| 1 |
smorovic |
1.1 |
\section{Signal extraction}
|
| 2 |
beaucero |
1.6 |
\label{sec:SignalExt}
|
| 3 |
ymaravin |
1.27 |
We separate backgrounds into three categories: physics background
|
| 4 |
ymaravin |
1.29 |
from \Z$\gamma$ and \ZZ processes, with a genuine \Z boson from
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| 5 |
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$\Z+jets$ processes, and finally without a genuine \Z boson from
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| 6 |
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$t\bar{t}$ and $\W+jet$ production.
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| 7 |
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|
| 8 |
ymaravin |
1.31 |
The first physics background from \ZZ production is estimated from
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| 9 |
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Monte Carlo simulation. We assigning a very conservative 100\%
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| 10 |
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uncertainty on the estimated \ZZ contribution due to modeling of
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| 11 |
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kinematics of the decay products. The second physics
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| 12 |
ymaravin |
1.29 |
background from \Z$\gamma$ processes is estimated from Monte Carlo
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| 13 |
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simulation as well, although it can be determined from data once the FSR
|
| 14 |
ymaravin |
1.31 |
$\Z\gamma$ signal is measured at CMS. We also assign a conservative 100\%
|
| 15 |
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systematic uncertainty on the \Z$\gamma$ background contribution due
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| 16 |
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to modeling of the photon conversion probability.
|
| 17 |
ymaravin |
1.29 |
|
| 18 |
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Instrumental backgrounds from processes with misidentified leptons
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| 19 |
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attributed to \Z candidate decay products can be estimated from the
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| 20 |
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side-bands of the \Z candidate invariant mass distribution. However,
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| 21 |
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the background is relatively small. We estimate this background to contribute
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| 22 |
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at about 6\% level to the \WZ signal sample and about 20\% of the full
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| 23 |
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background processes. That corresponds to less than 8 events combined
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| 24 |
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for all four signatures for integrated luminosity of 1 \invfb.
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| 25 |
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Thus, it is impractical to infer this background from a sideband
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| 26 |
ymaravin |
1.31 |
fit. Thus, we estimate this background from Monte Carlo simulation
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| 27 |
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and we assign a conservative 100\% systematic uncertainty on the contribution
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| 28 |
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due to modeling of the $t\bar{t}+jets$ and $\W+jets$ background in
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| 29 |
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Monte Carlo simulation.
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| 30 |
ymaravin |
1.10 |
|
| 31 |
ymaravin |
1.29 |
The remaining, largest background is from \Z+misidentified lepton processes
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| 32 |
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that we describe in details below.
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| 33 |
beaucero |
1.8 |
|
| 34 |
ymaravin |
1.29 |
\subsection{Matrix method}
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| 35 |
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\label{sec:D0Matrix}
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| 36 |
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In this Section the ``loose'' and ``tight'' lepton requirements
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| 37 |
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are defined in Section~\ref{sec:looseTight}.
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| 38 |
beaucero |
1.22 |
|
| 39 |
ymaravin |
1.29 |
The idea of a method is to apply ``loose'' identification criteria
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| 40 |
ymaravin |
1.10 |
on the third lepton after \Z boson candidate is identified
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| 41 |
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and count the number of the observed events, $N_{loose}$.
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| 42 |
ymaravin |
1.29 |
These events contain events with real leptons $N_{l}$
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| 43 |
ymaravin |
1.10 |
and events with misidentified jets $N_j$:
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| 44 |
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\begin{equation}
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| 45 |
vuko |
1.21 |
\label{eq:matrixEq1}
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| 46 |
ymaravin |
1.29 |
N_{loose} = N_l + N_j.
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| 47 |
ymaravin |
1.10 |
\end{equation}
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| 48 |
beaucero |
1.4 |
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| 49 |
ymaravin |
1.29 |
If we are to apply ``tight'' selection on the third lepton, the number
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| 50 |
ymaravin |
1.10 |
of the observed events $N_{tight}$ would change as following
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| 51 |
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\begin{equation}
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| 52 |
vuko |
1.21 |
\label{eq:matrixEq2}
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| 53 |
ymaravin |
1.29 |
N_{tight} = \epsilon_{tight} N_l + p_{fake} N_j,
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| 54 |
ymaravin |
1.10 |
\end{equation}
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| 55 |
ymaravin |
1.29 |
where $\epsilon_{tight}$ and $p_{fake}$ are efficiency of ``tight''
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| 56 |
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criteria with respect to ``loose'' requirements for leptons and
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| 57 |
ymaravin |
1.10 |
misidentified jets, respectively. As $N_{loose}$ and $N_{tight}$
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| 58 |
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are directly observable, to extract the number of $Z+jet$ events
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| 59 |
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in the final sample, one needs to measure $\epsilon_{tight}$
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| 60 |
ymaravin |
1.29 |
and $p_{fake}$ in control data samples as described in the next
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| 61 |
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two sections.
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| 62 |
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| 63 |
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If $\epsilon_{tight}$ and $p_{fake}$ are measured as functions of some
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| 64 |
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variable, for example, lepton $p_T$, then it is possible to estimate
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| 65 |
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the background as function of $p_T$ by applying the matrix method to
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| 66 |
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binned distribution of $dN_{tight}/dp_T$ and $dN_{loose}/dp_T$.
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| 67 |
smorovic |
1.1 |
|
| 68 |
beaucero |
1.8 |
\subsubsection{Determination of $\epsilon_{tight}$}
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| 69 |
smorovic |
1.9 |
|
| 70 |
ymaravin |
1.10 |
To estimate the $\epsilon_{tight}$ we apply ``tag-and-probe'' method
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| 71 |
ymaravin |
1.29 |
using $\Z \to \ell\ell$ from \Z+jets Chowder sample, including \W+jets
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| 72 |
smorovic |
1.9 |
and $t\bar{t}$ as background. \Z mass distribution is separated for two cases where
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| 73 |
ymaravin |
1.29 |
leptons from \Z boson decay either both pass ``tight'' selection (``tight-tight'' case), or only
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| 74 |
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one passes the ``tight'' selection, while the other electron passes ``loose'' but not ``tight''
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| 75 |
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selection (``tight-loose'' case).
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| 76 |
smorovic |
1.9 |
|
| 77 |
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Equation for determination of signal efficiency is given as
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| 78 |
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\begin{equation}
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| 79 |
ymaravin |
1.29 |
\epsilon_{tight}=\frac{ 2(N_{TT}-B_{TT}) }{ (N_{TL}-B_{TL})+2(N_{TT}-B_{TT}) }
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| 80 |
beaucero |
1.26 |
\label{eq:errmatrix}
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| 81 |
smorovic |
1.9 |
\end{equation}
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| 82 |
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|
| 83 |
ymaravin |
1.29 |
where $N_{TT}$, $B_{TT}$, $N_{TL}$, and $B_{TL}$ are numbers of signal plus background
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| 84 |
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and background events for ``tight-tight'' and ``loose-tight'' electron combinations,
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| 85 |
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respectively. We estimated an efficiency for both electrons and muons to be
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| 86 |
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$\epsilon_{tight}=0.98 \pm 0.01$.
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| 87 |
smorovic |
1.9 |
|
| 88 |
ymaravin |
1.10 |
\subsubsection{Determination of $p_{fake}$}
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| 89 |
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|
| 90 |
ymaravin |
1.29 |
The probability of a jet to be misidentified as a lepton depends on
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| 91 |
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$p_T$, $\eta$, and composition of quarks and gluons. Although the
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| 92 |
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light quark and gluons have a very similar misidentification rate
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| 93 |
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(see Fig.~\ref{fig:pfake_gg_qq}), this rate can be different for jets
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| 94 |
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enriched with heavy quark jets. Thus, we propose to measure the
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| 95 |
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$p_{fake}$ in the \W+jets sample, as jets in this sample has a very
|
| 96 |
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similar composition as those in \Z+jets process, the major background
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| 97 |
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to the signal.
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| 98 |
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|
| 99 |
ymaravin |
1.10 |
\begin{figure}[bt]
|
| 100 |
|
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\begin{center}
|
| 101 |
ymaravin |
1.29 |
\scalebox{0.4}{\includegraphics{figs/pfake_gg_qq.eps}}
|
| 102 |
|
|
\caption{The misidentification probability $p_{fake}$ measured in light-quark jets (left),
|
| 103 |
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and gluon jets (right) using multi-jet {\sl ALPGEN} Monte Carlo simulation.}
|
| 104 |
|
|
\label{fig:pfake_gg_qq}
|
| 105 |
ymaravin |
1.10 |
\end{center}
|
| 106 |
|
|
\end{figure}
|
| 107 |
|
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|
| 108 |
ymaravin |
1.29 |
We select the \W+jets sample for electron misidentification study as follows:
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| 109 |
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\begin{itemize}
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| 110 |
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\item event must be triggered by the HLTSingleMuonIso trigger,
|
| 111 |
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\item event must not have a \Z boson candidate with an invariant mass between 50 and 120 GeV,
|
| 112 |
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\item event must have a muon candidate within the acceptance with $p_T >$ 20 GeV satisfying
|
| 113 |
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isolation and impact parameter significance requirements; the transverse mass of the muon candidate
|
| 114 |
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and the MET in the event must exceed 50 GeV,
|
| 115 |
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\item event must have only one electron candidate that satisfies loose identification requirements with $p_T > 20$ GeV,
|
| 116 |
|
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isolated from the muon candidate by $\Delta R > 0.1$,
|
| 117 |
|
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\item muon and electron must have the same charge to suppress $t\bar{t}$ events with real muon and electrons from \W
|
| 118 |
|
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boson decays.
|
| 119 |
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\end{itemize}
|
| 120 |
|
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The ``tight'' criteria is just an application of the above-mentioned requirements with an additional criterion
|
| 121 |
|
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on the electron candidate to pass ``tight'' electron identification criteria.
|
| 122 |
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|
| 123 |
|
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The probability $p_{fake}$ is then measured as the ratio of the $p_T$ distribution of the ``tight'' electron
|
| 124 |
|
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candidates to the $p_T$ distribution of the ``loose'' electron candidates in the original sample. This
|
| 125 |
|
|
probability agrees well with the one obtained from the multi-jet sample and is given in Fig.~\ref{fig:pfake_w}.
|
| 126 |
|
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The errors correspond to statistical errors expected for a data sample with integrated luminosity of 300 \invpb.
|
| 127 |
|
|
Thus, it is possible to extract $p_{fake}$ with $\sim$10\% accuracy with early CMS data.
|
| 128 |
|
|
\begin{figure}[hbt]
|
| 129 |
vuko |
1.14 |
\begin{center}
|
| 130 |
ymaravin |
1.29 |
\scalebox{0.6}{\includegraphics{figs/pFake_300pb_WX_TTbar.eps}}
|
| 131 |
|
|
\caption{Probability of a misidentified jet from \W+jet processes that passed ``loose'' electron identification
|
| 132 |
|
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requirements to also pass tight ones as function of the candidate's $p_T$. The errors correspond to
|
| 133 |
|
|
statistical errors expected for a 300 \invpb integrated luminosity. The distribution is also fit to a
|
| 134 |
|
|
constant to extract the flat $p_{fake}$ factor. }
|
| 135 |
|
|
\label{fig:pfake_w}
|
| 136 |
vuko |
1.14 |
\end{center}
|
| 137 |
|
|
\end{figure}
|
| 138 |
|
|
|
| 139 |
ymaravin |
1.29 |
A similar method can be used to extract the $p_{fake}$ for the muon misidentification as well.
|
| 140 |
vuko |
1.14 |
|
| 141 |
ymaravin |
1.29 |
\subsubsection{Cross-check of the $p_{fake}$ using multi-jet sample}
|
| 142 |
vuko |
1.14 |
|
| 143 |
ymaravin |
1.29 |
In the following we perform an additional cross-check of $p_{fake}$ measured
|
| 144 |
|
|
in different control sample, enriched with multi-jet processes. In the sample,
|
| 145 |
|
|
selected with jet triggers, we select a ``loose'' electron candidates that are
|
| 146 |
|
|
separated from the jet that satisfied the trigger requirement. These candidates
|
| 147 |
|
|
are dominated by the misidentified light quark and gluon jets. The admixture
|
| 148 |
|
|
of converted photons from $\gamma + jets$ is small at the low-$p_T$ range and is
|
| 149 |
|
|
neglected.
|
| 150 |
|
|
The $p_{fake}$ function of $p_T$ and $\eta$ is obtained by dividing the $p_T$ and $\eta$
|
| 151 |
|
|
distributions for the electron candidate that satisfied ``tight''
|
| 152 |
ymaravin |
1.10 |
electron identification requirements to that for electron candidates
|
| 153 |
ymaravin |
1.29 |
that satisfied ``loose''. We estimate the $p_{fake}=0.32 \pm 0.04$ for
|
| 154 |
vuko |
1.20 |
electrons.
|
| 155 |
|
|
|
| 156 |
vuko |
1.17 |
For muons, a similar procedure has been applied. Since the bulk
|
| 157 |
|
|
of background muons is coming from heavy quark decays, we select
|
| 158 |
|
|
a $b\bar{b}$ sample as control sample. As an exercise, we selected
|
| 159 |
|
|
electron-triggered events on a $b\bar{b}$ Monte Carlo sample,
|
| 160 |
|
|
required one ``loose electron'' in the event and looked for
|
| 161 |
|
|
for muon candidates that are not close to the electron candidate,
|
| 162 |
ymaravin |
1.25 |
and determined $p_{fake}$ on this sample of muons. The $p_T$ spectrum
|
| 163 |
vuko |
1.17 |
for ``loose'' and ``tight'' muons and their ratio is shown in
|
| 164 |
vuko |
1.20 |
Figure~\ref{fig:mu_pfake}. The factor $p_{fake}$ for muons estimated
|
| 165 |
|
|
in this way amounts to $0.08 \pm 0.01$.
|
| 166 |
vuko |
1.17 |
|
| 167 |
|
|
|
| 168 |
ymaravin |
1.29 |
\begin{figure}[bt]
|
| 169 |
|
|
\begin{center}
|
| 170 |
|
|
\scalebox{0.6}{\includegraphics{figs/tight_eff_gumbo.eps}}
|
| 171 |
|
|
\caption{Fraction of electron candidates passing the ``tight'' criteria
|
| 172 |
|
|
in multi-jet event. No trigger requirement has been applied.}
|
| 173 |
|
|
\label{fig:qcd_efftight_noHLT}
|
| 174 |
|
|
\end{center}
|
| 175 |
|
|
\end{figure}
|
| 176 |
beaucero |
1.22 |
|
| 177 |
beaucero |
1.18 |
\begin{figure}[!bt]
|
| 178 |
|
|
\begin{center}
|
| 179 |
ymaravin |
1.29 |
\scalebox{0.6}{\includegraphics{figs/p0_p_fake_mu_fit.eps}}
|
| 180 |
|
|
\caption{Determination of $p_{fake}$ for muons. Top plot: $p_T$ spectrum
|
| 181 |
|
|
of muons passing the ``loose'' and ``tight'' criteria in $b\bar{b}$ events
|
| 182 |
|
|
in the ``Stew'' soup that corresponds to 20 \invpb of integrated luminosity,
|
| 183 |
|
|
accepted by electron triggers; bottom plot: fraction of muon candidates
|
| 184 |
|
|
passing the ``tight'' criteria. A constant fit is overlayed.}
|
| 185 |
|
|
\label{fig:mu_pfake}
|
| 186 |
beaucero |
1.18 |
\end{center}
|
| 187 |
|
|
\end{figure}
|
| 188 |
vuko |
1.21 |
|
| 189 |
|
|
|
| 190 |
ymaravin |
1.29 |
|
| 191 |
|
|
\subsubsection{Background determination results}
|
| 192 |
|
|
|
| 193 |
|
|
\begin{table}[h]
|
| 194 |
|
|
\begin{center}
|
| 195 |
|
|
\begin{tabular}{lcccc} \hline \hline
|
| 196 |
|
|
& 3e &2e1$\mu$ & 2$\mu$1e &3$\mu$\\ \hline
|
| 197 |
beaucero |
1.30 |
$N$ - ZZ - Z$\gamma$ - W+jets - $t\bar{t}$ & 18.1$\pm$1.7 & 17.7$\pm$6.2 & 22.3$\pm$1.4 & 20.0$\pm$5.9\\ \hline
|
| 198 |
|
|
$N^{genuine~Z}$ (matrix method) & 10.1 $\pm$3.2 & 9.4 $\pm$6.7 & 14.5 $\pm$2.9 & 9.4 $\pm$6.4\\ \hline
|
| 199 |
|
|
$N^{WZ}$ & 8.0 $\pm$3.6 & 8.3 $\pm$9.1 & 7.8 $\pm$3.2 & 10.6 $\pm$8.7\\ \hline
|
| 200 |
ymaravin |
1.29 |
\WZ from MC &8.1&9.0& 9.2 &11.3\\
|
| 201 |
|
|
\hline
|
| 202 |
|
|
\end{tabular}
|
| 203 |
|
|
\caption{Expected number of events for an integrated luminosity of 300 \invpb for the signal
|
| 204 |
|
|
and estimated background for 81 GeV $< M_Z < $ 101 GeV with ``loose'' \W lepton criteria.}
|
| 205 |
|
|
\label{tab:FinalNoFitloose}
|
| 206 |
|
|
\end{center}
|
| 207 |
|
|
\end{table}
|
| 208 |
|
|
|
| 209 |
|
|
\begin{table}[h]
|
| 210 |
|
|
\begin{center}
|
| 211 |
|
|
\begin{tabular}{lcccc} \hline \hline
|
| 212 |
|
|
& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
|
| 213 |
beaucero |
1.30 |
$N$ - ZZ -Z$\gamma$ - W+jets - $t\bar{t}$ &11.1$\pm$1.3 &8.2$\pm$0.9 &12.1$\pm$1.2 &10.5$\pm$0.8\\ \hline
|
| 214 |
|
|
$N^{genuine~Z}$ (matrix method) &3.2 $\pm$1.7 &0.6 $\pm$0.8 &4.6 $\pm$2.0 &0.6 $\pm$0.9\\ \hline
|
| 215 |
|
|
$N^{\WZ}$ &7.9 $\pm$2.1 &7.6 $\pm$1.2 &7.5 $\pm$2.3 &10.0$\pm$1.2\\ \hline
|
| 216 |
ymaravin |
1.29 |
\WZ from MC &7.9&8.1& 9.0 &10.1\\ \hline
|
| 217 |
|
|
\end{tabular}
|
| 218 |
|
|
\caption{Expected number of events for an integrated luminosity of 300 \invpb for the signal
|
| 219 |
|
|
and estimated background for 81 GeV $< M_Z < $ 101 GeV and ``tight'' \W lepton requirement.}
|
| 220 |
|
|
\label{tab:FinalNoFit}
|
| 221 |
|
|
\end{center}
|
| 222 |
|
|
\end{table}
|
| 223 |
|
|
|
| 224 |
|
|
Using the values of $\epsilon_{tight}$ and $p_{fake}$ obtained
|
| 225 |
|
|
from the methods described in the previous sections, we estimated
|
| 226 |
|
|
the backgrounds from genuine \Z decays by solving Eqs.~\ref{eq:matrixEq1}
|
| 227 |
|
|
and \ref{eq:matrixEq2} for $N_j$. The comparisons between predicted and true MC
|
| 228 |
|
|
backgrounds are given in Tables~\ref{tab:FinalNoFitloose} and \ref{tab:FinalNoFit}
|
| 229 |
|
|
for ``loose'' and ``tight'' \W lepton, respectively.
|
| 230 |
|
|
The agreement between estimated and MC true backgrounds is excellent.
|
| 231 |
|
|
|
| 232 |
|
|
|
| 233 |
beaucero |
1.30 |
\clearpage
|
