| 3 |
|
|
| 4 |
|
%{\bf \color{red} The numbers in this Section need to be double checked.} |
| 5 |
|
|
| 6 |
+ |
\subsection{Limit on number of events} |
| 7 |
+ |
\label{sec:limnumevents} |
| 8 |
|
As discussed in Section~\ref{sec:results}, we see one event |
| 9 |
|
in the signal region, defined as SumJetPt$>$300 GeV and |
| 10 |
|
\met/$\sqrt{\rm SumJetPt}>8.5$ GeV$^{\frac{1}{2}}$. |
| 11 |
|
|
| 12 |
< |
The background prediction from the SM Monte Carlo is |
| 11 |
< |
1.3 events. |
| 12 |
> |
The background prediction from the SM Monte Carlo is 1.3 events. |
| 13 |
|
%, where the uncertainty comes from |
| 14 |
|
%the jet energy scale (30\%, see Section~\ref{sec:systematics}), |
| 15 |
|
%the luminosity (10\%), and the lepton/trigger |
| 17 |
|
%the modeling of $t\bar{t}$ in MadGraph have not been evaluated. |
| 18 |
|
%The uncertainty on $pp \to \sigma(t\bar{t})$ is also not included.}. |
| 19 |
|
The data driven background predictions from the ABCD method |
| 20 |
< |
and the $P_T(\ell\ell)$ method are $1.5 \pm 0.9({\rm stat}) \pm 0.3({\rm syst})$ |
| 21 |
< |
and $4.3 \pm 3.0({\rm stat}) \pm 1.2({\rm syst})$, respectively. |
| 20 |
> |
and the $P_T(\ell\ell)$ method are $1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$ |
| 21 |
> |
and $2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$, respectively. |
| 22 |
|
|
| 23 |
|
These three predictions are in good agreement with each other |
| 24 |
|
and with the observation of one event in the signal region. |
| 25 |
|
We calculate a Bayesian 95\% CL upper limit\cite{ref:bayes.f} |
| 26 |
|
on the number of non SM events in the signal region to be 4.1. |
| 27 |
< |
We have also calculated this limit using a profile likelihood method |
| 28 |
< |
as implemented in the cl95cms software, and we also find 4.1. |
| 29 |
< |
These limits were calculated using a background prediction of $N_{BG}=1.7 \pm 1.1$ |
| 30 |
< |
events. The upper limit is not very sensitive to the choice of |
| 27 |
> |
We have also calculated this limit using |
| 28 |
> |
% a profile likelihood method |
| 29 |
> |
% as implemented in |
| 30 |
> |
the cl95cms software\cite{ref:cl95cms}, |
| 31 |
> |
and we also find 4.1. (This is not surprising, since cl95cms |
| 32 |
> |
also gives baysean upper limits with a flat prior). |
| 33 |
> |
These limits were calculated using a background prediction of $N_{BG} = 1.4 \pm 0.8$ |
| 34 |
> |
events, the error-weighted average of the ABCD and $P_T(\ell\ell)$ background |
| 35 |
> |
predictions. The upper limit is not very sensitive to the choice of |
| 36 |
|
$N_{BG}$ and its uncertainty. |
| 37 |
|
|
| 38 |
|
To get a feeling for the sensitivity of this search to some |
| 39 |
|
popular SUSY models, we remind the reader of the number of expected |
| 40 |
< |
LM0 and LM1 events from Table~\ref{tab:sigcont}: $6.3 \pm 1.3$ |
| 41 |
< |
events and $2.6 \pm 0.4$ |
| 36 |
< |
respectively, where the uncertainties |
| 40 |
> |
LM0 and LM1 events from Table~\ref{tab:sigcont}: $8.6 \pm 1.6$ |
| 41 |
> |
events and $3.6 \pm 0.5$ events respectively, where the uncertainties |
| 42 |
|
are from energy scale (Section~\ref{sec:systematics}), luminosity, |
| 43 |
< |
and lepton efficiency. Note that these expected SUSY yields |
| 39 |
< |
are computed using LO cross-sections, and are therefore underestimated. |
| 43 |
> |
and lepton efficiency. |
| 44 |
|
|
| 45 |
+ |
|
| 46 |
+ |
\subsection{Outreach} |
| 47 |
+ |
\label{sec:outreach} |
| 48 |
|
Conveying additional useful information about the results of |
| 49 |
|
a generic ``signature-based'' search such as the one described |
| 50 |
< |
in this note is a difficult issue. The next paragraph represent |
| 51 |
< |
our attempt at doing so. |
| 50 |
> |
in this note is a difficult issue. |
| 51 |
> |
Here we attempt to present our result in the most general |
| 52 |
> |
way. |
| 53 |
|
|
| 54 |
< |
Other models of new physics in the dilepton final state |
| 54 |
> |
Models of new physics in the dilepton final state |
| 55 |
|
can be confronted in an approximate way by simple |
| 56 |
|
generator-level studies that |
| 57 |
< |
compare the expected number of events in 35 pb$^{-1}$ |
| 57 |
> |
compare the expected number of events in 34.0~pb$^{-1}$ |
| 58 |
|
with our upper limit of 4.1 events. The key ingredients |
| 59 |
|
of such studies are the kinematical cuts described |
| 60 |
|
in this note, the lepton efficiencies, and the detector |
| 61 |
< |
responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$. These |
| 54 |
< |
quantities have been evaluated with Spring10 MC samples, |
| 55 |
< |
and we are currently checking if any of them change after |
| 56 |
< |
switching to Fall10 MC. |
| 61 |
> |
responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$. |
| 62 |
|
The muon identification efficiency is $\approx 95\%$; |
| 63 |
|
the electron identification efficiency varies from $\approx$ 63\% at |
| 64 |
|
$P_T = 10$ GeV to 91\% for $P_T > 30$ GeV. The isolation |
| 65 |
|
efficiency in top events varies from $\approx 83\%$ (muons) |
| 66 |
|
and $\approx 89\%$ (electrons) at $P_T=10$ GeV to |
| 67 |
< |
$\approx 95\%$ for $P_T>60$ GeV. The average detector |
| 67 |
> |
$\approx 95\%$ for $P_T>60$ GeV. |
| 68 |
> |
%{\bf \color{red} The following numbers were derived from Fall 10 samples. } |
| 69 |
> |
The average detector |
| 70 |
|
responses for SumJetPt and $\met/\sqrt{\rm SumJetPt}$ are |
| 71 |
< |
$1.00 \pm 0.05$ and $0.94 \pm 0.05$ respectively, where |
| 71 |
> |
$1.02 \pm 0.05$ and $0.94 \pm 0.05$ respectively, where |
| 72 |
|
the uncertainties are from the jet energy scale uncertainty. |
| 73 |
< |
The experimental resolutions on these quantities are 10\% and |
| 74 |
< |
14\% respectively. |
| 73 |
> |
The experimental resolutions on these quantities are 11\% and |
| 74 |
> |
16\% respectively. |
| 75 |
|
|
| 76 |
|
To justify the statements in the previous paragraph |
| 77 |
|
about the detector responses, we plot |
| 81 |
|
signal region. |
| 82 |
|
% (SumJetPt $>$ 300 GeV and \met/$\sqrt{\rm SumJetPt} > 8.5$ |
| 83 |
|
% Gev$^{\frac{1}{2}}$). |
| 84 |
+ |
%{\bf \color{red} The following numbers were derived from Fall10 samples } |
| 85 |
|
We find that the average SumJetPt response |
| 86 |
< |
in the Monte Carlo |
| 87 |
< |
is very close to one, with an RMS of order 10\% while |
| 88 |
< |
the |
| 81 |
< |
response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an |
| 82 |
< |
RMS of 14\%. |
| 86 |
> |
in the Monte Carlo is about 1.02, with an RMS of order 11\% while |
| 87 |
> |
the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an |
| 88 |
> |
RMS of 16\%. |
| 89 |
|
|
| 90 |
|
%Using this information as well as the kinematical |
| 91 |
|
%cuts described in Section~\ref{sec:eventSel} and the lepton efficiencies |
| 96 |
|
|
| 97 |
|
\begin{figure}[tbh] |
| 98 |
|
\begin{center} |
| 99 |
< |
\includegraphics[width=\linewidth]{selectionEff.png} |
| 99 |
> |
\includegraphics[width=\linewidth]{selectionEffDec10.png} |
| 100 |
|
\caption{\label{fig:response} Left plots: the efficiencies |
| 101 |
|
as a function of the true quantities for the SumJetPt (top) and |
| 102 |
|
tcMET/$\sqrt{\rm SumJetPt}$ (bottom) requirements for the signal |
| 107 |
|
The response is defined as the ratio of the reconstructed quantity |
| 108 |
|
to the true quantity in MC. These plots are done using the LM0 |
| 109 |
|
Monte Carlo, but they are not expected to depend strongly on |
| 110 |
< |
the underlying physics.} |
| 110 |
> |
the underlying physics. |
| 111 |
> |
%{\bf \color{red} These plots were made with Fall10 samples. } |
| 112 |
> |
} |
| 113 |
> |
\end{center} |
| 114 |
> |
\end{figure} |
| 115 |
> |
|
| 116 |
> |
|
| 117 |
> |
|
| 118 |
> |
%%% Nominal |
| 119 |
> |
% ----------------------------------------- |
| 120 |
> |
% observed events 1 |
| 121 |
> |
% relative error on acceptance 0.000 |
| 122 |
> |
% expected background 1.400 |
| 123 |
> |
% absolute error on background 0.770 |
| 124 |
> |
% desired confidence level 0.95 |
| 125 |
> |
% integration upper limit 30.00 |
| 126 |
> |
% integration step size 0.0100 |
| 127 |
> |
% ----------------------------------------- |
| 128 |
> |
% Are the above correct? y |
| 129 |
> |
% 1 16.685 0.29375E-06 |
| 130 |
> |
% |
| 131 |
> |
% limit: less than 4.112 signal events |
| 132 |
> |
|
| 133 |
> |
|
| 134 |
> |
|
| 135 |
> |
%%% Add 20% acceptance uncertainty based on LM0 |
| 136 |
> |
% ----------------------------------------- |
| 137 |
> |
% observed events 1 |
| 138 |
> |
% relative error on acceptance 0.200 |
| 139 |
> |
% expected background 1.400 |
| 140 |
> |
% absolute error on background 0.770 |
| 141 |
> |
% desired confidence level 0.95 |
| 142 |
> |
% integration upper limit 30.00 |
| 143 |
> |
% integration step size 0.0100 |
| 144 |
> |
% ----------------------------------------- |
| 145 |
> |
% Are the above correct? y |
| 146 |
> |
% 1 29.995 0.50457E-06 |
| 147 |
> |
% |
| 148 |
> |
% limit: less than 4.689 signal events |
| 149 |
> |
|
| 150 |
> |
|
| 151 |
> |
\subsection{mSUGRA scan} |
| 152 |
> |
\label{sec:mSUGRA} |
| 153 |
> |
We also perform a scan of the mSUGRA parameter space, as recomended |
| 154 |
> |
by the SUSY group convenors\cite{ref:scan}. |
| 155 |
> |
The goal of the scan is to determine an exclusion region in the |
| 156 |
> |
$m_0$ vs. $m_{1/2}$ plane for |
| 157 |
> |
$\tan\beta=3$, |
| 158 |
> |
sign of $\mu = +$, and $A_{0}=0$~GeV. This scan is based on events |
| 159 |
> |
generated with FastSim. |
| 160 |
> |
|
| 161 |
> |
The first order of business is to verify that results using |
| 162 |
> |
Fastsim and Fullsim are compatible. To this end we compare the |
| 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 |
> |
using FastSim for this study. |
| 167 |
> |
|
| 168 |
> |
The FastSim events are generated with different values of $m_0$ |
| 169 |
> |
and $m_{1/2}$ in steps of 10 GeV. For each point in the |
| 170 |
> |
$m_0$ vs. $m_{1/2}$ plane, we compute the expected number of |
| 171 |
> |
events at NLO. We then also calculate an upper limit $N_{UL}$ |
| 172 |
> |
using cl95cms at each point using the following inputs: |
| 173 |
> |
\begin{itemize} |
| 174 |
> |
\item Number of BG events = 1.40 $\pm$ 0.77 |
| 175 |
> |
\item Luminosity uncertainty = 11\% |
| 176 |
> |
\item The acceptance uncertainty is calculated at each point |
| 177 |
> |
as the quadrature sum of |
| 178 |
> |
\begin{itemize} |
| 179 |
> |
\item The uncertainty due to JES for that point, as calculated |
| 180 |
> |
using the method described in Section~\ref{sec:systematics} |
| 181 |
> |
\item A 5\% uncertainty due to lepton efficiencies |
| 182 |
> |
\item An uncertaity on the NLO cross-section obtained by varying the |
| 183 |
> |
factorization and renormalization scale by a factor of two\cite{ref:sanjay}. |
| 184 |
> |
\item The PDF uncertainty on the product of cross-section and acceptance |
| 185 |
> |
calculated using the method of Reference~\cite{ref:pdf}. |
| 186 |
> |
\end{itemize} |
| 187 |
> |
\item We use the ``log-normal'' model for the nuisance parameters |
| 188 |
> |
in cl95cms |
| 189 |
> |
\end{itemize} |
| 190 |
> |
|
| 191 |
> |
An mSUGRA point is excluded if the resulting $N_{UL}$ is smaller |
| 192 |
> |
than the expected number of events. Because of the quantization |
| 193 |
> |
of the available MC points in the $m_0$ vs $m_{1/2}$ plane, the |
| 194 |
> |
boundaries of the excluded region are also quantized. We smooth |
| 195 |
> |
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 was |
| 199 |
> |
calculated using the CLA function also available in cl95cms. |
| 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 |
> |
|
| 216 |
> |
|
| 217 |
> |
\begin{figure}[tbh] |
| 218 |
> |
\begin{center} |
| 219 |
> |
\includegraphics[width=\linewidth]{exclusion_noPDF.pdf} |
| 220 |
> |
\caption{\label{fig:msugra}\protect Exclusion curves in the mSUGRA parameter space, |
| 221 |
> |
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
| 222 |
> |
THE PDF UNCERTAINTIES. WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.} |
| 223 |
> |
\end{center} |
| 224 |
> |
\end{figure} |
| 225 |
> |
|
| 226 |
> |
|
| 227 |
> |
\subsubsection{Check of the nuisance parameter models} |
| 228 |
> |
We repeat the procedure outlined above but changing the |
| 229 |
> |
lognormal nuisance parameter model to a gaussian or |
| 230 |
> |
gamma-function model. The results are shown in |
| 231 |
> |
Figure~\ref{fig:nuisance}. (In this case, |
| 232 |
> |
to avoid smoothing artifacts, we |
| 233 |
> |
show the raw results, without smoothing). |
| 234 |
> |
|
| 235 |
> |
\begin{figure}[tbh] |
| 236 |
> |
\begin{center} |
| 237 |
> |
\includegraphics[width=0.5\linewidth]{nuissance.png} |
| 238 |
> |
\caption{\label{fig:nuisance}\protect Exclusion curves in the |
| 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 UNCERTAINTIES ARE NOT INCLUDED.} |
| 243 |
> |
\end{center} |
| 244 |
> |
\end{figure} |
| 245 |
> |
|
| 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 |
| 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. |
| 262 |
> |
The yields in the control regions |
| 263 |
> |
$A$, $B$, and $C$ (Table~\ref{tab:datayield}) are just |
| 264 |
> |
as expected in the SM, and the check |
| 265 |
> |
of the $P_T(\ell \ell)$ method in the control region is |
| 266 |
> |
also consistent with expectations (Table~\ref{tab:victory}). |
| 267 |
> |
Since we have two data driven methods, with different |
| 268 |
> |
signal contamination issues, giving consistent |
| 269 |
> |
results that are in agreement with the SM, we |
| 270 |
> |
argue for not making any correction to our procedure |
| 271 |
> |
because of signal contamination. In some sense this would |
| 272 |
> |
be equivalent to using the SM background prediction, and using |
| 273 |
> |
the data driven methods as confirmations of that prediction. |
| 274 |
> |
|
| 275 |
> |
Nevertheless, here we explore the possible effect of |
| 276 |
> |
signal contamination. The procedure suggested to us |
| 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 $S$ refer to the number of observed data |
| 281 |
> |
events and expected SUSY events, respectively, in a given region. |
| 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 |
| 291 |
> |
point. In region $C$ we have a SM prediction of 5.1 |
| 292 |
> |
events and $C_D = 4$ in agreement with the Standard Model, |
| 293 |
> |
see Table~\ref{tab:datayield}. From the LM0 Monte Carlo, |
| 294 |
> |
we find $C_S = 8.6$ events. Thus, including information |
| 295 |
> |
on $C_D$ and $C_S$ should {\bf strengthen} the limit, since there |
| 296 |
> |
is clearly a deficit of events in the $C$ region in the |
| 297 |
> |
LM0 hypothesis. Instead, we now get a negative ABCD |
| 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} |
| 307 |
> |
\caption{\label{fig:sigcont}\protect Exclusion curves in the |
| 308 |
> |
mSUGRA parameter space, |
| 309 |
> |
assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
| 310 |
> |
with and without the effects of signal contamination. |
| 311 |
> |
PDF UNCERTAINTIES ARE NOT INCLUDED.} |
| 312 |
> |
\end{center} |
| 313 |
> |
\end{figure} |
| 314 |
> |
|
| 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, 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} |
| 323 |
> |
|
| 324 |
> |
For completeness, we also show the exclusion regions calculated |
| 325 |
> |
using $\tan\beta = 10$ (Figure~\ref{fig:msugratb10}). |
| 326 |
> |
|
| 327 |
> |
\begin{figure}[tbh] |
| 328 |
> |
\begin{center} |
| 329 |
> |
\includegraphics[width=\linewidth]{exclusion_tanbeta10.pdf} |
| 330 |
> |
\caption{\label{fig:msugratb10}\protect Exclusion curves in the mSUGRA parameter space, |
| 331 |
> |
assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
| 332 |
> |
THE PDF UNCERTAINTIES. WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.} |
| 333 |
|
\end{center} |
| 334 |
|
\end{figure} |
| 335 |
+ |
|
| 336 |
+ |
|
| 337 |
+ |
|
| 338 |
+ |
|
| 339 |
+ |
|
| 340 |
+ |
|
