| 227 |
|
mSUGRA parameter space, |
| 228 |
|
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
| 229 |
|
using different models for the nuisance parameters. |
| 230 |
< |
PDF UNCERTAINTOES ARE NOT INCLUDED.} |
| 230 |
> |
PDF UNCERTAINTIES ARE NOT INCLUDED.} |
| 231 |
|
\end{center} |
| 232 |
|
\end{figure} |
| 233 |
|
|
| 234 |
< |
We find that the set of excluded points is identical for the |
| 235 |
< |
lognormal and gamma models. There are small differences for the |
| 236 |
< |
gaussian model. Following the recommendation of Reference~\cite{ref:cousins}, |
| 237 |
< |
we use the lognormal nuisance parameter model. |
| 234 |
> |
We find that different assumptions on the PDFs for the nuisance |
| 235 |
> |
parameters make very small differences to the set of excluded |
| 236 |
> |
points. |
| 237 |
> |
Following the recommendation of Reference~\cite{ref:cousins}, |
| 238 |
> |
we use the lognormal nuisance parameter model as the default. |
| 239 |
|
|
| 240 |
|
|
| 241 |
|
\clearpage |
| 243 |
|
|
| 244 |
|
\subsubsection{Effect of signal contamination} |
| 245 |
|
\label{sec:contlimit} |
| 246 |
+ |
|
| 247 |
|
Signal contamination could affect the limit by inflating the |
| 248 |
|
background expectation. In our case we see no evidence of signal |
| 249 |
|
contamination, within statistics. |
| 262 |
|
|
| 263 |
|
Nevertheless, here we explore the possible effect of |
| 264 |
|
signal contamination. The procedure suggested to us |
| 265 |
< |
is the following: |
| 264 |
< |
\begin{itemize} |
| 265 |
< |
\item At each point in mSUGRA space we modify the |
| 265 |
> |
for the ABCD method is to modify the |
| 266 |
|
ABCD background prediction from $A_D \cdot C_D/B_D$ to |
| 267 |
|
$(A_D-A_S) \cdot (C_D-C_S) / (B_D - B_S)$, where the |
| 268 |
< |
subscripts $D$ and $S$ referes to the number of observed data |
| 268 |
> |
subscripts $D$ and $S$ refer to the number of observed data |
| 269 |
|
events and expected SUSY events, respectively, in a given region. |
| 270 |
< |
\item Similarly, at each point in mSugra space we modify the |
| 271 |
< |
$P_T(\ell\ell)$ background prediction from |
| 272 |
< |
$K \cdot K_C \cdot D'_D$ to $K \cdot K_C \cdot (D'_D - D'_S)$, |
| 273 |
< |
where the subscript $D$ and $S$ are defined as above. |
| 274 |
< |
\item At each point in mSUGRA space we recalculate $N_{UL}$ |
| 275 |
< |
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 $N_{UL}$. |
| 270 |
> |
We then recalculate $N_{UL}$ at each point using this modified |
| 271 |
> |
ABCD background estimation. For simplicity we ignore |
| 272 |
> |
information from the $P_T(\ell \ell)$ |
| 273 |
> |
background estimation. This is conservative, since |
| 274 |
> |
the $P_T(\ell\ell)$ background estimation happens to |
| 275 |
> |
be numerically larger than the one from ABCD. |
| 276 |
|
|
| 277 |
|
Note, however, that in some cases this procedure is |
| 278 |
|
nonsensical. For example, take LM0 as a SUSY |
| 286 |
|
BG prediction (which is nonsense, so we set it to zero), |
| 287 |
|
and therefore a weaker limit. |
| 288 |
|
|
| 289 |
+ |
|
| 290 |
+ |
|
| 291 |
+ |
|
| 292 |
|
\begin{figure}[tbh] |
| 293 |
|
\begin{center} |
| 294 |
|
\includegraphics[width=0.5\linewidth]{sigcont.png} |
| 300 |
|
\end{center} |
| 301 |
|
\end{figure} |
| 302 |
|
|
| 303 |
< |
Despite these reservations, we follow the procedure suggested |
| 304 |
< |
to us. A comparison of the exclusion region with and without |
| 307 |
< |
the signal contamination is shown in Figure~\ref{fig:sigcont} |
| 303 |
> |
A comparison of the exclusion region with and without |
| 304 |
> |
signal contamination is shown in Figure~\ref{fig:sigcont} |
| 305 |
|
(with no smoothing). The effect of signal contamination is |
| 306 |
< |
small. |
| 306 |
> |
small, of the same order as the quantization of the scan. |
| 307 |
> |
|
| 308 |
|
|
| 309 |
|
\subsubsection{mSUGRA scans with different values of tan$\beta$} |
| 310 |
|
\label{sec:tanbetascan} |
