| 1 |
\section{Non $t\bar{t}$ Backgrounds}
|
| 2 |
\label{sec:othBG}
|
| 3 |
|
| 4 |
Backgrounds from divector bosons and single top
|
| 5 |
can be reliably estimated from Monte Carlo.
|
| 6 |
They are negligible compared to $t\bar{t}$.
|
| 7 |
|
| 8 |
%Backgrounds from Drell Yan are also expected
|
| 9 |
%to be negligible from MC. However one always
|
| 10 |
%worries about the modeling of tails of the \met.
|
| 11 |
%In the context of other dilepton analyses we
|
| 12 |
%have developed a data driven method to estimate
|
| 13 |
%the number of Drell Yan events\cite{ref:dy}.
|
| 14 |
%The method is based on counting the number of
|
| 15 |
%$Z$ candidates passing the full selection, and
|
| 16 |
%then scaling by the expected ratio of Drell Yan
|
| 17 |
%events outside vs. inside the $Z$ mass
|
| 18 |
%window.\footnote{A correction based on $e\mu$ events
|
| 19 |
%is also applied.} This ratio is called $R_{out/in}$
|
| 20 |
%and is obtained from Monte Carlo.
|
| 21 |
|
| 22 |
%To estimate the Drell-Yan contribution in the four $ABCD$
|
| 23 |
%regions, we count the numbers of $Z \to ee$ and $Z \to \mu\mu$
|
| 24 |
%events falling in each region, we subtract off the number
|
| 25 |
%of $e\mu$ events with $76 < M(e\mu) < 106$ GeV, and
|
| 26 |
%we multiply the result by $R_{out/in}$ from Monte Carlo.
|
| 27 |
%The results are summarized in Table~\ref{tab:ABCD-DY}.
|
| 28 |
|
| 29 |
%\begin{table}[hbt]
|
| 30 |
%\begin{center}
|
| 31 |
%\caption{\label{tab:ABCD-DY} Drell-Yan estimations
|
| 32 |
%in the four
|
| 33 |
%regions of Figure~\ref{fig:abcdData}. The yields are
|
| 34 |
%for dileptons with invariant mass consistent with the $Z$.
|
| 35 |
%The factor
|
| 36 |
%$R_{out/in}$ is from MC. All uncertainties
|
| 37 |
%are statistical only. In regions $A$ and $D$ there is no statistics
|
| 38 |
%in the Monte Carlo to calculate $R_{out/in}$.}
|
| 39 |
%\begin{tabular}{|l|c|c|c||c|}
|
| 40 |
%\hline
|
| 41 |
%Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\
|
| 42 |
%\hline
|
| 43 |
%$A$ & 0 & 0 & ?? & ??$\pm$xx \\
|
| 44 |
%$B$ & 5 & 1 & 2.5$\pm$1.0 & 9$\pm$xx \\
|
| 45 |
%$C$ & 0 & 0 & 1.$\pm$1. & 0$\pm$xx \\
|
| 46 |
%$D$ & 0 & 0 & ?? & 0$\pm$xx \\
|
| 47 |
%\hline
|
| 48 |
%\end{tabular}
|
| 49 |
%\end{center}
|
| 50 |
%\end{table}
|
| 51 |
|
| 52 |
|
| 53 |
|
| 54 |
%When find no dilepton events with invariant mass
|
| 55 |
%consistent with the $Z$ in the signal region.
|
| 56 |
%Using the value of 0.1 for the ratio described above, this
|
| 57 |
%means that the Drell Yan background in our signal
|
| 58 |
%region is $< 0.23\%$ events at the 90\% confidence level.
|
| 59 |
%{\color{red} (If we find 1 event this will need to be adjusted)}.
|
| 60 |
|
| 61 |
As discussed in Section~\ref{sec:victory}, residual Drell-Yan
|
| 62 |
events can have a significant effect on the data driven background
|
| 63 |
prediction based on $P_T(\ell\ell)$. This is taken into account,
|
| 64 |
based on MC expectations,
|
| 65 |
by the $K_C$ factor described in that Section.
|
| 66 |
As a cross-check, we use a separate data driven method to
|
| 67 |
estimate the impact of Drell Yan events on the
|
| 68 |
background prediction based on $P_T(\ell\ell)$.
|
| 69 |
In this method\cite{ref:top} we count the number
|
| 70 |
of $Z$ candidates\footnote{$e^+e^-$ and $\mu^+\mu^-$
|
| 71 |
with invariant mass between 76 and 106 GeV.}
|
| 72 |
passing the same selection as
|
| 73 |
region $D$ except that the $\met/\sqrt{\rm SumJetPt}$ requirement is
|
| 74 |
replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement
|
| 75 |
(we call this the ``region $D'$ selection'').
|
| 76 |
We subtract off the number of $e\mu$ events with
|
| 77 |
invariant mass in the $Z$ passing the region $D'$ selection.
|
| 78 |
Finally, we multiply the result by ratio $R_{out/in}$ derived
|
| 79 |
from Monte Carlo as the ratio of Drell-Yan events
|
| 80 |
outside/inside the $Z$ mass window
|
| 81 |
in the $D'$ region.
|
| 82 |
|
| 83 |
We find $N^{D'}(ee+\mu\mu)=2$, $N^{D'}(e\mu)=0$,
|
| 84 |
$R^{D'}_{out/in}=0.18\pm0.16$ (stat.).
|
| 85 |
Thus we estimate the number of Drell Yan events in region $D'$ to
|
| 86 |
be $0.36\pm 0.36$.
|
| 87 |
|
| 88 |
We also perform the DY estimate in the region $A'$. Here we find
|
| 89 |
$N^{A'}(ee+\mu\mu)=5$, $N^{A'}(e\mu)=0$,
|
| 90 |
$R^{D'}_{out/in}=0.50\pm0.43$ (stat.), giving an estimated
|
| 91 |
number of Drell Yan events in region $A'$ to
|
| 92 |
be $2.5 \pm 2.4$.
|
| 93 |
|
| 94 |
|
| 95 |
This Drell Yan method could also be used to estimate
|
| 96 |
the number of DY events in the signal region (region $D$).
|
| 97 |
However, there is not enough statistics in the Monte
|
| 98 |
Carlo to make a measurement of $R_{out/in}$ in region
|
| 99 |
$D$. In any case, no $Z \to \ell\ell$ candidates are
|
| 100 |
found in region $D$.
|
| 101 |
|
| 102 |
|
| 103 |
|
| 104 |
%In the context of other dilepton analyses we
|
| 105 |
%have developed a data driven method to estimate
|
| 106 |
%the number of Drell Yan events\cite{ref:dy}.
|
| 107 |
%The method is based on counting the number of
|
| 108 |
%$Z$ candidates passing the full selection, and
|
| 109 |
%then scaling by the expected ratio of Drell Yan
|
| 110 |
%events outside vs. inside the $Z$ mass
|
| 111 |
%window.\footnote{A correction based on $e\mu$ events
|
| 112 |
%is also applied.} This ratio is called $R_{out/in}$
|
| 113 |
%and is obtained from Monte Carlo.
|
| 114 |
|
| 115 |
|
| 116 |
|
| 117 |
|
| 118 |
%As a cross-check, we use the same Drell Yan background
|
| 119 |
%estimation method described above to estimate the
|
| 120 |
%number of DY events in the regions $A'B'C'D'$.
|
| 121 |
%The region $A'$ is defined in the same way as the region $A$
|
| 122 |
%except that the $\met/\sqrt{\rm SumJetPt}$ requirement is
|
| 123 |
%replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement.
|
| 124 |
%The regions B',
|
| 125 |
%C', and D' are defined in a similar way. The results are
|
| 126 |
%summarized in Table~\ref{tab:ABCD-DYptll}.
|
| 127 |
|
| 128 |
%\begin{table}[hbt]
|
| 129 |
%\begin{center}
|
| 130 |
%\caption{\label{tab:ABCD-DYptll} Drell-Yan estimations
|
| 131 |
%in the four
|
| 132 |
%regions $A'B'C'D'$ defined in the text. The yields are
|
| 133 |
%for dileptons with invariant mass consistent with the $Z$.
|
| 134 |
%The factor
|
| 135 |
%$R_{out/in}$ is from MC. All uncertainties
|
| 136 |
%are statistical only.}
|
| 137 |
%\begin{tabular}{|l|c|c|c||c|}
|
| 138 |
%\hline
|
| 139 |
%Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\
|
| 140 |
%\hline
|
| 141 |
%$A'$ & 3 & 0 & 0.7$\pm$0.3 & 2.1$\pm$xx \\
|
| 142 |
%$B'$ & 3 & 0 & 2.5$\pm$2.1 & 7.5$\pm$xx \\
|
| 143 |
%$C'$ & 0 & 0 & 0.1$\pm$0.1 & 0$\pm$xx \\
|
| 144 |
%$D'$ & 1 & 0 & 0.4$\pm$0.3 & 0.4$\pm$xx \\
|
| 145 |
%\hline
|
| 146 |
%\end{tabular}
|
| 147 |
%\end{center}
|
| 148 |
%\end{table}
|
| 149 |
|
| 150 |
|
| 151 |
Finally, we can use the ``Fake Rate'' method\cite{ref:FR}
|
| 152 |
to predict
|
| 153 |
the number of events with one fake lepton. We select
|
| 154 |
events where one of the leptons passes the full selection and
|
| 155 |
the other one fails the full selection but passes the
|
| 156 |
``Fakeable Object'' selection of
|
| 157 |
Reference~\cite{ref:FR}.\footnote{For electrons we use
|
| 158 |
the V3 fakeable object definition to avoid complications
|
| 159 |
associated with electron ID cuts applied in the trigger.}
|
| 160 |
We then weight each event passing the full selection
|
| 161 |
by FR/(1-FR) where FR is the ``fake rate'' for the
|
| 162 |
fakeable object. {\color{red} \bf The results are...}
|
| 163 |
|
| 164 |
{\color{red} \bf We will do the same thing that we did for
|
| 165 |
the top analysis, but we will only do it on the full dataset.}
|
