claudioc/dilNoteICHEP/fakerate.tex

\section{Fake Rate}
\label{sec:FR}

\subsection{Intro}
The Fake Rate (FR) method has been described in a
separate analysis note~\cite{ref:FR} and applied
to a number of Monte Carlo studies\cite{ref:topdil2009},
\cite{ref:WW},\cite{ref:SSSusy}.  Briefly, jet data
is used to measure a lepton FR as a function of 
lepton $P_T$ and $|\eta|$ which is defined as the probability
for a lepton candidate passing loose cuts to also pass the
analysis cuts.  Leptons passing loose cuts are called 
``Fakeable Objects'' (FO).  

In a given analysis the FR is then used to estimate the
background due to ``fake'' leptons\footnote{Here ``fake'' leptons
refer to truly fake leptons as well as leptons from heavy flavor decays.}
as follows:
\begin{itemize}
\item Events are selected using all analysis cuts, except
for the lepton selection.  Dilepton backgrounds 
with one real lepton and one fake lepton are estimated by 
selecting one lepton passing the full lepton selection 
and one failing it but passing the FO selection.
Backgrounds with two fake leptons (QCD) are estimated by requiring
both lepton candidates to pass the FO selection and fail
the full selection.
\item For the QCD backgrounds considered in this note,
each event is weighted by the product of the two factors
of FR/(1-FR), where FR is the Fake
Rate for each of the two FO.  
\item The sum of the weights over the selected events is the
background prediction.
\end{itemize}

\subsection{Fakeable Object Definitions}
\label{sec:FODefinition}

Fakeable Objects are defined starting from the full
lepton selection by relaxing some combination of the identification
and isolation requirements.  Since most muons in QCD events are
from heavy flavor decays, relaxing the identification requirements
is not very useful.  Thus our muon FO definition consists mainly 
of relaxing the isolation requirement.  On the other hand, for 
electrons we have more freedom and we use three separate definitions
of the FR.  Broadly speaking these correspond to relaxing either
isolation, or ID, or both.  Our FO definitions are given below

Muon FO definition: relax the following muon requirements from
Section~\ref{sec:muID}:
\begin{itemize}

\item $\chi^2$/ndof of global fit $<$ 50 (was $<$ 10).
\item Transverse impact parameter with respect to the beamspot
$<$ 2 mm (was $<$ 200 $\mu$m).
\item $Iso < 0.4$ (was $<$ 0.15).

\end{itemize}

Electron V1 FO definition: relax the following electron requirements from
Section~\ref{sec:eleID}:
\begin{itemize}
\item Remove the VBTF90 requirement.
\item $Iso < 0.4$ (was $<$ 0.15).
\item The impact parameter cut was removed (used to be $<$ 400 $\mu$m).
\end{itemize}

Electron V2 FO definition: relax the following electron requirements from
Section~\ref{sec:eleID}:
\begin{itemize}
\item Remove the VBTF90 requirement.
\item The impact parameter cut was removed (used to be $<$ 400 $\mu$m).
\end{itemize}

Electron V3 FO definition: relax the following electron requirements from
Section~\ref{sec:eleID}:
\begin{itemize}
\item $Iso < 0.4$ (was $<$ 0.15).
\item The impact parameter cut was removed (used to be $<$ 400 $\mu$m).
\end{itemize}


\subsection{Measuring the FR on jet data}
\label{sec:FRjet}
The FR is measured by studying lepton candidates in jet data.
The jet data come from the JetMetTau and JetTauMonitor 
Primary/Secondary datasets, see Section~\ref{sec:datasets}.
We measure the FR on different jet triggers.  The stability
of the FR in these different jet samples is a measure of the 
robustness of our procedure.  We select the following triggers:
\begin{itemize}
\item HLT\_L1\_Jet6U from JetMetTauMonitor
\item HLT\_L1\_Jet10U from JetMetTauMonitor
\item HLT\_Jet15U from JetMetTau
\item HLT\_Jet30U from JetMetTau
\end{itemize}

In order to eliminate a possible trigger bias, we scan the list
of HLT objects associated with the given jet trigger.  If there 
is only one such object above threshold, we only consider
lepton candidates well separated ($\Delta R > 1$) from it.

Furthermore, even on jet triggers it is possible to collect
some $W$ and $Z$ leptonic decays.  These events would cause 
a significant bias to the FR at high $P_T$.  To minimize
this problem, we reject events with tcMet $>$ 20 GeV and 
events with two opposite sign FO that make a mass within
20 GeV of the $Z$ mass 
We believe that the bias from leftover $W$ and 
Drell Yan events in the jet sample is small, but it remains to
be estimated.

The FR are measured as a function of $P_T$ and $|\eta|$.
The FR projections on the $P_T$ and $|\eta|$ axes for the muon FR and for
the three (V1, V2, V3) electron FR in the different trigger samples
are displayed in 
{\color{red} Figures~\ref{fig:muFR} and~\ref{fig:eleFR} (old)} and 
{\color{blue}Figures~\ref{fig:muFR2} and~\ref{fig:eleFR2} (new)}.


\begin{figure}[htb]
\begin{center}
{\color{red}
\includegraphics[width=0.48\linewidth]{MuFakeRatesJune1.pdf}
\includegraphics[width=0.48\linewidth]{muFReta.pdf}
\caption{\label{fig:muFR}The muon fake rate as a function of $P_T$ 
and $|\eta|$ in the different jet samples. (Old plots updated below).}
}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
{\color{blue}
\includegraphics[width=0.31\linewidth, angle=90]{MuFakeRatesJuly7.pdf}
\includegraphics[width=0.31\linewidth, angle=90]{muFReta7July.pdf}
\caption{\label{fig:muFR2}The muon fake rate as a function of $P_T$ 
and $|\eta|$ in the different jet samples.  Note that these now start at 
$P_T=$ 10 GeV instead of $P_T=$5 GeV as they did in the earlier analysis
because of a preselection aplied in our data handling.  For this reason
the $\eta$-projections cannot be directly compared since the this is
dominated by muons of $P_T$ near threshold.  Note also that the 
muon identification requirements have changed a little bit, as 
described in Section 3.1.5. (New updated plots).}
}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
{\color{red}
\includegraphics[width=\linewidth]{ElFakeRatesJune1.pdf}
\includegraphics[width=\linewidth]{eFReta.pdf}
\caption{\label{fig:eleFR}The electron fake rates 
(V1,V2,V3) as a function of $P_T$ and $|\eta|$ 
in the different jet samples. (Old plots updated below).}
}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
{\color{blue}
\includegraphics[width=0.4\linewidth,angle=90 ]{ElFakeRatesJuly7.pdf}
\includegraphics[width=0.4\linewidth,angle=90]{eFRetaJuly7.pdf}
\caption{\label{fig:eleFR2}The electron fake rates 
(V1,V2,V3) as a function of $P_T$ and $|\eta|$ 
in the different jet samples.
Note that the spike removal has been added to the electron
selection since the earlier analysis.  This is a very
small effect. (New updated plots).}
}
\end{center}
\end{figure}


The fake rates are reasonably stable with respect to 
jet trigger variations, within the $\approx 50\%$ which 
we believe to be a realistic goal for the FR systematics.  
There is some evidence for the V2 electron FR to be more stable than
the V1 and V3 versions.  This is expected from earlier MC studies: the FO
V2 isolation requirement is the same as in  the full electron selection,
and thus the dependence on the amount of jet activity near the electron
candidate is minimized.

The FR binning
is quite coarse, because of the lack of statistics.  This will improve
as we collect more data.  In any case, the
FR does not appear to change very fast as a function of $P_T$.


\clearpage

\subsection{Loosening the isolation requirement for the muon FO}
Loosening the isolation requirement for the muon FO would reduce the
muon FR.  This is in general ``a good thing''\texttrademark.
However, the price one then pays is that the jet dependence of the 
FR increases.  This is illustrated in Figure~\ref{fig:FRlooseIso}.

In the $P_T \approx 8$ GeV bin, the ratio of FR in the two extreme triggers
(HLT\_L1Jet6U and HLT\_Jet30U) increases from 1.6 (FO-Iso $<$ 0.4) to 2.0
(FO-Iso $<$ 0.6) to 2.4 (FO-Iso $<$ 0.8) to 2.9 (FO-Iso $<$ 1.0). Given this 
behavior, for now we keep the FO isolation requirement to 0.4.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.7\linewidth,angle=90]{muonFR_differentIso.pdf}
\caption{\label{fig:FRlooseIso}Muon FR as a function of $P_T$ in different 
trigger samples for different choices of the maximum isolation 
requirement on the muon FO (0.4, 0.6, 0.8, 1.0).}
\end{center}
\end{figure}


\subsection{Bias due to lepton triggers?}
Another possible bias is related to the fact that events used to 
measure the FR are collected with jet triggers.  On the other hand
the dilepton analysis is performed using events collected with
the photon and muon trigger, see Section~\ref{sec:trigger}. 
If the FR depends on the firing of the muon/photon trigger,
the situation becomes more complicated and 
we may be forced to define different FR depending on whether or 
not the muon/photon trigger fired.

To test this hypothesis, we select events collected with the
HLT\_L1\_Jet15U trigger; we then compare the FR computed
in the standard way (Figures~\ref{fig:muFR} and~\ref{fig:eleFR})
with the FR on the subset of leptons where the HLT\_Mu5 or 
HLT\_Photon10\_L1R trigger fired\footnote{We made sure that the
trigger fired, and that the HLT object that fired the trigger was 
matched in $\Delta R$ to the lepton candidate.}.
The results are displayed in Figures~\ref{fig:muFRtrg} 
and~\ref{fig:eleFRtrg}. 

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.7\linewidth]{MuFakeRatesMu5June1.pdf}
\caption{\label{fig:muFRtrg}The muon fake rate in HLT\_L1\_Jet15U
as a function of $P_T$ with and without a requirement on the HLT\_Mu5
trigger.}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
\includegraphics[width=\linewidth]{ElFakeRatesPhoton10June1.pdf}
\caption{\label{fig:eleFRtrg}The electron fake rates 
(V1,V2,V3) in HLT\_L1\_Jet15U
as a function of $P_T$ with and without a requirement on the 
HLT\_Photon10\_L1R trigger.}
\end{center}
\end{figure}

The statistics are not very good, but the lepton trigger bias 
does not seem to be a significant effect.  We tentatively neglect it.

\clearpage
Revision:	1.7
Committed:	Thu Jul 8 11:37:50 2010 UTC (14 years, 10 months ago) by claudioc
Content type:	application/x-tex
Branch:	MAIN
CVS Tags:	v8, HEAD
Changes since 1.6:	+6 -6 lines
Log Message:	No OS update
#	User	Rev	Content
1	claudioc	1.1	\section{Fake Rate}
2			\label{sec:FR}
3
4			\subsection{Intro}
5			The Fake Rate (FR) method has been described in a
6			separate analysis note~\cite{ref:FR} and applied
7			to a number of Monte Carlo studies\cite{ref:topdil2009},
8			\cite{ref:WW},\cite{ref:SSSusy}. Briefly, jet data
9			is used to measure a lepton FR as a function of
10			lepton $P_T$ and $\|\eta\|$ which is defined as the probability
11			for a lepton candidate passing loose cuts to also pass the
12			analysis cuts. Leptons passing loose cuts are called
13			``Fakeable Objects'' (FO).
14
15			In a given analysis the FR is then used to estimate the
16			background due to ``fake'' leptons\footnote{Here ``fake'' leptons
17			refer to truly fake leptons as well as leptons from heavy flavor decays.}
18			as follows:
19			\begin{itemize}
20			\item Events are selected using all analysis cuts, except
21			for the lepton selection. Dilepton backgrounds
22			with one real lepton and one fake lepton are estimated by
23			selecting one lepton passing the full lepton selection
24			and one failing it but passing the FO selection.
25	claudioc	1.5	Backgrounds with two fake leptons (QCD) are estimated by requiring
26	claudioc	1.1	both lepton candidates to pass the FO selection and fail
27			the full selection.
28	claudioc	1.5	\item For the QCD backgrounds considered in this note,
29			each event is weighted by the product of the two factors
30			of FR/(1-FR), where FR is the Fake
31			Rate for each of the two FO.
32	claudioc	1.1	\item The sum of the weights over the selected events is the
33			background prediction.
34			\end{itemize}
35
36			\subsection{Fakeable Object Definitions}
37			\label{sec:FODefinition}
38
39			Fakeable Objects are defined starting from the full
40			lepton selection by relaxing some combination of the identification
41			and isolation requirements. Since most muons in QCD events are
42			from heavy flavor decays, relaxing the identification requirements
43			is not very useful. Thus our muon FO definition consists mainly
44			of relaxing the isolation requirement. On the other hand, for
45			electrons we have more freedom and we use three separate definitions
46			of the FR. Broadly speaking these correspond to relaxing either
47			isolation, or ID, or both. Our FO definitions are given below
48
49			Muon FO definition: relax the following muon requirements from
50			Section~\ref{sec:muID}:
51			\begin{itemize}
52
53			\item $\chi^2$/ndof of global fit $<$ 50 (was $<$ 10).
54			\item Transverse impact parameter with respect to the beamspot
55			$<$ 2 mm (was $<$ 200 $\mu$m).
56			\item $Iso < 0.4$ (was $<$ 0.15).
57
58			\end{itemize}
59
60			Electron V1 FO definition: relax the following electron requirements from
61			Section~\ref{sec:eleID}:
62			\begin{itemize}
63			\item Remove the VBTF90 requirement.
64			\item $Iso < 0.4$ (was $<$ 0.15).
65			\item The impact parameter cut was removed (used to be $<$ 400 $\mu$m).
66			\end{itemize}
67
68			Electron V2 FO definition: relax the following electron requirements from
69			Section~\ref{sec:eleID}:
70			\begin{itemize}
71			\item Remove the VBTF90 requirement.
72			\item The impact parameter cut was removed (used to be $<$ 400 $\mu$m).
73			\end{itemize}
74
75			Electron V3 FO definition: relax the following electron requirements from
76			Section~\ref{sec:eleID}:
77			\begin{itemize}
78			\item $Iso < 0.4$ (was $<$ 0.15).
79			\item The impact parameter cut was removed (used to be $<$ 400 $\mu$m).
80			\end{itemize}
81
82
83			\subsection{Measuring the FR on jet data}
84			\label{sec:FRjet}
85			The FR is measured by studying lepton candidates in jet data.
86			The jet data come from the JetMetTau and JetTauMonitor
87			Primary/Secondary datasets, see Section~\ref{sec:datasets}.
88			We measure the FR on different jet triggers. The stability
89			of the FR in these different jet samples is a measure of the
90			robustness of our procedure. We select the following triggers:
91			\begin{itemize}
92			\item HLT\_L1\_Jet6U from JetMetTauMonitor
93			\item HLT\_L1\_Jet10U from JetMetTauMonitor
94			\item HLT\_Jet15U from JetMetTau
95			\item HLT\_Jet30U from JetMetTau
96			\end{itemize}
97
98			In order to eliminate a possible trigger bias, we scan the list
99			of HLT objects associated with the given jet trigger. If there
100			is only one such object above threshold, we only consider
101			lepton candidates well separated ($\Delta R > 1$) from it.
102
103			Furthermore, even on jet triggers it is possible to collect
104			some $W$ and $Z$ leptonic decays. These events would cause
105			a significant bias to the FR at high $P_T$. To minimize
106			this problem, we reject events with tcMet $>$ 20 GeV and
107			events with two opposite sign FO that make a mass within
108			20 GeV of the $Z$ mass
109			We believe that the bias from leftover $W$ and
110			Drell Yan events in the jet sample is small, but it remains to
111			be estimated.
112
113			The FR are measured as a function of $P_T$ and $\|\eta\|$.
114	claudioc	1.3	The FR projections on the $P_T$ and $\|\eta\|$ axes for the muon FR and for
115	claudioc	1.1	the three (V1, V2, V3) electron FR in the different trigger samples
116	claudioc	1.6	are displayed in
117	claudioc	1.7	{\color{red} Figures~\ref{fig:muFR} and~\ref{fig:eleFR} (old)} and
118			{\color{blue}Figures~\ref{fig:muFR2} and~\ref{fig:eleFR2} (new)}.
119	claudioc	1.6
120	claudioc	1.1
121
122			\begin{figure}[htb]
123			\begin{center}
124	claudioc	1.6	{\color{red}
125	claudioc	1.3	\includegraphics[width=0.48\linewidth]{MuFakeRatesJune1.pdf}
126			\includegraphics[width=0.48\linewidth]{muFReta.pdf}
127	claudioc	1.1	\caption{\label{fig:muFR}The muon fake rate as a function of $P_T$
128	claudioc	1.7	and $\|\eta\|$ in the different jet samples. (Old plots updated below).}
129	claudioc	1.6	}
130	claudioc	1.1	\end{center}
131			\end{figure}
132
133	claudioc	1.6
134
135	claudioc	1.1	\begin{figure}[htb]
136			\begin{center}
137	claudioc	1.6	{\color{blue}
138			\includegraphics[width=0.31\linewidth, angle=90]{MuFakeRatesJuly7.pdf}
139			\includegraphics[width=0.31\linewidth, angle=90]{muFReta7July.pdf}
140			\caption{\label{fig:muFR2}The muon fake rate as a function of $P_T$
141			and $\|\eta\|$ in the different jet samples. Note that these now start at
142			$P_T=$ 10 GeV instead of $P_T=$5 GeV as they did in the earlier analysis
143			because of a preselection aplied in our data handling. For this reason
144			the $\eta$-projections cannot be directly compared since the this is
145			dominated by muons of $P_T$ near threshold. Note also that the
146			muon identification requirements have changed a little bit, as
147	claudioc	1.7	described in Section 3.1.5. (New updated plots).}
148	claudioc	1.6	}
149			\end{center}
150			\end{figure}
151
152
153
154			\begin{figure}[htb]
155			\begin{center}
156			{\color{red}
157	claudioc	1.1	\includegraphics[width=\linewidth]{ElFakeRatesJune1.pdf}
158	claudioc	1.3	\includegraphics[width=\linewidth]{eFReta.pdf}
159	claudioc	1.1	\caption{\label{fig:eleFR}The electron fake rates
160	claudioc	1.3	(V1,V2,V3) as a function of $P_T$ and $\|\eta\|$
161	claudioc	1.7	in the different jet samples. (Old plots updated below).}
162	claudioc	1.6	}
163	claudioc	1.1	\end{center}
164			\end{figure}
165
166	claudioc	1.6
167
168			\begin{figure}[htb]
169			\begin{center}
170			{\color{blue}
171			\includegraphics[width=0.4\linewidth,angle=90 ]{ElFakeRatesJuly7.pdf}
172			\includegraphics[width=0.4\linewidth,angle=90]{eFRetaJuly7.pdf}
173			\caption{\label{fig:eleFR2}The electron fake rates
174			(V1,V2,V3) as a function of $P_T$ and $\|\eta\|$
175			in the different jet samples.
176			Note that the spike removal has been added to the electron
177			selection since the earlier analysis. This is a very
178	claudioc	1.7	small effect. (New updated plots).}
179	claudioc	1.6	}
180			\end{center}
181			\end{figure}
182
183
184	claudioc	1.1	The fake rates are reasonably stable with respect to
185			jet trigger variations, within the $\approx 50\%$ which
186			we believe to be a realistic goal for the FR systematics.
187			There is some evidence for the V2 electron FR to be more stable than
188			the V1 and V3 versions. This is expected from earlier MC studies: the FO
189			V2 isolation requirement is the same as in the full electron selection,
190			and thus the dependence on the amount of jet activity near the electron
191			candidate is minimized.
192
193			The FR binning
194			is quite coarse, because of the lack of statistics. This will improve
195			as we collect more data. In any case, the
196			FR does not appear to change very fast as a function of $P_T$.
197
198	claudioc	1.4
199	claudioc	1.6	\clearpage
200
201	claudioc	1.4	\subsection{Loosening the isolation requirement for the muon FO}
202			Loosening the isolation requirement for the muon FO would reduce the
203			muon FR. This is in general ``a good thing''\texttrademark.
204			However, the price one then pays is that the jet dependence of the
205			FR increases. This is illustrated in Figure~\ref{fig:FRlooseIso}.
206
207			In the $P_T \approx 8$ GeV bin, the ratio of FR in the two extreme triggers
208			(HLT\_L1Jet6U and HLT\_Jet30U) increases from 1.6 (FO-Iso $<$ 0.4) to 2.0
209			(FO-Iso $<$ 0.6) to 2.4 (FO-Iso $<$ 0.8) to 2.9 (FO-Iso $<$ 1.0). Given this
210			behavior, for now we keep the FO isolation requirement to 0.4.
211
212			\begin{figure}[htb]
213			\begin{center}
214			\includegraphics[width=0.7\linewidth,angle=90]{muonFR_differentIso.pdf}
215			\caption{\label{fig:FRlooseIso}Muon FR as a function of $P_T$ in different
216			trigger samples for different choices of the maximum isolation
217			requirement on the muon FO (0.4, 0.6, 0.8, 1.0).}
218			\end{center}
219			\end{figure}
220
221
222	claudioc	1.1	\subsection{Bias due to lepton triggers?}
223			Another possible bias is related to the fact that events used to
224			measure the FR are collected with jet triggers. On the other hand
225			the dilepton analysis is performed using events collected with
226			the photon and muon trigger, see Section~\ref{sec:trigger}.
227			If the FR depends on the firing of the muon/photon trigger,
228			the situation becomes more complicated and
229			we may be forced to define different FR depending on whether or
230			not the muon/photon trigger fired.
231
232			To test this hypothesis, we select events collected with the
233			HLT\_L1\_Jet15U trigger; we then compare the FR computed
234			in the standard way (Figures~\ref{fig:muFR} and~\ref{fig:eleFR})
235			with the FR on the subset of leptons where the HLT\_Mu5 or
236			HLT\_Photon10\_L1R trigger fired\footnote{We made sure that the
237			trigger fired, and that the HLT object that fired the trigger was
238			matched in $\Delta R$ to the lepton candidate.}.
239			The results are displayed in Figures~\ref{fig:muFRtrg}
240			and~\ref{fig:eleFRtrg}.
241
242			\begin{figure}[htb]
243			\begin{center}
244			\includegraphics[width=0.7\linewidth]{MuFakeRatesMu5June1.pdf}
245			\caption{\label{fig:muFRtrg}The muon fake rate in HLT\_L1\_Jet15U
246			as a function of $P_T$ with and without a requirement on the HLT\_Mu5
247			trigger.}
248			\end{center}
249			\end{figure}
250
251
252			\begin{figure}[htb]
253			\begin{center}
254			\includegraphics[width=\linewidth]{ElFakeRatesPhoton10June1.pdf}
255			\caption{\label{fig:eleFRtrg}The electron fake rates
256			(V1,V2,V3) in HLT\_L1\_Jet15U
257			as a function of $P_T$ with and without a requirement on the
258			HLT\_Photon10\_L1R trigger.}
259			\end{center}
260			\end{figure}
261
262			The statistics are not very good, but the lepton trigger bias
263			does not seem to be a significant effect. We tentatively neglect it.
264
265	claudioc	1.5	\clearpage