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\label{sec:gen} |
| 3 |
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\subsection{Monte Carlo generators} |
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The signal and background samples for the full detector simulation |
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< |
were generated with the leading order event generator PYTHIA~\cite{Sjostrand:2003wg}. To |
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< |
accomodate NLO effect constant k-factors were applied. |
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< |
Additionally the cross section calculator MCFM~\cite{Campbell:2005} was used to determine |
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the next-to-leading order differential cross section for the WZ |
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production process. To estimate the PDF uncertainty for the signal |
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process at NLO the NLO event generator MC@NLO 3.1~\cite{Frixione:2002ik} together with PDF set |
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CTEQ6M was used. |
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|
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\subsection{Signal Definition} |
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|
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This analysis is studying the final state of on-shell $W$ and $Z$ |
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boson, both of them decaying leptonically. The fully final leptonic |
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final state $l^+ l^- l^\pm \nu$ also receives a contribution from the |
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< |
$W\gamma *$ process, where the $\gamma *$ stands for a virtual photon |
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< |
through the $WW\gamma$ vertex. In this analysis, only events with $l^+ |
| 20 |
< |
l^-$ invariant mass consistent with $Z$ mass will be considered. |
| 5 |
> |
are generated with the leading order (LO) event generators |
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> |
{\sl PYTHIA}~\cite{Sjostrand:2003wg}, {\sl ALPGEN} and {\sl COMPHEP}. |
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> |
To accommodate the next-to-leading (NLO) effects, constant $k$-factors are applied |
| 8 |
> |
except for the signal where a $p_T$-dependence has been taken into account |
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> |
and some of the backgrounds, $e.g.$ $t\bar{t}$, $W+jets$, and $Z+jets$ samples, |
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> |
officially produced with NLO effects taken into account. |
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> |
|
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> |
The $p_T$-dependent $k$-factor for the signal is estimated using |
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the NLO cross section calculator {\sl MCFM}~\cite{Campbell:2005}. |
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We estimate the PDF uncertainty on the cross-section using |
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> |
{\sl MC@NLO 3.1}~\cite{Frixione:2002ik} NLO event generator |
| 16 |
> |
together with CTEQ6M PDF set. |
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> |
|
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> |
\subsection{Signal definition} |
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> |
The goal of this analysis is to study the associative production of the on-shell |
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> |
$\W$ and $\Z$ bosons that decay into three leptons and a neutrino. In the |
| 21 |
> |
following we refer to a lepton to as either a muon or an electron, unless |
| 22 |
> |
specified otherwise. |
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> |
|
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> |
Using {\sl MCFM} we estimate the total NLO $\WZ$ cross-section to be |
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> |
\begin{equation} |
| 26 |
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\sigma_{NLO} ( pp \rightarrow W^+\Z; \sqrt{s}=14~{\rm TeV}) = 30.5~{\rm pb}, |
| 27 |
> |
\end{equation} |
| 28 |
> |
\begin{equation} |
| 29 |
> |
\sigma_{NLO} ( pp \rightarrow W^-\Z; \sqrt{s}=14~{\rm TeV}) = 19.1~{\rm pb}. |
| 30 |
> |
\end{equation} |
| 31 |
> |
|
| 32 |
> |
The LO and NLO distributions of the \Z boson transverse momentum are |
| 33 |
> |
shown in Fig.~\ref{fig:LOvsNLO} with the case of $W^+$ on the left and $W^-$ |
| 34 |
> |
on the right side. The NLO/LO ratio, $k$-factor, is also presented on the figure, |
| 35 |
> |
and it is increasing with $p_T(\Z)$. We take into account the $p_T$ dependence |
| 36 |
> |
by re-weighting the LO Monte Carlo simulation as a function of the $p_T(\Z)$. |
| 37 |
> |
% |
| 38 |
> |
% |
| 39 |
> |
%The $p_T$ dependence of the $k$-factor |
| 40 |
> |
%becomes important when a proper NLO description of the $\Z$ boson transverse |
| 41 |
> |
%momentum must be obtained, $e.g$ to measure the strength of the $WWZ$ coupling. |
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> |
%As the focus of this analysis is to prepare for the cross-section measurement, |
| 43 |
> |
%we take a $p_{T}$-averaged value of the $k$-factor, equal to 1.84. |
| 44 |
> |
|
| 45 |
> |
\begin{figure}[!bt] |
| 46 |
> |
\begin{center} |
| 47 |
> |
\scalebox{0.8}{\includegraphics{figs/LOvsNLOZPtWminuns.eps}\includegraphics{figs/LOvsNLOZPtWplus.eps}} |
| 48 |
> |
\caption{$p_T(Z)$ distribution for LO (solid black histogram) and NLO (dashed black histogram) |
| 49 |
> |
in $W^-\Z$ events (left) and $W^+\Z$ events (right). The ratio NLO/LO is also given as a red |
| 50 |
> |
solid line. |
| 51 |
> |
} |
| 52 |
> |
\label{fig:LOvsNLO} |
| 53 |
> |
\end{center} |
| 54 |
> |
\end{figure} |
| 55 |
|
|
| 56 |
|
%# for bbll: |
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|
%#CS NLO ((Z/gamma*->l+l-)bb) = 830pb = 345 pb * 2.4, where: |
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|
%# 830x0.173 (== XS x eff.) = 143.59pb |
| 61 |
|
|
| 62 |
|
|
| 63 |
< |
\begin{table}[tbh] |
| 30 |
< |
\begin{tabular}{llllll} \hline |
| 31 |
< |
Sample & Generator & Sample name & Events & $\sigma \cdot \epsilon \cdot k$ & k-factor \\ \hline |
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< |
WZ & Pythia & /WZ/CMSSW\_1\_6\_7-CSA07-1195663763/RECO & 58897 & 0.585 pb & 1.92 \\ |
| 33 |
< |
$Zb\bar{b}$ & COMPHEP & /comphep-bbll/CMSSW\_1\_6\_7-CSA07-1198677426/RECO & 143.59 pb & 2.4 \\ |
| 34 |
< |
``Chowder'' & ALPGEN & /CSA07AllEvents/CMSSW\_1\_6\_7-CSA07-Chowder-A1-PDAllEvents-ReReco-100pb/RECO & 25 M & event weights & - \\ |
| 35 |
< |
\hline |
| 36 |
< |
\end{tabular} |
| 63 |
> |
\subsection{Signal and background Monte Carlo samples} |
| 64 |
|
|
| 65 |
< |
\caption{Monte Carlo samples used in this analysis} |
| 65 |
> |
The signal Monte Carlo sample is produced using {\sl PYTHIA} |
| 66 |
> |
generator. The decay for the \W lepton is forced to $e\nu_e$, |
| 67 |
> |
$\mu\nu_{\mu}$ or $\tau\nu_{\tau}$ final state, while the \Z decays |
| 68 |
> |
into electrons or muons only. |
| 69 |
> |
|
| 70 |
> |
The background to the \WZ final state can be divided in physics and |
| 71 |
> |
instrumental. The only physics background is from $Z^0Z^0$ production |
| 72 |
> |
where one of the leptons is either mis-reconstructed or lost. |
| 73 |
> |
|
| 74 |
> |
The instrumental backgrounds are all due to mis-identified electron candidates |
| 75 |
> |
from either jets or photons. These backgrounds include production of $\W$ and $\Z$ bosons |
| 76 |
> |
with jets and $t\bar{t}$ processes and $Z^0\gamma$ process. The background from $W\gamma$ |
| 77 |
> |
production, where the $\gamma$ converts and produces a dielectron system is neglected |
| 78 |
> |
due to a requirement on the $\ell^+\ell^-$ invariant mass to be consistent with the nominal \Z boson mass. |
| 79 |
> |
|
| 80 |
> |
All non-negligible instrumental backgrounds are summarized below. |
| 81 |
> |
\begin{itemize} |
| 82 |
> |
\item $\Z + jets$: this background is one of the dominant to the \WZ final state. Although |
| 83 |
> |
the misidentification rate for a jet to be misidentified as a lepton is quite small, the |
| 84 |
> |
$\Z+jets$ cross-section is 35 times larger than the signal one. We use the {\sl ALPGEN} |
| 85 |
> |
generated official samples of $\Z+jet$ production Monte Carlo samples for different |
| 86 |
> |
values of the jet transverse momentum. |
| 87 |
> |
\item $t\bar{t}$: each of the top quarks decay into a $\W b$ pair producing at least two |
| 88 |
> |
leptons and two $b$-quark jets. Although this process does not have a genuine $\Z$ |
| 89 |
> |
candidate and can be suppressed be a $\Z$ candidate invariant mass requirement, |
| 90 |
> |
the probability for a $b$-quark jet to decay semi-leptonically and be misidentified |
| 91 |
> |
as a lepton is higher than that from a light-quark jets. The cross-section of the $t\bar{t}$ |
| 92 |
> |
production is also exceed by about 15 times the cross-section of the \WZ production. |
| 93 |
> |
Thus, this background is also one of the most dominant. We use the official $t\bar{t}$ |
| 94 |
> |
samples produced with {\sl ALPGEN} generator to estimate this background. |
| 95 |
> |
\item $\Z + b\bar{b}$: this process is produced by the {\sl COMPHEP} |
| 96 |
> |
generator and have a genuine $\Z$ candidate in the final state. One of the $b$-quark |
| 97 |
> |
jets are misidentified as the third lepton from the $\W$ boson. |
| 98 |
> |
\item $\W+jets$: in this process, the \W boson produces a genuine lepton, |
| 99 |
> |
while the other two leptons are misidentified jets. As the misidentification |
| 100 |
> |
probability is low, this channel does not contribute significantly to the \WZ |
| 101 |
> |
final state. The additional \Z candidate invariant mass requirement suppresses |
| 102 |
> |
this background further. We use the officially produced sample of $\W+jets$ processes |
| 103 |
> |
for different number of jets in the final state generated by the {\sl ALPGEN} |
| 104 |
> |
generator. |
| 105 |
> |
\item $Z^0\gamma$: this process is calculated with {\sl PYTHIA}. |
| 106 |
> |
\end{itemize} |
| 107 |
> |
|
| 108 |
> |
All the samples we use in this study are a part of the CSA07 production and |
| 109 |
> |
are generated using $\mathrm{CMSSW}\_1\_4_\_6$ using the full {\sl GEANT} |
| 110 |
> |
simulation of the CMS detector. The digitization and reconstruction are |
| 111 |
> |
done using a newer $\mathrm{CMSSW}\_1\_6_\_7$ release with a |
| 112 |
> |
misalignment/miscalibration of the detector scenario expected |
| 113 |
> |
to be achieved after collection of $\sim$ 100~pb$^{-1}$ of data. |
| 114 |
> |
All {\sl ALPGEN} samples are mixed together in further referred to as to a |
| 115 |
> |
``Chowder soup''. |
| 116 |
> |
|
| 117 |
> |
The summary of all datasets used for signal and background is given in |
| 118 |
> |
Table~\ref{tab:MC}. We use the RECO production level to access to |
| 119 |
> |
low-level detector information, such as reconstructed hits. This lets |
| 120 |
> |
us to use full granularity of the CMS sub-detectors to use isolation |
| 121 |
> |
discriminants. |
| 122 |
> |
|
| 123 |
> |
Analysis of the samples is done using CMSSW$\_1\_6\_7$ CMS software |
| 124 |
> |
release. The information is stored in ROOT trees using a code in |
| 125 |
> |
CVS:/UserCode/Vuko/WZAnalysis, which is based on Physics Tools candidates. |
| 126 |
> |
|
| 127 |
> |
\begin{table}[!tb] |
| 128 |
> |
%\begin{tabular}{llllll} \hline |
| 129 |
> |
%Sample & Generator & Sample name & Events & $\sigma \cdot \epsilon |
| 130 |
> |
%\cdot k$ & k-factor \\ \hline WZ & Pythia & |
| 131 |
> |
%/WZ/CMSSW\_1\_6\_7-CSA07-1195663763/RECO & 58897 & 0.585 pb & 1.92 \\ |
| 132 |
> |
%$Zb\bar{b}$ & COMPHEP & |
| 133 |
> |
%/comphep-bbll/CMSSW\_1\_6\_7-CSA07-1198677426/RECO & 143.59 pb & 2.4 |
| 134 |
> |
%\\ ``Chowder'' & ALPGEN & |
| 135 |
> |
%/CSA07AllEvents/CMSSW\_1\_6\_7-CSA07-Chowder-A1-PDAllEvents-ReReco-100pb/RECO |
| 136 |
> |
%& 25 M & event weights & - \\ |
| 137 |
> |
\begin{tabular}{|c|c|c|c|c|} \hline |
| 138 |
> |
Sample & cross section, pb & Events & Dataset name \\ \hline |
| 139 |
> |
$\WZ$ & 1.12 & 59K & /WZ/CMSSW$\_1\_6\_7$-CSA07-1195663763\\ \hline |
| 140 |
> |
$\Z b\bar{b}$ & 830*0.173 (NLO) & 1.9M & /comphep-bbll/CMSSW$\_1\_6\_7$-CSA07-1198677426\\ \hline |
| 141 |
> |
Chowder & Event Weight & $\sim$ 21M & /CSA07AllEvents/\\ & & & CMSSW$\_1\_6\_7$-CSA07-Chowder-A1-PDAllEvents-ReReco |
| 142 |
> |
-100pb\\ \hline |
| 143 |
> |
$\Z\Z$ inclusive & 16.1 (NLO) & $\sim$ 140k & /ZZ$\_$incl/CMSSW$\_1\_6\_7$-CSA07-1194964234/RECO\\ \hline |
| 144 |
> |
$\Z\gamma \rightarrow e^+e^-\gamma$ & 1.08 (NLO) & $\sim$125k &/Zeegamma/CMSSW$\_1\_6\_7$-CSA07-1198935518/RECO \\ \hline |
| 145 |
> |
$\Z\gamma \rightarrow \mu^+\mu^-\gamma$ & 1.08 (NLO) & $\sim$ 93k & /Zmumugamma/CMSSW$\_1\_6\_7$-CSA07-1194806860/RECO\\ \hline |
| 146 |
> |
\end{tabular} |
| 147 |
> |
\label{tab:MC} |
| 148 |
> |
\caption{Monte Carlo samples used in this analysis using 100 pb$^{-1}$ scenario} |
| 149 |
|
\end{table} |
| 150 |
|
|
| 41 |
– |
\subsection{Signal and Background Monte Carlo samples} |
| 42 |
– |
|
| 151 |
|
|
| 152 |
|
|
| 153 |
|
|
