| 1 |
|
\section{Signal extraction} |
| 2 |
< |
%\label{sec:gen} |
| 3 |
< |
\subsection{Z+jets background fraction} |
| 4 |
< |
|
| 5 |
< |
After applying "Official Tight" selection on electron decaying from W, there |
| 6 |
< |
is still a significant fraction of Z+jets events passing selection, due to |
| 7 |
< |
two orders of magnitude bigger cross section of the background processes. |
| 8 |
< |
In this section we describe a method to estimate fake rate coming from Z+jets |
| 9 |
< |
background, which has a significant contribution in channels where $W^{\pm}$ |
| 10 |
< |
decays into $e^{pm}$ and neutrino. |
| 11 |
< |
|
| 12 |
< |
Z bosons from Z+jet events will be with the same efficiency reconstructed with |
| 13 |
< |
a Z mass between a $\pm 20$ window. Background rate is already reduced after applying |
| 14 |
< |
"Simple Tight" selection to the W electron. We first apply "Tight Loose" selection for |
| 15 |
< |
$W\pm$ electron, while later we apply "Simple Tight" selection to count number of events |
| 16 |
< |
passing selection in both cases. Number of events are named respectively, $N_l$ and $N_t$. |
| 17 |
< |
|
| 18 |
< |
$Nl$ contains an unknown numbers of signal and background events, $N_s$ and $N_b$, so a |
| 19 |
< |
number of "Simple Loose" events is $Nl=Ns+Nb$ Number of events passing "Simple Tight is |
| 20 |
< |
$N_t=\epsilon_s * N_s + \epsilon_b * N_b$. It is possible to calculate background fraction |
| 21 |
< |
$N_b/(N_s+N_b)$ if we are able to estimate $\epsilon_s$ and $\epsilon_b$, signal and background |
| 22 |
< |
efficiency. Their estimation is done using control data samples, which contain either electrons |
| 23 |
< |
or jets with high purity. Tag and probe method is used to determine signal efficiency $\epsilon_b$. |
| 24 |
< |
The rate will be derived from $Z \to e^+e^-$ samples. In the following text we describe method |
| 25 |
< |
used to determine $\epsilon_{B}$. |
| 26 |
< |
|
| 27 |
< |
\subsection{Method description} |
| 28 |
< |
|
| 29 |
< |
We apply "Simple Loose" selection on jets from QCD and photon+jet control samples for fake rate |
| 30 |
< |
estimation of Z+jets jet selected as $W\pm$ electron. The samples used in analysis are CSA07 |
| 31 |
< |
Gumbo samples, with Pythia ID filtering so that only events from photon+jets, QCD and minimum |
| 32 |
< |
bias event are used. As the sample contains event classes with different event weight, separated |
| 33 |
< |
by $\hat{P_t}$ value and Pythia ID, we calculate weight as $w_i=\frac{\sigma_i}{N_i}$ where |
| 34 |
< |
$\sigma_i$ and $N_i$ are respective cross section and event number for event class with the |
| 35 |
< |
same event weight. "Simple Loose" selection is applied to each reconstructed pixel-matched GSF electron found in event. |
| 36 |
< |
In case of having more than one reconstructed electron objects per event passing selection, |
| 37 |
< |
we appy the same weight to each. Efficiency, defined as a ratio of number of objects passing "Simple Tight" |
| 38 |
< |
and "Simple Loose" selection, given as a function of $Pt$ and $\eta$, is showed in plots \ref{fig:qcd_zjet_est}. |
| 39 |
< |
|
| 40 |
< |
Since the data collected by the CMS is filtered by the trigger, the trigger bias study was done one the Gumbo |
| 41 |
< |
control sample. After requiring all events to pass a HLT1jet trigger path, which cuts on a 200 GeV Pt treshold |
| 42 |
< |
of the single jet, there is significant drop of the efficiency in the area of interest, 20-100 GeV, as shown |
| 43 |
< |
in the plot \ref{fig:qcd_zjet_est-missing}. First assumption, that removing objects within a $0.1 \Delta R$ cone to |
| 44 |
< |
a HLT Jet object which triggered the HLT1jet path would restore efficiency as seen without trigger requirement, |
| 45 |
< |
prooved insufficient, with efficiency still being significantly biased in the 20-100 GeV range. We assume that |
| 46 |
< |
this is due to other jets in the event having similar energy to the triggering jet, so with the leading jet of |
| 47 |
< |
200 GeV Pt or higher this effectively removes events with jets from the lower Pt range. New attempt was made to |
| 48 |
< |
remove all reconstructed electrons from the selection within the $\Delta R$ cone with any of the jets triggering |
| 49 |
< |
HLT1jet, HLT2jet, HLT3jet and HLT4jet trigger paths, with respective jet tresholds 200, 150, 85 and 60 GeV. |
| 50 |
< |
Since the tresholds are lower, we assume to have more events with real jets in low Pt range (50-100 GeV). |
| 51 |
< |
Resulting efficiency is shown in the plot \ref{fig:tight_eff_gumbo-missing2}. |
| 2 |
> |
\label{sec:SignalExt} |
| 3 |
> |
Two kind of background are affected this analysis: background having |
| 4 |
> |
already a $Z$ boson in the final state such as $Z+jets$ and |
| 5 |
> |
$Z+b\bar{b}$, background without a $Z$ boson such as $W+jets$ and |
| 6 |
> |
$t\bar{t}$. The first one will be peaking as the signal in the $Z$ |
| 7 |
> |
mass distribution while the second should be flat.As a starting point, |
| 8 |
> |
we will use this properties to separate the two background. |
| 9 |
> |
|
| 10 |
> |
\subsection{Study of non peaking background} |
| 11 |
> |
In order to measure this background, a fit of the signal and |
| 12 |
> |
background is done. In order to fit the signal peak we use a Gaussian |
| 13 |
> |
convulated with a Breit-Wigner. The background is fitted by a line. |
| 14 |
> |
An example of the fit of the distribution composed by the sum of |
| 15 |
> |
signal and background for the 3 electrons final state is shown on |
| 16 |
> |
figure~\ref{fig:ZFit}. |
| 17 |
> |
\begin{figure}[!bp] |
| 18 |
> |
\begin{center} |
| 19 |
> |
\scalebox{0.4}{\includegraphics{figs/FitBkg3eTight.eps}} |
| 20 |
> |
\caption{$Z$ mass distribution which contains the sum of signal and background on which a fit is performed to extract the number of non peaking background events within the 81 GeV and 101GeV.} |
| 21 |
> |
\label{fig:ZFit} |
| 22 |
> |
\end{center} |
| 23 |
> |
\end{figure} |
| 24 |
|
|
| 25 |
+ |
The comparison between the Monte Carlo information and the value |
| 26 |
+ |
obtain by the fit for a $Z$ mass range [81,101] GeV is given in |
| 27 |
+ |
table~\ref{tab:FitVsMC}. |
| 28 |
+ |
|
| 29 |
+ |
\begin{table}[!tb] |
| 30 |
+ |
\begin{center} |
| 31 |
+ |
|
| 32 |
+ |
\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline |
| 33 |
+ |
Channel & $Z+jets$ & $Zb\bar{b}$ & $t\bar{t}$ & $W+jets$ & $t\bar{t}$ + $W+jets$ & Fit result \\ \hline |
| 34 |
+ |
$3e$ Loose & 196.5 & 67.4 & 35.7 & 0 & 35.7& 37.8 \\ \hline |
| 35 |
+ |
$3e$ Tight & 78.9 & 38.5 & 28.1 & 0 & 28.1 & 32.9 \\ \hline |
| 36 |
+ |
$2\mu 1e$ Loose & 189.6 & 52.6 & 4.7 & 0 & 4.7 & 5.7 \\ \hline |
| 37 |
+ |
$2\mu 1e$ Tight & 63.1 & 18.2 & 1.3 & 0 & 1.3 & 1.5 \\ \hline |
| 38 |
+ |
$2e1\mu$ & 10.4 & 9.1 & 30.7 & 2.9 & 33.6 & 29.2 \\ \hline |
| 39 |
+ |
$3\mu$ & 1.9 & 7.7 & 0.7 & 0 & 0.7 & 0\\ \hline |
| 40 |
+ |
\end{tabular} |
| 41 |
+ |
|
| 42 |
+ |
\end{center} |
| 43 |
+ |
\caption{Comparison between monte carlo expectation for the analysis and the results of the fit for the non peaking background. Number of event are integrated between [81,101] GeV. The Loose and Tight criteria apply so far, for final state where $W\rightarrow e\nu$. One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples. |
| 44 |
+ |
} |
| 45 |
+ |
\label{tab:FitVsMC} |
| 46 |
+ |
\end{table} |
| 47 |
+ |
|
| 48 |
+ |
|
| 49 |
+ |
\subsection{Study of peaking background} |
| 50 |
+ |
\label{sec:D0Matrix} |
| 51 |
+ |
The probability to misidentify a jet as a muon is very low while for |
| 52 |
+ |
the case of the electron, $\pi^0$ in jets can be misidentified as |
| 53 |
+ |
electrons. When considering the subtraction of the background in this |
| 54 |
+ |
analysis, we will mainly concentrate on the final state where the $W$ |
| 55 |
+ |
is decaying to an electron. The same studies is still on going for the |
| 56 |
+ |
muon case. |
| 57 |
+ |
|
| 58 |
+ |
\subsubsection{Z+jets background fraction} |
| 59 |
+ |
The main background remaining even after having applied all our selection |
| 60 |
+ |
in the case of the $W$ decaying to electron is the $Z+jets$ |
| 61 |
+ |
production. As signal and background have a \Z boson in the final |
| 62 |
+ |
state, we will concentrate on the third lepton which is an electron in |
| 63 |
+ |
this study. |
| 64 |
+ |
|
| 65 |
+ |
In order to select the \Z candidate in the events, we apply loose |
| 66 |
+ |
criteria. The loose sample contain a given number of signal events |
| 67 |
+ |
which contains a third isolated electron and a given number of |
| 68 |
+ |
background events which do not contains a third isolated |
| 69 |
+ |
electron. When we apply the tight criteria the fraction of signal and |
| 70 |
+ |
background events is changing according to the efficiency of the |
| 71 |
+ |
criteria. This can be expressed by this formula: |
| 72 |
+ |
\begin{eqnarray} |
| 73 |
+ |
N_{loose} & = & \hspace*{0.9cm} N_e + \hspace*{0.9cm} N_{j} \\ |
| 74 |
+ |
N_{tight} & = & \epsilon_{tight} N_e + p_{fake} N_{j} |
| 75 |
+ |
\end{eqnarray} |
| 76 |
+ |
Where $N_{loose}$ and $N_{tight}$ are the numbers of events in |
| 77 |
+ |
the loose and tight samples, respectively, $N_e$ is the number of events with a third |
| 78 |
+ |
isolated electron, $N_j$ is the number of events without a third |
| 79 |
+ |
isolated electron, $\epsilon_{tight}$ is the efficiency of the tight |
| 80 |
+ |
criteria on electron, $p_{fake}$ is the probability for a jet identified |
| 81 |
+ |
as a loose electron to be also identified as a tight electron. By |
| 82 |
+ |
solving this set of equations we obtain: |
| 83 |
+ |
$$ |
| 84 |
+ |
N_e = \frac{N_{tight}-p_{fake} N_{loose}} { \epsilon_{tight} -p_{fake}} \ \ \ \mbox{and} \ \ \ |
| 85 |
+ |
N_{j} = \frac{ \epsilon_{tight} N_{loose} - N_e}{ \epsilon_{tight} -p_{fake}} |
| 86 |
+ |
$$ |
| 87 |
+ |
|
| 88 |
+ |
The estimation of $\epsilon_{tight}$ and $p_{fake}$ can be done using control |
| 89 |
+ |
samples, containing electrons and jet respectively with high purity. The Tag and probe |
| 90 |
+ |
method is used to determine signal efficiency $\epsilon_{tight}$. The rate |
| 91 |
+ |
will be derived from $Z \to e^+e^-$ samples. In the following section we |
| 92 |
+ |
describe the method used to determine $p_{fake}$. |
| 93 |
+ |
|
| 94 |
+ |
\subsubsection{Determination of $p_{fake}$} |
| 95 |
+ |
|
| 96 |
+ |
As the events will be most of the time triggered by the leptons coming |
| 97 |
+ |
from \Z boson, we assume that the third lepton is unbiased toward |
| 98 |
+ |
trigger requirement. Ideally we need a sample of pure multi-jet events |
| 99 |
+ |
in order to compute the probability for a jet identified as a loose |
| 100 |
+ |
electron to be also identified as a tight electron. In selecting such |
| 101 |
+ |
a sample in data, one has to avoid any bias from the trigger |
| 102 |
+ |
requirements on the loose electron candidate. |
| 103 |
+ |
%Such sample will not |
| 104 |
+ |
%exist in data as they will be bias by the trigger requirement. |
| 105 |
|
\begin{figure}[bt] |
| 106 |
|
\begin{center} |
| 107 |
< |
\scalebox{0.8}{\includegraphics{figs/tight_eff_gumbo.eps}} |
| 108 |
< |
\caption{Efficiency of "Simple Tight" over "Simple Loose" reconstructed fake electrons on Gumbo sample |
| 109 |
< |
(QCD, photon+jets and minimum-bias events). Distributions are shown in $P_t$ and $\eta$.} |
| 110 |
< |
\label{fig:tight_eff_gumbo} |
| 107 |
> |
\scalebox{0.6}{\includegraphics{figs/tight_eff_gumbo.eps}} |
| 108 |
> |
\caption{Fraction of electron candidates passing the tight criteria |
| 109 |
> |
in QCD event. No trigger requirement has been applied.} |
| 110 |
> |
\label{fig:qcd_efftight_noHLT} |
| 111 |
|
\end{center} |
| 112 |
|
\end{figure} |
| 113 |
|
|
| 114 |
+ |
From a sample of multi-jet events triggered by an ``OR'' of multi-jet |
| 115 |
+ |
triggers, we will select loose electron candidates that are not |
| 116 |
+ |
matched to any of the triggering object |
| 117 |
+ |
%we will reject the object matched with the triggering |
| 118 |
+ |
%objects. This will allow us to have a unbiased sample of multi-jet |
| 119 |
+ |
%events. For the purpose of the study, we have used CSA07 Gumbo |
| 120 |
+ |
%samples, with Pythia ID filtering in order to keep only events from |
| 121 |
+ |
%photon+jets, QCD and minimum bias events. |
| 122 |
+ |
The removal of the object matched with the triggering object is done |
| 123 |
+ |
using a matching cone of $\Delta R =0.2$. "Simple Loose" selection is |
| 124 |
+ |
applied to each reconstructed electron from this sample of jets from |
| 125 |
+ |
QCD and photon+jet. Then the tight criteria is applied on such loose |
| 126 |
+ |
electrons and the $p_{fake}$ is simply the ratio of this two |
| 127 |
+ |
population. This ratio, given as a function of $Pt$ and $\eta$, is |
| 128 |
+ |
showed in plots \ref{fig:qcd_zjet_est}. |
| 129 |
|
|
| 130 |
< |
|
| 131 |
< |
%for the last part, it is still to be seen if the method works, though. |
| 130 |
> |
\subsubsection{Determination of $\epsilon_{tight}$} |
| 131 |
> |
TO BE WRITTEN... SRECKO??? |
