| 15 |
|
To estimate this contribution we use an opposite-flavor subtraction |
| 16 |
|
technique which takes advantage of the fact that the \ttbar yield in the |
| 17 |
|
opposite-flavor final state ($e\mu$) is the same as in the same-flavor final state |
| 18 |
< |
($ee+\mu\mu$), modulo differences in efficiency in the $e$ vs. $\mu$ selection. |
| 18 |
> |
($ee+\mu\mu$) (see figure \ref{fig:ttbar}), |
| 19 |
> |
modulo differences in efficiency in the $e$ vs. $\mu$ selection. |
| 20 |
|
Hence the \ttbar yield in the same-flavor final state can be estimated |
| 21 |
|
using the corresponding yield in the opposite-flavor final state. |
| 22 |
|
It is important to note that other backgrounds for which the lepton flavors are |
| 23 |
< |
uncorrelated (for example $VV$ and DY$\rightarrow \tau\tau$) will also be included in |
| 23 |
> |
uncorrelated (for example $WW$ and DY$\rightarrow \tau\tau$) will also be included in |
| 24 |
|
this estimate. |
| 25 |
|
|
| 26 |
|
The simplest option |
| 27 |
|
is to take the $e\mu$ yield inside the \Z mass window and scale this |
| 28 |
|
to predict the $ee$ and $\mu\mu$ yields, based on $e$ and $\mu$ selection efficiencies. |
| 29 |
|
Only the ratio of muon to electron selection efficiency is needed, which we evaluate |
| 30 |
< |
as $\epsilon_{\mu e} = \sqrt{\frac{N_{Z\mu\mu}}{N_{Zee}}}$. |
| 30 |
> |
as $R_{\mu e} = \sqrt{\frac{N_{Z\mu\mu}}{N_{Zee}}}$. |
| 31 |
|
Here $N_{Zee}$ ($N_{Z\mu\mu}$) is the total number of events in the $ee$ ($\mu\mu$) |
| 32 |
|
final state passing the pre-selection in Section~\ref{sec:yields}, |
| 33 |
|
without the requirement of at least 2 jets. We find |
| 34 |
< |
$\epsilon_{\mu e}=1.11 \pm 0.01$ (stat). (Note that in the following |
| 35 |
< |
$\epsilon_{e\mu} = 1/\epsilon_{\mu e}$.) |
| 36 |
< |
Systematic uncertainties on the prediction are assessed in section~\ref{sec:systematicsof}, and only statistical uncertainties are given in this section. |
| 34 |
> |
$R_{\mu e}=1.068 \pm 0.001$ (stat). %2011 |
| 35 |
> |
% $R_{\mu e}=1.11 \pm 0.01$ (stat). %2010 |
| 36 |
> |
(Note that in the following $R_{e\mu} = 1/R_{\mu e}$.) |
| 37 |
> |
Systematic uncertainties on the prediction are assessed in section~\ref{sec:systematicsof}, |
| 38 |
> |
and only statistical uncertainties are given in this section. |
| 39 |
|
|
| 40 |
|
This procedure yields the following predicted yields $n_{pred}$, |
| 41 |
< |
based on an observed yield of 3 $e\mu$ events in the loose signal region: |
| 41 |
> |
based on an observed yield of |
| 42 |
> |
49 %976/pb ; %12 %204/pb |
| 43 |
> |
$e\mu$ events %3 events in 2010 (met 60) |
| 44 |
> |
in the loose signal region |
| 45 |
> |
(the corresponding predictions in the tight |
| 46 |
> |
signal region are shown in table \ref{tab:ttbpredk} |
| 47 |
> |
and in figures~\ref{fig:pfmet_ee} and \ref{fig:pfmet_mm}): |
| 48 |
|
|
| 49 |
|
\begin{equation} |
| 50 |
< |
n_{pred}(\mu\mu) = \frac{1}{2}n(e\mu)\epsilon_{\mu e} = 1.67 \pm 0.96 |
| 50 |
> |
n_{pred}(\mu\mu) = \frac{1}{2}n(e\mu)R_{\mu e} = 26.2 \pm 3.74 %2011--met 100 976/pb |
| 51 |
> |
%n_{pred}(\mu\mu) = \frac{1}{2}n(e\mu)R_{\mu e} = 6.40 \pm 1.85 %2011--met 100 204/pb |
| 52 |
|
\end{equation} |
| 53 |
|
\begin{equation} |
| 54 |
< |
n_{pred}(ee) = \frac{1}{2}n(e\mu)\epsilon_{e\mu} = 1.35 \pm 0.78 |
| 54 |
> |
n_{pred}(ee) = \frac{1}{2}n(e\mu)R_{e\mu} = 22.9 \pm 3.27 %2011--met 100 976/pb |
| 55 |
> |
%n_{pred}(ee) = \frac{1}{2}n(e\mu)R_{e\mu} = 5.62 \pm 1.62 %2011--met 100 204/pb |
| 56 |
|
\end{equation} |
| 57 |
|
|
| 58 |
< |
The predicted same flavor \ttbar yields agree well with the MC expectation of 2.0 ($\mu\mu$) %really |
| 59 |
< |
and 1.9 ($ee$) %really |
| 60 |
< |
as shown in Fig.~\ref{fig:ttbar}. |
| 61 |
< |
Due to the small statistics, the errors on the predicted yields using this procedure are quite large. |
| 58 |
> |
The predicted same flavor \ttbar yields |
| 59 |
> |
can be compared |
| 60 |
> |
%agree well %well, it's just over 1 sigma for mm, just under for ee |
| 61 |
> |
with the MC expectation of |
| 62 |
> |
18.6 %976/pb (w trig eff) |
| 63 |
> |
%4.3 %204/pb (no trig eff) |
| 64 |
> |
($\mu\mu$) and |
| 65 |
> |
17.8 %976/pb (w trig eff) |
| 66 |
> |
%3.7 %204/pb (no trig eff) |
| 67 |
> |
($ee$) as shown in Table \ref{sigyieldtableloose}. |
| 68 |
> |
Due to the relatively small statistics, the errors on the predicted yields |
| 69 |
> |
using this procedure are fairly large. |
| 70 |
|
To improve the statistical errors, we instead determine the $e\mu$ yield |
| 71 |
|
without requiring the leptons to fall in the \Z mass window. |
| 72 |
< |
This yield is scaled by a factor determined from MC, $K= 0.16$, |
| 72 |
> |
This yield is scaled by a factor determined from MC, $K= 0.16$, %same in 2011 as 2010 |
| 73 |
|
which accounts for the fraction of \ttbar events expected to fall in the $Z$ mass |
| 74 |
|
window. This procedure yields the following |
| 75 |
< |
predicted yields based on 27 observed $e\mu$ events: |
| 75 |
> |
predicted yields based on |
| 76 |
> |
319 %(976/pb) %74 (204/pb) |
| 77 |
> |
observed $e\mu$ events: %27 events in 2010 (met 60) |
| 78 |
|
|
| 79 |
|
\begin{equation} |
| 80 |
< |
n_{pred}(\mu\mu) = \frac{1}{2}n(e\mu)K\epsilon_{\mu e} = 2.34 \pm 0.45 |
| 80 |
> |
n_{pred}(\mu\mu) = \frac{1}{2}n(e\mu)KR_{\mu e} = 27.0 \pm 1.5 %2011--met 100 976/pb |
| 81 |
> |
%n_{pred}(\mu\mu) = \frac{1}{2}n(e\mu)KR_{\mu e} = 6.26 \pm 0.73 %2011--met 100 204/pb |
| 82 |
|
\end{equation} |
| 83 |
|
\begin{equation} |
| 84 |
< |
n_{pred}(ee) = \frac{1}{2}n(e\mu)K\epsilon_{e\mu} = 1.90 \pm 0.36 |
| 84 |
> |
n_{pred}(ee) = \frac{1}{2}n(e\mu)KR_{e\mu} = 23.6 \pm 1.3 %2011--met 100 976/pb |
| 85 |
> |
%n_{pred}(ee) = \frac{1}{2}n(e\mu)KR_{e\mu} = 5.50 \pm 0.64 %2011--met 100 204/pb |
| 86 |
|
\end{equation} |
| 87 |
|
|
| 88 |
< |
Notice that the yields are consistent with those predicted without using $K$, but the relative statistical uncertainty is reduced by a factor of approximately 2. |
| 88 |
> |
Notice that the yields are consistent with those predicted without using $K$, but the relative statistical uncertainty is reduced by a factor of approximately 2. (See table \ref{tab:ttbpredk}.) |
| 89 |
|
Since the total uncertainty is expected to be statistically-dominated, the second method yields a better prediction and we use this as our estimate |
| 90 |
< |
of the \ttbar~background. Predicted yields for the tight signal region are given in the tables under Figs.~\ref{fig:pfmet_eemm}-\ref{fig:pfmet_mm}. |
| 90 |
> |
of the \ttbar background. |
| 91 |
> |
%moved this up |
| 92 |
> |
%Predicted yields for the tight signal region are given in the tables under Figs.~\ref{fig:pfmet_eemm}-\ref{fig:pfmet_mm}. |
| 93 |
> |
|
| 94 |
|
% while the systematic uncertainty has increased slightly. This systematic |
| 95 |
|
%uncertainty is a preliminary, conservative estimate. The total uncertainty on the prediction is improved significantly using the second method. |
| 96 |
|
|
| 97 |
+ |
|
| 98 |
+ |
\begin{table}[hbt] |
| 99 |
+ |
\begin{center} |
| 100 |
+ |
\caption{ |
| 101 |
+ |
\label{tab:ttbpredk} |
| 102 |
+ |
The \ttbar prediction for each MET cut used with and without using the K value. |
| 103 |
+ |
For all MET cuts, the values are consistent, but the value without K |
| 104 |
+ |
has a larger statistical uncertainty. |
| 105 |
+ |
} |
| 106 |
+ |
\begin{tabular}{lcccc} |
| 107 |
+ |
\hline |
| 108 |
+ |
\resulttitle |
| 109 |
+ |
\hline |
| 110 |
+ |
%976/pb |
| 111 |
+ |
$t\bar{t}$ pred with K & 246.61 $\pm$ 6.26 & 152.50 $\pm$ 4.92 & 50.63 $\pm$ 2.83 & 3.17 $\pm$ 0.71 \\ |
| 112 |
+ |
$t\bar{t}$ pred without K & 249.55 $\pm$ 15.81 & 165.37 $\pm$ 12.87 & 49.11 $\pm$ 7.02 & 3.01 $\pm$ 1.74 \\ |
| 113 |
+ |
|
| 114 |
+ |
%204/pb |
| 115 |
+ |
%$t\bar{t}$ pred with K & 54.77 $\pm$ 2.95 & 34.73 $\pm$ 2.35 & 11.76 $\pm$ 1.37 & 1.13 $\pm$ 0.46 \\ |
| 116 |
+ |
%$t\bar{t}$ pred without K & 55.12 $\pm$ 7.43 & 42.09 $\pm$ 6.49 & 12.03 $\pm$ 3.47 & 2.00 $\pm$ 1.42 \\ |
| 117 |
+ |
|
| 118 |
+ |
\hline |
| 119 |
+ |
\end{tabular} |
| 120 |
+ |
\end{center} |
| 121 |
+ |
\end{table} |
| 122 |
+ |
|
| 123 |
+ |
|
| 124 |
|
\begin{figure}[hbt] |
| 125 |
|
\begin{center} |
| 126 |
|
\resizebox{0.75\linewidth}{!}{\includegraphics{plots/flavorsubdata.png}} |
| 127 |
< |
\caption{Dilepton mass distribution for events passing the loose signal region selection. The solid histograms represent the yields in the same-flavor |
| 128 |
< |
final state for each SM contribution, while the solid black line (OFOS) indicates the sum of the MC contributions in the opposite-flavor final state. |
| 127 |
> |
\caption{MC dilepton mass distribution for events passing the loose signal region selection. |
| 128 |
> |
The solid histograms represent the yields in the same-flavor |
| 129 |
> |
final state for each SM contribution, while the black data points (OFOS) indicates the |
| 130 |
> |
sum of the \ttbar MC contributions in the opposite-flavor final state. |
| 131 |
|
%The observed ttbar yields inside the $Z$ mass window in the $ee$ and $\mu\mu$ final states are indicated. |
| 132 |
|
The \ttbar distribution in the same-flavor final state is well-modeled by the OFOS prediction.} |
| 133 |
|
\label{fig:ttbar} |
| 134 |
|
\end{center} |
| 135 |
|
\end{figure} |
| 136 |
|
|
| 82 |
– |
% |
| 83 |
– |
|
| 84 |
– |
%\begin{wrapfigure}{r}{0.6\textwidth} |
| 85 |
– |
%\vspace{-25pt} |
| 86 |
– |
%\begin{center} |
| 87 |
– |
%\includegraphics[width=0.8\textwidth]{plots/flavorsubdata} |
| 88 |
– |
% \caption{ \label{fig:ttbar} Dilepton mass distribution for events passing the signal region selection. The solid histograms represent the yields in the same-flavor |
| 89 |
– |
% final state for each SM contribution, while the solid black line (OFOS) indicates the sum of the MC contributions in the opposite-flavor final state. |
| 90 |
– |
% %The observed ttbar yields inside the $Z$ mass window in the $ee$ and $\mu\mu$ final states are indicated. |
| 91 |
– |
% The ttbar distribution in the same-flavor final state is well-modeled by the OFOS prediction.} |
| 92 |
– |
%\end{center} |
| 93 |
– |
%\vspace{-20pt} |
| 94 |
– |
%\end{wrapfigure} |
| 95 |
– |
|
| 96 |
– |
|
| 97 |
– |
|
| 98 |
– |
|
