| 12 |
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of the individual leptons, and, in the case of muons, the $|\eta|$ |
| 13 |
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of the muons. We believe that this model is adequate for |
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the trigger efficiency precision needed for this analysis. |
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Details are given in Appendix~\ref{sec:appendix_trigger}. |
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|
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The model assumptions are the following |
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|
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\begin{itemize} |
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|
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\item Muon and electron trigger turn-ons as a function of $P_T$ |
| 22 |
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are infinitely sharp. {\color{red} Can we add references?} |
| 23 |
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|
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\item All electron triggers with no ID have 100\% |
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efficiency for electrons passing our analysis cuts. {\color{red} |
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Can we add a reference? Pehaps the top documentation?} |
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|
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\item Electron triggers with (Tight(er))CaloEleId have 100\% |
| 28 |
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efficiency with respect to our offline selection. This we |
| 29 |
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verified via tag-and-probe on $Z\to ee$. |
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|
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\item Electron triggers with EleId have somewhat lower |
| 32 |
< |
efficiency. This was also measured by tag-and-probe. |
| 33 |
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|
| 34 |
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\item The single muon trigger has zero efficiency for $|\eta|>2.1$. |
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This is conservative, the trigger efficiency here is of order |
| 36 |
< |
$\approx 40\%$. |
| 37 |
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|
| 38 |
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\item If a muon in $|\eta|>2.1$ fails the single muon trigger, it |
| 39 |
< |
will also fail the double muon trigger. |
| 40 |
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|
| 41 |
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\item The double muon trigger has efficiency |
| 42 |
< |
equal to the square of the single muon efficiency. |
| 43 |
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|
| 44 |
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\item The $e\mu$ triggers have no efficiency if the muon has $|\eta|>2.1$. |
| 45 |
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|
| 46 |
< |
\end{itemize} |
| 47 |
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|
| 48 |
< |
The model also uses some luminosity fractions and some trigger |
| 49 |
< |
efficiencies. |
| 50 |
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|
| 51 |
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\begin{itemize} |
| 52 |
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|
| 53 |
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\item $\epsilon_{\mu}$=xx, the single muon trigger efficiency plateau. |
| 54 |
< |
|
| 55 |
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\item $f9$=xx: fraction of data with the Mu9 trigger unprescaled. |
| 56 |
< |
(run$\le 147116$). |
| 57 |
< |
|
| 58 |
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\item $f11$=xx fraction of data with the Mu9 trigger prescaled and |
| 59 |
< |
the Mu11 trigger unprescaled. |
| 60 |
< |
(147196 $\leq$ run $\leq$ 148058). |
| 61 |
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|
| 62 |
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\item $e10$=xx: fraction of data with the 10 GeV unprescaled electron triggers. |
| 63 |
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(run$\le 139980$). |
| 64 |
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|
| 65 |
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\item $e15$=xx: fraction of data with the 15 GeV unprescaled electron triggers. |
| 66 |
< |
(139980 $<$ run $\leq$ 144114). |
| 67 |
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|
| 68 |
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\item $e17$=xx: fraction of data with the 100\% efficient 17 GeV unprescaled electron triggers. |
| 69 |
< |
(144114 $<$ run $\leq$ 147116). |
| 70 |
< |
|
| 71 |
< |
\item $e17b$=xx: fraction of data with 17 GeV unprescaled electron triggers |
| 72 |
< |
with efficiency $\epsilon_e^b=90\%$ (as measured by tag-and-probe). |
| 73 |
< |
(147116 $<$ run $\leq$ 148058). |
| 74 |
< |
|
| 75 |
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\item $emess$=xx: the remainder of the run with several different electron |
| 76 |
< |
triggers, all of $P_T>17$ GeV. For this period we measure the |
| 77 |
< |
luminosity-weighted |
| 78 |
< |
trigger efficiency $\epsilon(P_T)$ via tag and probe to be 99\% |
| 79 |
< |
($17<P_T<22$, 97\% ($22<P_T<27$), 98\% ($27<P_T<32$) and |
| 80 |
< |
100\% ($P_T>32$). |
| 81 |
< |
|
| 82 |
< |
\end{itemize} |
| 83 |
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|
| 84 |
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The full trigger efficiency model is described separately for |
| 85 |
< |
$ee$, $e\mu$, and $\mu\mu$. |
| 86 |
< |
|
| 87 |
< |
\subsection{$ee$ efficiency model} |
| 88 |
< |
\label{sec:eemodel} |
| 89 |
< |
|
| 90 |
< |
This is the easiest. Throughout the 2010 run we have always |
| 91 |
< |
had dielectron triggers with thresholds lower than our (20,10) |
| 92 |
< |
analysis thresholds. Since electron triggers are 100\% efficient, |
| 93 |
< |
the trigger efficiency for $ee$ is 100\%. We have verified that |
| 94 |
< |
the efficiency of the dielectron trigger is 100\% with respect |
| 95 |
< |
to the single electron trigger using $Z \to ee$ data. |
| 96 |
< |
|
| 97 |
< |
\subsection{$\mu\mu$ efficiency model} |
| 98 |
< |
\label{sec:mmmodel} |
| 99 |
< |
|
| 100 |
< |
We consider different cases. |
| 101 |
< |
|
| 102 |
< |
\subsubsection{Both muons in $|\eta|<2.1$ and with $P_T>15$ GeV} |
| 103 |
< |
This is the bulk of the $\mu\mu$. |
| 104 |
< |
|
| 105 |
< |
\begin{center} |
| 106 |
< |
$\epsilon = 1 - (1-\epsilon_{\mu})^2$ |
| 107 |
< |
\end{center} |
| 108 |
< |
|
| 109 |
< |
\subsubsection{Both muons in $|\eta|<2.1$, one muon with $11<P_T<15$ GeV} |
| 110 |
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In this case there must be a muon with $P_T>20$ GeV. The single muon |
| 111 |
< |
trigger is operative for the full dataset on this muon. Some loss |
| 112 |
< |
of efficiency can be recovered when the 2nd muon fires the trigger. |
| 113 |
< |
But this can happen only for a fraction of the run. The dimuon trigger |
| 114 |
< |
cannot fire in our model to recover any of the efficiency lost by |
| 115 |
< |
the single muon trigger on the high $P_T$ muon. |
| 116 |
< |
|
| 117 |
< |
\begin{center} |
| 118 |
< |
$\epsilon = \epsilon_{\mu} + (1-\epsilon_{\mu})\epsilon_{\mu}(f9+f11)$ |
| 119 |
< |
\end{center} |
| 120 |
< |
|
| 121 |
< |
\subsubsection{Both muons in $|\eta|<2.1$, one muon with $10<P_T<11$ GeV} |
| 122 |
< |
Same basic idea as above. |
| 123 |
< |
|
| 124 |
< |
\begin{center} |
| 125 |
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$\epsilon = \epsilon_{\mu} + (1-\epsilon_{\mu})\epsilon_{\mu}f9$ |
| 126 |
< |
\end{center} |
| 127 |
< |
|
| 128 |
< |
\subsubsection{Both muons with $|\eta|>2.1$} |
| 129 |
< |
This is a very small fraction of events. In our model they can only be |
| 130 |
< |
triggered by the dimuon trigger. |
| 131 |
< |
|
| 132 |
< |
\begin{center} |
| 133 |
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$\epsilon = \epsilon_{\mu}^2$ |
| 134 |
< |
\end{center} |
| 135 |
< |
|
| 136 |
< |
\subsubsection{First muon with $P_T>15$ and $|\eta|<2.1$; second muon |
| 137 |
< |
with $|\eta|>2.1$} |
| 138 |
< |
The single muon trigger is always operative. If it fails the double muon |
| 139 |
< |
trigger also fails. |
| 140 |
< |
|
| 141 |
< |
\begin{center} |
| 142 |
< |
$\epsilon = \epsilon_{\mu}$ |
| 143 |
< |
\end{center} |
| 144 |
< |
|
| 145 |
< |
\subsubsection{First muon with $11<P_T<15$ and $|\eta|<2.1$; second muon |
| 146 |
< |
with $|\eta|>2.1$} |
| 147 |
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The single muon trigger is operative only for a fraction of the run. |
| 148 |
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For the remaining fraction, we must rely on the double muon trigger. |
| 149 |
< |
|
| 150 |
< |
\begin{center} |
| 151 |
< |
$\epsilon = (f9+f11)\epsilon_{\mu} + (1-f9-f11)\epsilon_{\mu}^2$ |
| 152 |
< |
\end{center} |
| 153 |
< |
|
| 154 |
< |
\subsubsection{First muon with $10<P_T<11$ and $|\eta|<2.1$; second muon |
| 155 |
< |
with $|\eta|>2.1$} |
| 156 |
< |
Same basic idea as above. |
| 157 |
< |
|
| 158 |
< |
\begin{center} |
| 159 |
< |
$\epsilon = f9~\epsilon_{\mu} + (1-f9)\epsilon_{\mu}^2$ |
| 160 |
< |
\end{center} |
| 161 |
< |
|
| 162 |
< |
\subsection{$e\mu$ efficiency model} |
| 163 |
< |
\label{sec:emumodel} |
| 164 |
< |
|
| 165 |
< |
This is the most complicated case. The idea is that the muon trigger |
| 166 |
< |
is used to get the bulk of the efficiency. Then the single electron |
| 167 |
< |
trigger(s) and the $e\mu$ triggers are used to get back dome of the |
| 168 |
< |
efficiency loss. The various cases are listed below. |
| 169 |
< |
|
| 170 |
< |
\subsubsection{Muon with $|\eta|<2.1$ and $P_T>15$} |
| 171 |
< |
This is the bulk of the acceptance. |
| 172 |
< |
|
| 173 |
< |
\begin{center} |
| 174 |
< |
$\epsilon = \epsilon_{\mu} + (1-\epsilon_{\mu})\Delta_1$ |
| 175 |
< |
\end{center} |
| 176 |
< |
|
| 177 |
< |
where $\Delta_1$ is the efficiency from the electron trigger: |
| 178 |
< |
\begin{itemize} |
| 179 |
< |
\item $P_T(ele)<15 \to \Delta_1=e10$ |
| 180 |
< |
\item $15<P_T(ele)<17 \to \Delta_1=e10+e15$ |
| 181 |
< |
\item $P_T(ele)>15 \to \Delta_1=e10+e15+e17+\epsilon_e^b~e17b+\epsilon(P_T)~emess$ |
| 182 |
< |
\end{itemize} |
| 183 |
< |
|
| 184 |
< |
|
| 185 |
< |
\subsubsection{Muon with $|\eta|<2.1$ and $11<P_T>15$} |
| 186 |
< |
|
| 187 |
< |
This is the similar to the previous case, except that the muon |
| 188 |
< |
trigger is operative only for a subset of the data taking period. |
| 189 |
< |
|
| 190 |
< |
\begin{center} |
| 191 |
< |
$\epsilon = (f11+f9)\epsilon_{\mu} + \Delta_2 + \Delta_3$ |
| 192 |
< |
\end{center} |
| 193 |
< |
|
| 194 |
< |
Here $\Delta_2$ is associated with the period where the muon |
| 195 |
< |
trigger was at 15 GeV, in which case we use electron triggers or |
| 196 |
< |
$e\mu$ triggers. Note that the electron in this case must be |
| 197 |
< |
above 20 GeV. This can happen only in the latter part of the run, |
| 198 |
< |
thus we write |
| 199 |
< |
\begin{center} |
| 200 |
< |
$\Delta_2 = (1-f11-f9)~(\epsilon_{\mu}~+~ |
| 201 |
< |
(1-\epsilon_{\mu})\epsilon(P_T))$ |
| 202 |
< |
\end{center} |
| 203 |
< |
\noindent where the first term is for the $e\mu$ trigger and the |
| 204 |
< |
second term corresponds to $e\mu$ trigger failures, in which case we have |
| 205 |
< |
to rely on the electron trigger. |
| 206 |
< |
|
| 207 |
< |
Then, $\Delta_3$ is associated with muon trigger failures in early runs, |
| 208 |
< |
{\em i.e.}, run $<148819$. In this case the electron trigger picks it |
| 209 |
< |
up and the $e\mu$ trigger does not help. |
| 210 |
< |
|
| 211 |
< |
\begin{center} |
| 212 |
< |
$\Delta_3 = (f11+f9)(1-\epsilon_{\mu}) \cdot \epsilon_e$ |
| 213 |
< |
\end{center} |
| 214 |
< |
|
| 215 |
< |
\noindent where $\epsilon_e$ is the efficiency of the electron |
| 216 |
< |
trigger for $P_T>20$. This is 100\% up to run 147716 (fraction |
| 217 |
< |
$(e10_e15+e17)/(f11+f9)$; then it is somewhat lower up to |
| 218 |
< |
run 148058, then it becomes very close to 100\% again. |
| 219 |
< |
For this latter part of the run we approximate it as $\epsilon_e^b$. |
| 220 |
< |
Thus: |
| 221 |
< |
|
| 222 |
< |
\begin{center} |
| 223 |
< |
$\epsilon_e = (e10_e15+e17)/(f11+f9) + |
| 224 |
< |
\epsilon_e^b(f11+f9-e10-e15-e17)/(f11+f9)$ |
| 225 |
< |
\end{center} |
| 226 |
< |
|
| 227 |
< |
\subsubsection{Muon with $|\eta|<2.1$ and $9<P_T>11$} |
| 228 |
< |
|
| 229 |
< |
Identical to the previous case, but replace $(f11+f9)$ with $f9$ everywhere. |
| 230 |
< |
|
| 231 |
< |
\subsubsection{Muon with $|\eta|>2.1$} |
| 232 |
< |
|
| 233 |
< |
This is a 10\% effect to start with. We assume no single muon efficiency, |
| 234 |
< |
no $e\mu$ efficiency. Then we can only ise the single electron trigger. |
| 235 |
< |
|
| 236 |
< |
\begin{center} |
| 237 |
< |
$\epsilon = \Delta_1$ |
| 238 |
< |
\end{center} |
| 17 |
> |
We take the trigger efficiency for $ee$ as 100\%. The trigger efficiency |
| 18 |
> |
for the $e\mu$ and $\mu\mu$ final states is summarized in |
| 19 |
> |
Figures~\ref{fig:emuModel} and~\ref{fig:mumuModel}. |
| 20 |
> |
We estimate the systematic uncertainties on the trigger modeling |
| 21 |
> |
to be at the level of 1\%, which is approximately the difference in signal |
| 22 |
> |
yields between using 100\% trigger efficiency and the full trigger |
| 23 |
> |
efficiency model. |
