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%\section{Systematics Uncertainties on the Background Prediction} |
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%\label{sec:systematics} |
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|
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[ADD INTRODUCTORY BLURB ON UNCERTAINTIES \\ |
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ADD COMPARISONS OF ALL THE ALTERNATIVE SAMPLES FOR ALL THE SIGNAL |
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REGIONS \\ |
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LIST ALL THE UNCERTAINTIES INCLUDED AND THEIR VALUES] |
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[DESCRIBE HERE ONE BY ONE THE UNCERTAINTIES THAT ARE PRESENT IN THE SPREADSHHET |
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FROM WHICH WE CALCULATE THE TOTAL UNCERTAINTY. WE KNOW HOW TO DO THIS |
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AND |
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WE HAVE THE TECHNOLOGY FROM THE 7 TEV ANALYSIS TO PROPAGATE ALL |
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UNCERTAINTIES |
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CORRECTLY THROUGH. WE WILL DO IT ONCE WE HAVE SETTLED ON THE |
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INDIVIDUAL PIECES WHICH ARE STILL IN FLUX] |
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In this Section we discuss the systematic uncertainty on the BG |
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prediction. This prediction is assembled from the event |
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counts in the peak region of the transverse mass distribution as |
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well as Monte Carlo |
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with a number of correction factors, as described previously. |
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The |
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final uncertainty on the prediction is built up from the uncertainties in these |
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individual |
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components. |
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The calculation is done for each signal |
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region, |
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for electrons and muons separately. |
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The choice to normalizing to the peak region of $M_T$ has the |
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advantage that some uncertainties, e.g., luminosity, cancel. |
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It does however introduce complications because it couples |
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some of the uncertainties in non-trivial ways. For example, |
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the primary effect of an uncertainty on the rare MC cross-section |
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is to introduce an uncertainty in the rare MC background estimate |
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which comes entirely from MC. But this uncertainty also affects, |
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for example, |
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the $t\bar{t} \to$ dilepton BG estimate because it changes the |
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$t\bar{t}$ normalization to the peak region (because some of the |
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events in the peak region are from rare processes). These effects |
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are carefully accounted for. The contribution to the overall |
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uncertainty from each BG source is tabulated in |
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Section~\ref{sec:bgunc-bottomline}. |
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First, however, we discuss the uncertainties one-by-one and we comment |
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on their impact on the overall result, at least to first order. |
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Second order effects, such as the one described, are also included. |
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\subsection{Statistical uncertainties on the event counts in the $M_T$ |
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peak regions} |
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These vary between XX and XX \%, depending on the signal region |
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(different |
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signal regions have different \met\ requirements, thus they also have |
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different $M_T$ regions used as control. |
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Since |
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the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this |
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fractional uncertainty is pretty much carried through all the way to |
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the end. There is also an uncertainty from the finite MC event counts |
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in the $M_T$ peak regions. This is also included, but it is smaller. |
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\subsection{Uncertainty from the choice of $M_T$ peak region} |
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IN 7 TEV DATA WE HAD SOME SHAPE DIFFERENCES IN THE MTRANS REGION THAT |
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LED US TO CONSERVATIVELY INCLUDE THIS UNCERTAINTY. WE NEED TO LOOK |
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INTO THIS AGAIN |
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|
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\subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections} |
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These are taken as 50\%, uncorrelated. |
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The primary effect is to introduce a 50\% |
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uncertainty |
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on the $W +$ jets and rare BG |
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background predictions, respectively. However they also |
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have an effect on the other BGs via the $M_T$ peak normalization |
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in a way that tends to reduce the uncertainty. This is easy |
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to understand: if the $W$ cross-section is increased by 50\%, then |
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the $W$ background goes up. But the number of $M_T$ peak events |
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attributed to $t\bar{t}$ goes down, and since the $t\bar{t}$ BG is |
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scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$ |
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BG goes down. |
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\subsection{Scale factors for the tail-to-peak ratios for lepton + |
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jets top and W events} |
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These tail-to-peak ratios are described in Section~\ref{sec:ttp}. |
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They are studied in CR1 and CR2. The studies are described |
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in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where |
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we also give the uncertainty on the scale factors. |
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\subsection{Uncertainty on extra jet radiation for dilepton |
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background} |
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As discussed in Section~\ref{sec:jetmultiplicity}, the |
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jet distribution in |
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$t\bar{t} \to$ |
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dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make |
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it agree with the data. The XX\% uncertainties on $K_3$ and $K_4$ |
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comes from data/MC statistics. This |
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result directly in a XX\% uncertainty on the dilepton BG, which is by far |
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the most important one. |
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\subsection{Uncertainty on the \ttll\ Acceptance} |
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Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the |
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hadronisation, while POWHEG uses Pythia6. |
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\item Modeling of taus: The alternative sample does not include |
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Tauola and is otherwise identical to the Powheg sample. [DONE AT |
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7TEV AND FOUND TO BE NEGLIGIBLE] |
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Tauola and is otherwise identical to the Powheg sample. |
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This effect was studied earlier using 7~TeV samples and found to be negligible. |
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\item The PDF uncertainty is estimated following the PDF4LHC |
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recommendations[CITE]. The events are reweighted using alternative |
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PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
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addition, the NNPDF2.1 set with 100 replicas. The central value is |
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determined from the mean and the uncertainty is derived from the |
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$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
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alternative predictions and their uncertainties. [DONE AT 7 TEV AND |
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FOUND TO BE NEGLIGIBLE] |
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\end{itemize} |
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alternative predictions and their uncertainties. |
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This effect was studied earlier using 7~TeV samples and found to be negligible. |
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\end{itemize} |
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\begin{figure}[hbt] |
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alternative sample predictions are indicated by the |
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datapoints. The uncertainties on the alternative predictions |
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correspond to the uncorrelated statistical uncertainty from |
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the size of the alternative sample only.} |
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the size of the alternative sample only. |
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[TO BE UPDATED WITH THE LATEST SELECTION AND SFS]} |
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\end{center} |
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\end{figure} |
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\clearpage |
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% |
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% |
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%\end{center} |
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%\end{table} |
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\subsection{Uncertainty from the isolated track veto} |
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This is the uncertainty associated with how well the isolated track |
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veto performance is modeled by the Monte Carlo. This uncertainty |
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only applies to the fraction of dilepton BG events that have |
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a second e/$\mu$ or a one prong $\tau \to h$, with |
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$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is 1/3 (THIS WAS THE |
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7 TEV NUMBER, CHECK). The uncertainty for these events |
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is XX\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto} |
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|
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\subsection{Isolated Track Veto: Tag and Probe Studies} |
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\subsubsection{Isolated Track Veto: Tag and Probe Studies} |
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\label{sec:trkveto} |
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[EVERYTHING IS 7TEV HERE, UPDATE WITH NEW RESULTS \\ |
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ADD TABLE WITH FRACTION OF EVENTS THAT HAVE A TRUE ISOLATED TRACK] |
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% \end{center} |
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%\end{figure} |
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\subsection{Summary of uncertainties} |
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\label{sec:bgunc-bottomline}. |
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THIS NEEDS TO BE WRITTEN |
