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the boundaries using the method recommended by the SUSY |
| 196 |
|
group\cite{ref:smooth}. In addition, we show a limit |
| 197 |
|
curve based on the LO cross-section, as well as the |
| 198 |
< |
``expected'' limit curve. The expected limit curve is |
| 198 |
> |
``expected'' limit curve. The expected limit curve was |
| 199 |
|
calculated using the CLA function also available in cl95cms. |
| 200 |
< |
Cross-section uncertainties due to variations of the factorization |
| 200 |
> |
In general we found that the ``expected'' limit is very close |
| 201 |
> |
to the observed limit, which is not surprising since the |
| 202 |
> |
expected BG (1.4 $\pm$ 0.8 events) is fully consistent |
| 203 |
> |
with the observation (1 event). Because of the quantization, |
| 204 |
> |
we find that the expected and observed limits are either |
| 205 |
> |
identical or differ by one or at most two grid points. |
| 206 |
> |
We have approximated the expected limit as the observed limit |
| 207 |
> |
minus 10 GeV\footnote{We show the expected limit only because |
| 208 |
> |
this is what is recommended by SUSY management. We believe that |
| 209 |
> |
quoting the agreement between the expected BG and the |
| 210 |
> |
observation should be enough....}. |
| 211 |
> |
Finally, we note that the sross-section uncertainties due to |
| 212 |
> |
variations of the factorization |
| 213 |
|
and renormalization scale are not included for the LO curve. |
| 214 |
|
The results are shown in Figure~\ref{fig:msugra} |
| 215 |
|
|
| 239 |
|
mSUGRA parameter space, |
| 240 |
|
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
| 241 |
|
using different models for the nuisance parameters. |
| 242 |
< |
PDF UNCERTAINTOES ARE NOT INCLUDED.} |
| 242 |
> |
PDF UNCERTAINTIES ARE NOT INCLUDED.} |
| 243 |
|
\end{center} |
| 244 |
|
\end{figure} |
| 245 |
|
|
| 246 |
< |
We find that the set of excluded points is identical for the |
| 247 |
< |
lognormal and gamma models. There are small differences for the |
| 248 |
< |
gaussian model. Following the recommendation of Reference~\cite{ref:cousins}, |
| 249 |
< |
we use the lognormal nuisance parameter model. |
| 246 |
> |
We find that different assumptions on the PDFs for the nuisance |
| 247 |
> |
parameters make very small differences to the set of excluded |
| 248 |
> |
points. |
| 249 |
> |
Following the recommendation of Reference~\cite{ref:cousins}, |
| 250 |
> |
we use the lognormal nuisance parameter model as the default. |
| 251 |
|
|
| 252 |
|
|
| 253 |
< |
\clearpage |
| 253 |
> |
% \clearpage |
| 254 |
|
|
| 255 |
|
|
| 256 |
|
\subsubsection{Effect of signal contamination} |
| 257 |
|
\label{sec:contlimit} |
| 258 |
+ |
|
| 259 |
|
Signal contamination could affect the limit by inflating the |
| 260 |
|
background expectation. In our case we see no evidence of signal |
| 261 |
|
contamination, within statistics. |
| 274 |
|
|
| 275 |
|
Nevertheless, here we explore the possible effect of |
| 276 |
|
signal contamination. The procedure suggested to us |
| 277 |
< |
is the following: |
| 264 |
< |
\begin{itemize} |
| 265 |
< |
\item At each point in mSUGRA space we modify the |
| 277 |
> |
for the ABCD method is to modify the |
| 278 |
|
ABCD background prediction from $A_D \cdot C_D/B_D$ to |
| 279 |
|
$(A_D-A_S) \cdot (C_D-C_S) / (B_D - B_S)$, where the |
| 280 |
< |
subscripts $D$ and $S$ referes to the number of observed data |
| 280 |
> |
subscripts $D$ and $S$ refer to the number of observed data |
| 281 |
|
events and expected SUSY events, respectively, in a given region. |
| 282 |
< |
\item Similarly, at each point in mSugra space we modify the |
| 283 |
< |
$P_T(\ell\ell)$ background prediction from |
| 284 |
< |
$K \cdot K_C \cdot D'_D$ to $K \cdot K_C \cdot (D'_D - D'_S)$, |
| 285 |
< |
where the subscript $D$ and $S$ are defined as above. |
| 286 |
< |
\item At each point in mSUGRA space we recalculate $N_{UL}$ |
| 287 |
< |
using the weighted average of the modified $ABCD$ and |
| 276 |
< |
$P_T(\ell\ell)$ method predictions. |
| 277 |
< |
\end{itemize} |
| 278 |
< |
|
| 279 |
< |
\noindent This procedure results in a reduced background prediction, |
| 280 |
< |
and therefore a less stringent $N_{UL}$. |
| 282 |
> |
We then recalculate $N_{UL}$ at each point using this modified |
| 283 |
> |
ABCD background estimation. For simplicity we ignore |
| 284 |
> |
information from the $P_T(\ell \ell)$ |
| 285 |
> |
background estimation. This is conservative, since |
| 286 |
> |
the $P_T(\ell\ell)$ background estimation happens to |
| 287 |
> |
be numerically larger than the one from ABCD. |
| 288 |
|
|
| 289 |
|
Note, however, that in some cases this procedure is |
| 290 |
|
nonsensical. For example, take LM0 as a SUSY |
| 298 |
|
BG prediction (which is nonsense, so we set it to zero), |
| 299 |
|
and therefore a weaker limit. |
| 300 |
|
|
| 301 |
+ |
|
| 302 |
+ |
|
| 303 |
+ |
|
| 304 |
|
\begin{figure}[tbh] |
| 305 |
|
\begin{center} |
| 306 |
|
\includegraphics[width=0.5\linewidth]{sigcont.png} |
| 312 |
|
\end{center} |
| 313 |
|
\end{figure} |
| 314 |
|
|
| 315 |
< |
Despite these reservations, we follow the procedure suggested |
| 316 |
< |
to us. A comparison of the exclusion region with and without |
| 307 |
< |
the signal contamination is shown in Figure~\ref{fig:sigcont} |
| 315 |
> |
A comparison of the exclusion region with and without |
| 316 |
> |
signal contamination is shown in Figure~\ref{fig:sigcont} |
| 317 |
|
(with no smoothing). The effect of signal contamination is |
| 318 |
< |
small. |
| 318 |
> |
small, of the same order as the quantization of the scan. |
| 319 |
> |
|
| 320 |
|
|
| 321 |
|
\subsubsection{mSUGRA scans with different values of tan$\beta$} |
| 322 |
|
\label{sec:tanbetascan} |
