| 163 |
|
expected yield for the LM1 point in FullSim (3.56 $\pm$ 0.06) and |
| 164 |
|
FastSim (3.29 $\pm$ 0.27), where the uncertainties are statistical only. |
| 165 |
|
These two numbers are in agreement, which gives us confidence in |
| 166 |
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usinf FastSim for this study. |
| 166 |
> |
using FastSim for this study. |
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|
| 168 |
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The FastSim events are generated with different values of $m_0$ |
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and $m_{1/2}$ in steps of 10 GeV. For each point in the |
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curve based on the LO cross-section, as well as the |
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``expected'' limit curve. The expected limit curve is |
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calculated using the CLA function also available in cl95cms. |
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+ |
Cross-section uncertainties due to variations of the factorization |
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+ |
and renormalization scale are not included for the LO curve. |
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The results are shown in Figure~\ref{fig:msugra} |
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|
| 204 |
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|
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|
\begin{figure}[tbh] |
| 206 |
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\begin{center} |
| 207 |
< |
\includegraphics[width=\linewidth]{exclusion.pdf} |
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> |
\includegraphics[width=\linewidth]{exclusion_noPDF.pdf} |
| 208 |
|
\caption{\label{fig:msugra}\protect Exclusion curves in the mSUGRA parameter space, |
| 209 |
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assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
| 210 |
< |
THE PDF UNCERTAINTIES.} |
| 210 |
> |
THE PDF UNCERTAINTIES. WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.} |
| 211 |
|
\end{center} |
| 212 |
|
\end{figure} |
| 213 |
|
|
| 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 |
< |
Red:gaussian. Blue:lognormal or gamma. |
| 229 |
< |
THIS IS STILL MISSING |
| 230 |
< |
THE PDF UNCERETAINTIES. MAYBE GOOD TO MAKE THIS PLOT A BIT |
| 231 |
< |
PRETTIER, EG, CANNOT DISTINGUISH THINGS WHEN USING BLACK AND |
| 232 |
< |
WHITE PRINTER} |
| 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: |
| 266 |
< |
\begin{itemize} |
| 267 |
< |
\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 |
| 278 |
< |
$P_T(\ell\ell)$ method predictions. |
| 279 |
< |
\end{itemize} |
| 280 |
< |
|
| 281 |
< |
\noindent This procedure results in a reduced background prediction, |
| 282 |
< |
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} |
| 295 |
|
\caption{\label{fig:sigcont}\protect Exclusion curves in the |
| 296 |
|
mSUGRA parameter space, |
| 297 |
|
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
| 298 |
< |
with (blue) and without (red) the effects of signal contamination. |
| 299 |
< |
THIS IS STILL MISSING |
| 304 |
< |
THE PDF UNCERETAINTIES. MAYBE GOOD TO MAKE THIS PLOT A BIT |
| 305 |
< |
PRETTIER, EG, CANNOT DISTINGUISH THINGS WHEN USING BLACK AND |
| 306 |
< |
WHITE PRINTER} |
| 298 |
> |
with and without the effects of signal contamination. |
| 299 |
> |
PDF UNCERTAINTIES ARE NOT INCLUDED.} |
| 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 |
| 312 |
< |
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} |
| 311 |
|
|
| 312 |
|
For completeness, we also show the exclusion regions calculated |
| 313 |
< |
using $\tan\beta = 10$ and $\tan\beta = 50$. |
| 313 |
> |
using $\tan\beta = 10$ (Figure~\ref{fig:msugratb10}). |
| 314 |
> |
|
| 315 |
> |
\begin{figure}[tbh] |
| 316 |
> |
\begin{center} |
| 317 |
> |
\includegraphics[width=\linewidth]{exclusion_tanbeta10.pdf} |
| 318 |
> |
\caption{\label{fig:msugratb10}\protect Exclusion curves in the mSUGRA parameter space, |
| 319 |
> |
assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
| 320 |
> |
THE PDF UNCERTAINTIES. WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.} |
| 321 |
> |
\end{center} |
| 322 |
> |
\end{figure} |
| 323 |
|
|
| 322 |
– |
NOT DONE YET. HERE I SUGGEST THAT WE PUT 3 CURVES (NLO LIMITS, |
| 323 |
– |
NO SIGNAL CONTAMINATION) ON THE SAME M0-M1/2 PLOT PERHAPS |
| 324 |
– |
LEAVING OUT THE REGIONS EXCLUDED BY OTHER EXPERIMENTS. |
| 324 |
|
|
| 325 |
|
|
| 326 |
|
|
