| 148 |
|
% limit: less than 4.689 signal events |
| 149 |
|
|
| 150 |
|
|
| 151 |
+ |
|
| 152 |
|
\subsection{mSUGRA scan} |
| 153 |
|
\label{sec:mSUGRA} |
| 154 |
|
We also perform a scan of the mSUGRA parameter space, as recomended |
| 164 |
|
expected yield for the LM1 point in FullSim (3.56 $\pm$ 0.06) and |
| 165 |
|
FastSim (3.29 $\pm$ 0.27), where the uncertainties are statistical only. |
| 166 |
|
These two numbers are in agreement, which gives us confidence in |
| 167 |
< |
usinf FastSim for this study. |
| 167 |
> |
using FastSim for this study. |
| 168 |
|
|
| 169 |
|
The FastSim events are generated with different values of $m_0$ |
| 170 |
|
and $m_{1/2}$ in steps of 10 GeV. For each point in the |
| 182 |
|
\item A 5\% uncertainty due to lepton efficiencies |
| 183 |
|
\item An uncertaity on the NLO cross-section obtained by varying the |
| 184 |
|
factorization and renormalization scale by a factor of two\cite{ref:sanjay}. |
| 185 |
< |
\item The PDF uncertainty on the product of cross-section and acceptance |
| 186 |
< |
calculated using the method of Reference~\cite{ref:pdf}. |
| 185 |
> |
\item A 13\% PDF uncertainty on the product of cross-section and acceptance. |
| 186 |
> |
This uncertainty was calculated using the method of Reference~\cite{ref:pdf} for a |
| 187 |
> |
number of points in the $m_0$ vs. $m_{1/2}$ plane, and was found to be |
| 188 |
> |
approximately independent of mSUGRA parameters, see Table~\ref{tab:pdf}. |
| 189 |
|
\end{itemize} |
| 190 |
|
\item We use the ``log-normal'' model for the nuisance parameters |
| 191 |
|
in cl95cms |
| 192 |
|
\end{itemize} |
| 193 |
+ |
We actually calculate three different values of $N_{UL}$: |
| 194 |
+ |
\begin{enumerate} |
| 195 |
+ |
\item Observed $N_{UL}$ asssuming the NLO cross-section. |
| 196 |
+ |
\item Observed $N_{UL}$ asssuming the LO cross-section. In this case |
| 197 |
+ |
uncertainties due to PDFs and renormlization/factorization scales are not |
| 198 |
+ |
included. |
| 199 |
+ |
\item Expected $N_{UL}$ sssuming the NLO cross-section. This is |
| 200 |
+ |
calculated using the the CLA function also available in cl95cms. |
| 201 |
+ |
\end{enumerate} |
| 202 |
+ |
|
| 203 |
+ |
\begin{table}[hbt] |
| 204 |
+ |
\begin{center} |
| 205 |
+ |
\caption{\label{tab:pdf} PDF uncertainties on the product of |
| 206 |
+ |
cross-section and acceptance for a number of representative points |
| 207 |
+ |
in the mSUGRA plane.} |
| 208 |
+ |
\begin{tabular}{c|c|c|c|c|c} |
| 209 |
+ |
$\tan\beta$ & $m_0$ & $m_{1/2}$ & sign of $\mu$ & $A_0$ & uncertanity (\%) \\ \hline |
| 210 |
+ |
3 & 50 & 260 & + & 0 & $^{+13}_{-9}$ \\ |
| 211 |
+ |
3 & 50 & 270 & + & 0 & $^{+13}_{-9}$ \\ |
| 212 |
+ |
3 & 60 & 260 & + & 0 & $^{+14}_{-9}$ \\ |
| 213 |
+ |
3 & 200 & 200 & + & 0 & $^{+12}_{-9}$ \\ |
| 214 |
+ |
3 & 200 & 210 & + & 0 & $^{+13}_{-10}$ \\ |
| 215 |
+ |
3 & 210 & 200 & + & 0 & $^{+11}_{-8}$ \\ |
| 216 |
+ |
3 & 200 & 140 & + & 0 & $^{+16}_{-12}$ \\ |
| 217 |
+ |
3 & 140 & 150 & + & 0 & $^{+08}_{-8}$ \\ |
| 218 |
+ |
3 & 150 & 140 & + & 0 & $^{+14}_{-10}$ \\ |
| 219 |
+ |
10 & 60 & 260 & + & 0 & $^{+16}_{-11}$ \\ |
| 220 |
+ |
10 & 100 & 260 & + & 0 & $^{+14}_{-10}$ \\ |
| 221 |
+ |
10 & 100 & 260 & + & 0 & $^{+12}_{-9}$ \\ |
| 222 |
+ |
10 & 90 & 260 & + & 0 & $^{+15}_{-10}$ \\ |
| 223 |
+ |
10 & 240 & 260 & + & 0 & $^{+10}_{-8}$ \\ |
| 224 |
+ |
10 & 240 & 260 & + & 0 & $^{+13}_{-10}$ \\ \hline |
| 225 |
+ |
\end{tabular} |
| 226 |
+ |
\end{center} |
| 227 |
+ |
\end{table} |
| 228 |
+ |
|
| 229 |
|
|
| 230 |
|
An mSUGRA point is excluded if the resulting $N_{UL}$ is smaller |
| 231 |
|
than the expected number of events. Because of the quantization |
| 232 |
|
of the available MC points in the $m_0$ vs $m_{1/2}$ plane, the |
| 233 |
< |
boundaries of the excluded region are also quantized. We smooth |
| 234 |
< |
the boundaries using the method recommended by the SUSY |
| 235 |
< |
group\cite{ref:smooth}. In addition, we show a limit |
| 236 |
< |
curve based on the LO cross-section, as well as the |
| 237 |
< |
``expected'' limit curve. The expected limit curve is |
| 238 |
< |
calculated using the CLA function also available in cl95cms. |
| 239 |
< |
The results are shown in Figure~\ref{fig:msugra} |
| 233 |
> |
boundaries of the excluded region are also quantized. The excluded points |
| 234 |
> |
are shown in Figure~\ref{fig:tanbeta3raw}; in this Figure we also show |
| 235 |
> |
ad-hoc curves that represent the excluded regions. |
| 236 |
> |
In Figure~\ref{fig:msugra} we show our results compared with |
| 237 |
> |
results from previous experiments. |
| 238 |
> |
|
| 239 |
> |
|
| 240 |
> |
\begin{figure}[tbh] |
| 241 |
> |
\begin{center} |
| 242 |
> |
\includegraphics[width=0.4\linewidth]{tanbeta3_NLO_observed.png} |
| 243 |
> |
\includegraphics[width=0.4\linewidth]{tanbeta3_NLO_expected.png} |
| 244 |
> |
\includegraphics[width=0.4\linewidth]{tanbeta3_LO_observed.png} |
| 245 |
> |
\caption{\label{fig:tanbeta3raw}\protect Excluded points in the |
| 246 |
> |
$m_0$ vs. $m_{1/2}$ plane for $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs. |
| 247 |
> |
Top left: observed, using the NLO cross-section. |
| 248 |
> |
Top right: expected using the NLO cross-section. |
| 249 |
> |
Bottom left: observed, using the LO cross-section. |
| 250 |
> |
The curves are meant to represent the excluded regions.} |
| 251 |
> |
\end{center} |
| 252 |
> |
\end{figure} |
| 253 |
|
|
| 254 |
|
|
| 255 |
|
\begin{figure}[tbh] |
| 256 |
|
\begin{center} |
| 257 |
|
\includegraphics[width=\linewidth]{exclusion.pdf} |
| 258 |
|
\caption{\label{fig:msugra}\protect Exclusion curves in the mSUGRA parameter space, |
| 259 |
< |
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
| 208 |
< |
THE PDF UNCERTAINTIES.} |
| 259 |
> |
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs.} |
| 260 |
|
\end{center} |
| 261 |
|
\end{figure} |
| 262 |
|
|
| 263 |
|
|
| 264 |
+ |
|
| 265 |
+ |
\clearpage |
| 266 |
+ |
|
| 267 |
|
\subsubsection{Check of the nuisance parameter models} |
| 268 |
|
We repeat the procedure outlined above but changing the |
| 269 |
|
lognormal nuisance parameter model to a gaussian or |
| 275 |
|
\begin{figure}[tbh] |
| 276 |
|
\begin{center} |
| 277 |
|
\includegraphics[width=0.5\linewidth]{nuissance.png} |
| 278 |
< |
\caption{\label{fig:nuisance}\protect Exclusion curves in the |
| 278 |
> |
\caption{\label{fig:nuisance}\protect Observed NLO exclusion curves in the |
| 279 |
|
mSUGRA parameter space, |
| 280 |
|
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
| 281 |
< |
using different models for the nuisance parameters. |
| 282 |
< |
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} |
| 281 |
> |
using different models for the nuisance parameters. (Note: this |
| 282 |
> |
plot was made without the PDF uncertainties.} |
| 283 |
|
\end{center} |
| 284 |
|
\end{figure} |
| 285 |
|
|
| 286 |
< |
We find that the set of excluded points is identical for the |
| 287 |
< |
lognormal and gamma models. There are small differences for the |
| 288 |
< |
gaussian model. Following the recommendation of Reference~\cite{ref:cousins}, |
| 289 |
< |
we use the lognormal nuisance parameter model. |
| 286 |
> |
We find that different assumptions on the PDFs for the nuisance |
| 287 |
> |
parameters make very small differences to the set of excluded |
| 288 |
> |
points. |
| 289 |
> |
Following the recommendation of Reference~\cite{ref:cousins}, |
| 290 |
> |
we use the lognormal nuisance parameter model as the default. |
| 291 |
|
|
| 292 |
|
|
| 293 |
< |
\clearpage |
| 293 |
> |
% \clearpage |
| 294 |
|
|
| 295 |
|
|
| 296 |
|
\subsubsection{Effect of signal contamination} |
| 297 |
|
\label{sec:contlimit} |
| 298 |
+ |
|
| 299 |
|
Signal contamination could affect the limit by inflating the |
| 300 |
|
background expectation. In our case we see no evidence of signal |
| 301 |
|
contamination, within statistics. |
| 314 |
|
|
| 315 |
|
Nevertheless, here we explore the possible effect of |
| 316 |
|
signal contamination. The procedure suggested to us |
| 317 |
< |
is the following: |
| 266 |
< |
\begin{itemize} |
| 267 |
< |
\item At each point in mSUGRA space we modify the |
| 317 |
> |
for the ABCD method is to modify the |
| 318 |
|
ABCD background prediction from $A_D \cdot C_D/B_D$ to |
| 319 |
|
$(A_D-A_S) \cdot (C_D-C_S) / (B_D - B_S)$, where the |
| 320 |
< |
subscripts $D$ and $S$ referes to the number of observed data |
| 320 |
> |
subscripts $D$ and $S$ refer to the number of observed data |
| 321 |
|
events and expected SUSY events, respectively, in a given region. |
| 322 |
< |
\item Similarly, at each point in mSugra space we modify the |
| 323 |
< |
$P_T(\ell\ell)$ background prediction from |
| 324 |
< |
$K \cdot K_C \cdot D'_D$ to $K \cdot K_C \cdot (D'_D - D'_S)$, |
| 325 |
< |
where the subscript $D$ and $S$ are defined as above. |
| 326 |
< |
\item At each point in mSUGRA space we recalculate $N_{UL}$ |
| 327 |
< |
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 $N_{UL}$. |
| 322 |
> |
We then recalculate $N_{UL}$ at each point using this modified |
| 323 |
> |
ABCD background estimation. For simplicity we ignore |
| 324 |
> |
information from the $P_T(\ell \ell)$ |
| 325 |
> |
background estimation. This is conservative, since |
| 326 |
> |
the $P_T(\ell\ell)$ background estimation happens to |
| 327 |
> |
be numerically larger than the one from ABCD. |
| 328 |
|
|
| 329 |
|
Note, however, that in some cases this procedure is |
| 330 |
|
nonsensical. For example, take LM0 as a SUSY |
| 338 |
|
BG prediction (which is nonsense, so we set it to zero), |
| 339 |
|
and therefore a weaker limit. |
| 340 |
|
|
| 341 |
+ |
|
| 342 |
+ |
|
| 343 |
+ |
|
| 344 |
|
\begin{figure}[tbh] |
| 345 |
|
\begin{center} |
| 346 |
|
\includegraphics[width=0.5\linewidth]{sigcont.png} |
| 347 |
< |
\caption{\label{fig:sigcont}\protect Exclusion curves in the |
| 347 |
> |
\caption{\label{fig:sigcont}\protect Observed NLO exclusion curves in the |
| 348 |
|
mSUGRA parameter space, |
| 349 |
|
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
| 350 |
< |
with (blue) and without (red) the effects of signal contamination. |
| 351 |
< |
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} |
| 350 |
> |
with and without the effects of signal contamination. |
| 351 |
> |
Note: PDF uncertainties are not included.} |
| 352 |
|
\end{center} |
| 353 |
|
\end{figure} |
| 354 |
|
|
| 355 |
< |
Despite these reservations, we follow the procedure suggested |
| 356 |
< |
to us. A comparison of the exclusion region with and without |
| 312 |
< |
the signal contamination is shown in Figure~\ref{fig:sigcont} |
| 355 |
> |
A comparison of the exclusion region with and without |
| 356 |
> |
signal contamination is shown in Figure~\ref{fig:sigcont} |
| 357 |
|
(with no smoothing). The effect of signal contamination is |
| 358 |
< |
small. |
| 358 |
> |
small, of the same order as the quantization of the scan. |
| 359 |
> |
|
| 360 |
|
|
| 361 |
|
\subsubsection{mSUGRA scans with different values of tan$\beta$} |
| 362 |
|
\label{sec:tanbetascan} |
| 363 |
|
|
| 364 |
< |
For completeness, we also show the exclusion regions calculated |
| 365 |
< |
using $\tan\beta = 10$ and $\tan\beta = 50$. |
| 364 |
> |
For completeness, we also show the exclusion region calculated |
| 365 |
> |
using $\tan\beta = 10$ (Figure~\ref{fig:msugratb10}). |
| 366 |
> |
|
| 367 |
> |
|
| 368 |
> |
\begin{figure}[tbh] |
| 369 |
> |
\begin{center} |
| 370 |
> |
\includegraphics[width=0.4\linewidth]{tanbeta10_NLO_observed.png} |
| 371 |
> |
\caption{\label{fig:tanbeta10raw}\protect Excluded points in the |
| 372 |
> |
$m_0$ vs. $m_{1/2}$ plane for $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs. |
| 373 |
> |
This plot is made using the NLO cross-sections. |
| 374 |
> |
The curves is meant to represent the excluded region.} |
| 375 |
> |
\end{center} |
| 376 |
> |
\end{figure} |
| 377 |
> |
|
| 378 |
> |
\begin{figure}[tbh] |
| 379 |
> |
\begin{center} |
| 380 |
> |
\includegraphics[width=\linewidth]{exclusion_tanbeta10.pdf} |
| 381 |
> |
\caption{\label{fig:msugratb10}\protect Exclusion curve in the mSUGRA parameter space, |
| 382 |
> |
assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.} |
| 383 |
> |
\end{center} |
| 384 |
> |
\end{figure} |
| 385 |
|
|
| 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. |
| 386 |
|
|
| 387 |
|
|
| 388 |
|
|
