }
\hline
Process & $\ee \rightarrow  \tilde \mu_R^+ \tilde \mu_R^-$ 
& $\ee \rightarrow  \tilde e_R^+ \tilde e_R^- $
& $\ee \rightarrow  \tilde e_L^+ \tilde e_L^- $ 
& $\ee \rightarrow  \tilde \nu_e \tilde \nu_e $  \\
\hline
                             &  $\sigma(fb)$ &$\sigma(fb)$ &$\sigma(fb)$ &$\sigma(fb)$ \\
beam polarization            &               & & & \\
$e^-$ :none~,~$e^+:$none     &~~~0.72       &~~~6.05           &3.06            &~~13.76\\
$e^-$ :L80\%,~$e^+: $none     &~~~0.46      &~~~2.59           &4.78            &~~21.90\\
$e^-$ :R80\%,~$e^+: $none     &~~~0.98      &~~~9.51           &1.34            &~~~~5.62 \\
$e^-$ :R80\%,~$e^+: $L60\%   &~~~1.15       &~11.40           &1.14            &~~~~4.56  \\
\hline
\end{tabular}
\end{table}

\section{Summary}
The accuracy of the slepton and gaugino mass determination and of the process cross section measurement 
in pair produced
$\tilde e_R, \tilde e_L, \tilde \mu_R$, and $\tilde \nu_e$ processes
has been studied at CLIC with the CLIC\_ILD\_CDR detector model for
two specific SUSY benchmark scenarios at \mbox{$\sqrt{s}=$ 3 TeV and 1.4 TeV}.
The analysis is based on two lepton and two lepton plus four jet final states.

The electron and muon energy resolution and the boson mass resolution
are not affected by the beam induced background, provided the detectors have timing
capabilities of the order of 1 nsec allowing for the application of PFO selection cuts.
The reconstructed boson mass accuracy allows 
$W^{\pm}$ and light $H$ final states to be distinguished;
$b$ tagging improves the purity of the $W^{\pm}$ and $H$ samples.

Slepton cross sections, slepton and gaugino masses can be extracted from the
lepton energy distributions. 
At \mbox{3.0 TeV}, for 2.0 $\mathrm{ab^{-1}}$ of integrated luminosity
the relative statistical error on the masses 
is in the range of 0.15 to 0.45\% for the sleptons and in the range of 0.5 to 2.8\% for the gauginos.
At \mbox{1.4 TeV}, for 1.5 $\mathrm{ab^{-1}}$ of integrated luminosity, the relative statistical errors,
on the slepton and gaugino masses are in the range of 0.1 to 0.2\%.

A major source of smearing of the kinematic edges of the lepton energy spectrum
is beamstrahlung and ISR. 
The measurement of the luminosity spectrum with Bhabha events, allows a good
control of the beamstrahlung.
The systematic errors on the slepton and gauginos masses due to the knowledge of
the luminosity spectrum were estimated.
At \mbox{3.0 TeV} 
for 2.0 $\mathrm{ab^{-1}}$ of integrated luminosity the statistical errors
are larger than the systematic errors. 
\section{Acknowledgments}
We are grateful to the colleagues who contributed to this study.
Daniel~Schulte for making available the beam spectrum and
the $\gamma \gamma \to \mathrm{hadron}$ background events.
D.Schlatter and A.Lucaci-Timoce for a thorough reading of the manuscript.



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