| 2 |
|
\label{sec:gen} |
| 3 |
|
\subsection{Monte Carlo generators} |
| 4 |
|
The signal and background samples for the full detector simulation |
| 5 |
< |
were generated with the leading order event generator PYTHIA~\cite{Sjostrand:2003wg}. To |
| 6 |
< |
accomodate NLO effect constant k-factors were applied. |
| 7 |
< |
Additionally the cross section calculator MCFM~\cite{Campbell:2005} was used to determine |
| 8 |
< |
the next-to-leading order differential cross section for the WZ |
| 9 |
< |
production process. To estimate the PDF uncertainty for the signal |
| 10 |
< |
process at NLO the NLO event generator MC@NLO 3.1~\cite{Frixione:2002ik} together with PDF set |
| 11 |
< |
CTEQ6M was used. |
| 12 |
< |
|
| 13 |
< |
\subsection{Signal Definition} |
| 14 |
< |
|
| 15 |
< |
This analysis is studying the final state of on-shell $W$ and $Z$ |
| 16 |
< |
boson, both of them decaying leptonically. The fully final leptonic |
| 17 |
< |
final state $l^+ l^- l^\pm \nu$ also receives a contribution from the |
| 18 |
< |
$W\gamma *$ process, where the $\gamma *$ stands for a virtual photon |
| 19 |
< |
through the $WW\gamma$ vertex. In this analysis, only events with $l^+ |
| 20 |
< |
l^-$ invariant mass consistent with $Z$ mass will be considered. CMS |
| 21 |
< |
detector have a very good energy resolution for electrons and muons, |
| 22 |
< |
the mass windows will be $\pm 10$ GeV around 91 GeV. |
| 5 |
> |
are generated with the leading order (LO) event generators |
| 6 |
> |
{\sl PYTHIA}~\cite{Sjostrand:2003wg}, {\sl ALPGEN} and {\sl COMPHEP}. |
| 7 |
> |
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. |
| 9 |
> |
|
| 10 |
> |
The $p_T$-dependent $k$-factor for the signal is estimated using |
| 11 |
> |
the NLO cross section calculator {\sl MCFM}~\cite{Campbell:2005}. |
| 12 |
> |
We estimate the PDF uncertainty on the cross-section using |
| 13 |
> |
{\sl MC@NLO 3.1} NLO event generator~\cite{Frixione:2002ik} |
| 14 |
> |
together with CTEQ6M PDF set. |
| 15 |
> |
|
| 16 |
> |
\subsection{Signal definition} |
| 17 |
> |
The goal of this analysis is to study the associative production of the on-shell |
| 18 |
> |
$\W$ and $\Z$ bosons that decay into three leptons and a neutrino. In the |
| 19 |
> |
following we refer to a lepton to as either a muon or an electron, unless |
| 20 |
> |
specified otherwise. |
| 21 |
|
|
| 22 |
< |
Using MCFM to estimate the total NLO cross section, we found: |
| 22 |
> |
Using {\sl MCFM} we estimate the total NLO $\WZ$ cross-section to be |
| 23 |
|
\begin{equation} |
| 24 |
< |
\sigma_{NLO} ( pp \rightarrow W^+Z^0; \sqrt{s}=14TeV) = 30.5 pb |
| 24 |
> |
\sigma_{NLO} ( pp \rightarrow W^+\Z; \sqrt{s}=14~{\rm TeV}) = 30.5~{\rm pb}, |
| 25 |
|
\end{equation} |
| 26 |
|
\begin{equation} |
| 27 |
< |
\sigma_{NLO} ( pp \rightarrow W^-Z^0; \sqrt{s}=14TeV) = 19.1 pb |
| 27 |
> |
\sigma_{NLO} ( pp \rightarrow W^-\Z; \sqrt{s}=14~{\rm TeV}) = 19.1~{\rm pb}. |
| 28 |
|
\end{equation} |
| 29 |
|
|
| 30 |
< |
The LO and NLO distribution of \Z transverse momentum are shown of |
| 31 |
< |
figure~\ref{fig:LOvsNLO} for the case of $W^+$ on the left and $W^-$ |
| 32 |
< |
on the right side. The ratio NLO/LO is also presented on the figure |
| 33 |
< |
and it is increasing as $P_T(Z)$ increased. In the following analysis |
| 34 |
< |
we consider a constant $k-factor$ of 1.84 as we concentrate on the |
| 35 |
< |
first data taking. On the other side, if in the future one wants to |
| 36 |
< |
use such distribution to study the effect of possible anomalous triple |
| 37 |
< |
gauge couplings, it will be necessary to take the $p_T$ dependance of |
| 38 |
< |
this $k-factor$ into account. |
| 30 |
> |
The LO and NLO distributions of the \Z boson transverse momentum are |
| 31 |
> |
shown in Fig.~\ref{fig:LOvsNLO}. The NLO/LO ratio, $k$-factor, is also presented on the figure, |
| 32 |
> |
and it is increasing with $p_T(\Z)$. We take into account the $p_T$ dependence |
| 33 |
> |
by re-weighting the LO Monte Carlo simulation as a function of the $p_T(\Z)$. |
| 34 |
> |
% |
| 35 |
> |
% |
| 36 |
> |
%The $p_T$ dependence of the $k$-factor |
| 37 |
> |
%becomes important when a proper NLO description of the $\Z$ boson transverse |
| 38 |
> |
%momentum must be obtained, $e.g$ to measure the strength of the $WWZ$ coupling. |
| 39 |
> |
%As the focus of this analysis is to prepare for the cross-section measurement, |
| 40 |
> |
%we take a $p_{T}$-averaged value of the $k$-factor, equal to 1.84. |
| 41 |
|
|
| 42 |
|
\begin{figure}[!bt] |
| 43 |
|
\begin{center} |
| 44 |
< |
\scalebox{0.8}{\includegraphics{figs/LOvsNLOZPtWminuns.eps}\includegraphics{figs/LOvsNLOZPtWplus.eps}} |
| 45 |
< |
\caption{$P_T(Z)$ in $W^-Z$ events on the left and $W^+Z$ events on the right |
| 46 |
< |
distribution for LO and NLO calculation. The ratio NLO/LO is also given. |
| 47 |
< |
} |
| 44 |
> |
\scalebox{0.8}{\includegraphics{figs/k_faktor_for_Note.eps}} |
| 45 |
> |
\caption{Top plot: comparison of $p_T(Z)$ distributions for NLO and LO for \WZ production |
| 46 |
> |
allowing off-shell vector bosons including photon contribution; |
| 47 |
> |
bottom plot: $k$-factor fit to a line.} |
| 48 |
|
\label{fig:LOvsNLO} |
| 49 |
|
\end{center} |
| 50 |
|
\end{figure} |
| 56 |
|
%# 830x0.173 (== XS x eff.) = 143.59pb |
| 57 |
|
|
| 58 |
|
|
| 59 |
< |
\subsection{Signal and Background Monte Carlo samples} |
| 60 |
< |
The signal monte carlo sample has been produced using PYTHIA |
| 61 |
< |
generator. The decay for the \W has been forced to be in $e\nu_e or |
| 62 |
< |
\mu\nu_{mu} or \tau\nu_{\tau}$ while the \Z is decaying into electrons |
| 63 |
< |
or muons only. |
| 64 |
< |
|
| 65 |
< |
The main background that we have to consider are all final states |
| 66 |
< |
having at least two isolated leptons from the same flavor and with |
| 67 |
< |
opposite charge. The third one can be a real isolated lepton or a misidentified |
| 68 |
< |
lepton. The probability to misidentify one isolated lepton is rather low, so |
| 69 |
< |
this is why we can considere safely starting from two |
| 70 |
< |
leptons. Moreover we will apply a cut on the invariant mass of the two |
| 71 |
< |
leptons so most of the background remaining are:\\ |
| 72 |
< |
\begin{itemize} |
| 73 |
< |
\item $W+jets$: $W$ boson will give us one isolated leptons. The probability that 2 additional jets will be misidentified as isolated lepton is very low and the criteria on the lepton invariant mass will definitely reduce such background. This channel is nevertheless useful to study other background for which data sample are not available such as $Wb\bar{b}$. The sample studied for this analysis, has been produced using ALPGEN generator per jet bin. |
| 74 |
< |
\item $Z + jets$: $Z$ boson is commun between signal and background. The thrid isolated lepton can come from a misidentified lepton. The cross section of production of this channel is around 600 time the signal studied.The sample studied for this analysis, has been produced using ALPGEN generator per jet bin. |
| 75 |
< |
\item $t\bar{t}$: top quark will decay to \W$b$ pair where each of the $W$ can decay via an isolated leptons. This leptons will have opposite charged. Even though combining the two leptons, we will not obtain a peak around the \Z mass, the cross section of this process is around 60 time the cross section of the signal studied. The sample studied for this analysis, has been produced using ALPGEN generator per jet bin. The third lepton will come from a semi leptonic decay of a $b$ quark which will be isolated. |
| 76 |
< |
\item $Z + b\bar{b}$: the presence of $Z$ boson will select such events. Moreover due to the semi leptonic decay of a $b$ quark, a thrid lepton can be easily identified and consider as isolated. The sample used has been produced by COMPHEP generator. |
| 77 |
< |
\item $ZZ$: the inclusive |
| 59 |
> |
\subsection{Signal and background Monte Carlo samples} |
| 60 |
> |
|
| 61 |
> |
The signal Monte Carlo sample is produced using {\sl PYTHIA} |
| 62 |
> |
generator. The decay for the \W lepton is forced to $e\nu_e$, |
| 63 |
> |
$\mu\nu_{\mu}$ or $\tau\nu_{\tau}$ final state, while the \Z decays |
| 64 |
> |
into electrons or muons only. |
| 65 |
> |
|
| 66 |
> |
The background to the \WZ final state can be divided in physics and |
| 67 |
> |
instrumental. The only physics background is from $Z^0Z^0$ production |
| 68 |
> |
where one of the leptons is either mis-reconstructed or lost. |
| 69 |
> |
|
| 70 |
> |
The instrumental backgrounds are all due to misidentified electron candidates |
| 71 |
> |
from either jets or photons. These backgrounds include production of $\W$ and $\Z$ bosons |
| 72 |
> |
with jets and $t\bar{t}$ processes and $Z^0\gamma$ process. The background from $W\gamma$ |
| 73 |
> |
production, where the $\gamma$ converts and produces a di-electron system is neglected |
| 74 |
> |
due to a requirement on the $\ell^+\ell^-$ invariant mass to be consistent with the nominal \Z boson mass. |
| 75 |
|
|
| 76 |
+ |
All non-negligible instrumental backgrounds are summarized below. |
| 77 |
+ |
\begin{itemize} |
| 78 |
+ |
\item $\Z + jets$: this background is one of the dominant to the \WZ final state. Although |
| 79 |
+ |
the misidentification rate for a jet to be misidentified as a lepton is quite small, the |
| 80 |
+ |
$\Z+jets$ cross-section is 35 times larger than the signal one. We use the {\sl ALPGEN} |
| 81 |
+ |
generated official samples of $\Z+jet$ production Monte Carlo samples for different |
| 82 |
+ |
values of the jet transverse momentum. |
| 83 |
+ |
\item $t\bar{t}$: each of the top quarks decay into a $\W b$ pair producing at least two |
| 84 |
+ |
leptons and two $b$-quark jets. Although this process does not have a genuine $\Z$ |
| 85 |
+ |
candidate and can be suppressed by a $\Z$ candidate invariant mass requirement, |
| 86 |
+ |
the probability for a $b$-quark jet to decay semi-leptonically and be misidentified |
| 87 |
+ |
as a lepton is higher than that from a light-quark jets. The cross-section of the $t\bar{t}$ |
| 88 |
+ |
production is also exceed by about 15 times the cross-section of the \WZ production. |
| 89 |
+ |
Thus, this background is also one of the most dominant. We use the official $t\bar{t}$ |
| 90 |
+ |
samples produced with {\sl ALPGEN} generator to estimate this background. |
| 91 |
+ |
\item $\Z + b\bar{b}$: this process is produced by the {\sl COMPHEP} |
| 92 |
+ |
generator and have a genuine $\Z$ candidate in the final state. One of the $b$-quark |
| 93 |
+ |
jets are misidentified as the third lepton from the $\W$ boson. |
| 94 |
+ |
\item $\W+jets$: in this process, the \W boson produces a genuine lepton, |
| 95 |
+ |
while the other two leptons are misidentified jets. As the misidentification |
| 96 |
+ |
probability is low, this channel does not contribute significantly to the \WZ |
| 97 |
+ |
final state. The additional \Z candidate invariant mass requirement suppresses |
| 98 |
+ |
this background further. We use the officially produced sample of $\W+jets$ processes |
| 99 |
+ |
for different number of jets in the final state generated by the {\sl ALPGEN} |
| 100 |
+ |
generator. |
| 101 |
+ |
\item $Z^0\gamma$: this process is calculated with {\sl PYTHIA}. |
| 102 |
|
\end{itemize} |
| 103 |
+ |
The background sources that have \Z bosons described above are simulated with the |
| 104 |
+ |
contribution from the virtual photon. |
| 105 |
|
|
| 106 |
< |
\begin{table}[tbh] |
| 107 |
< |
\begin{tabular}{llllll} \hline |
| 108 |
< |
Sample & Generator & Sample name & Events & $\sigma \cdot \epsilon |
| 109 |
< |
\cdot k$ & k-factor \\ \hline WZ & Pythia & |
| 110 |
< |
/WZ/CMSSW\_1\_6\_7-CSA07-1195663763/RECO & 58897 & 0.585 pb & 1.92 \\ |
| 111 |
< |
$Zb\bar{b}$ & COMPHEP & |
| 112 |
< |
/comphep-bbll/CMSSW\_1\_6\_7-CSA07-1198677426/RECO & 143.59 pb & 2.4 |
| 113 |
< |
\\ ``Chowder'' & ALPGEN & |
| 114 |
< |
/CSA07AllEvents/CMSSW\_1\_6\_7-CSA07-Chowder-A1-PDAllEvents-ReReco-100pb/RECO |
| 115 |
< |
& 25 M & event weights & - \\ |
| 116 |
< |
\hline |
| 106 |
> |
All the samples we use in this study are a part of the CSA07 production and |
| 107 |
> |
are generated using $\mathrm{CMSSW}\_1\_4_\_6$ using the full {\sl GEANT} |
| 108 |
> |
simulation of the CMS detector. The digitization and reconstruction are |
| 109 |
> |
done using a newer $\mathrm{CMSSW}\_1\_6_\_7$ release with a |
| 110 |
> |
misalignment/mis-calibration of the detector scenario expected |
| 111 |
> |
to be achieved after collection of $\sim$ 100~pb$^{-1}$ of data. |
| 112 |
> |
All {\sl ALPGEN} samples are mixed together in further referred to as to a |
| 113 |
> |
``Chowder soup''. |
| 114 |
> |
|
| 115 |
> |
The summary of all datasets used for signal and background is given in |
| 116 |
> |
Table~\ref{tab:MC}. We use the RECO production level to access to |
| 117 |
> |
low-level detector information, such as reconstructed hits. This lets |
| 118 |
> |
us to use full granularity of the CMS sub-detectors to use isolation |
| 119 |
> |
discriminants. |
| 120 |
> |
|
| 121 |
> |
Analysis of the samples is done using CMSSW$\_1\_6\_7$ CMS software |
| 122 |
> |
release. The information is stored in ROOT trees using a code in |
| 123 |
> |
CVS:/UserCode/Vuko/WZAnalysis, which is based on Physics Tools candidates. |
| 124 |
> |
|
| 125 |
> |
\begin{table}[!tb] |
| 126 |
> |
%\begin{tabular}{llllll} \hline |
| 127 |
> |
%Sample & Generator & Sample name & Events & $\sigma \cdot \epsilon |
| 128 |
> |
%\cdot k$ & k-factor \\ \hline WZ & Pythia & |
| 129 |
> |
%/WZ/CMSSW\_1\_6\_7-CSA07-1195663763/RECO & 58897 & 0.585 pb & 1.92 \\ |
| 130 |
> |
%$Zb\bar{b}$ & COMPHEP & |
| 131 |
> |
%/comphep-bbll/CMSSW\_1\_6\_7-CSA07-1198677426/RECO & 143.59 pb & 2.4 |
| 132 |
> |
%\\ ``Chowder'' & ALPGEN & |
| 133 |
> |
%/CSA07AllEvents/CMSSW\_1\_6\_7-CSA07-Chowder-A1-PDAllEvents-ReReco-100pb/RECO |
| 134 |
> |
%& 25 M & event weights & - \\ |
| 135 |
> |
\begin{tabular}{|c|c|c|c|c|} \hline |
| 136 |
> |
Sample & cross section, pb & Events & Dataset name \\ \hline |
| 137 |
> |
$\WZ$ & 1.12 & 59K & /WZ/CMSSW$\_1\_6\_7$-CSA07-1195663763\\ \hline |
| 138 |
> |
$\Z b\bar{b}$ & 830*0.173 (NLO) & 1.9M & /comphep-bbll/CMSSW$\_1\_6\_7$-CSA07-1198677426\\ \hline |
| 139 |
> |
Chowder & Event Weight & $\sim$ 25M & /CSA07AllEvents/\\ & & & CMSSW$\_1\_6\_7$-CSA07-Chowder-A1-PDAllEvents-ReReco |
| 140 |
> |
-100pb\\ \hline |
| 141 |
> |
$\Z\Z$ inclusive & 16.1 (NLO) & $\sim$ 140K & /ZZ$\_$incl/CMSSW$\_1\_6\_7$-CSA07-1194964234/RECO\\ \hline |
| 142 |
> |
$\Z\gamma \rightarrow e^+e^-\gamma$ & 1.08 (NLO) & $\sim$125K &/Zeegamma/CMSSW$\_1\_6\_7$-CSA07-1198935518/RECO \\ \hline |
| 143 |
> |
$\Z\gamma \rightarrow \mu^+\mu^-\gamma$ & 1.08 (NLO) & $\sim$ 93K & /Zmumugamma/CMSSW$\_1\_6\_7$-CSA07-1194806860/RECO\\ \hline |
| 144 |
|
\end{tabular} |
| 145 |
< |
|
| 146 |
< |
\caption{Monte Carlo samples used in this analysis} |
| 145 |
> |
\label{tab:MC} |
| 146 |
> |
\caption{Monte Carlo samples used in this analysis using 100 pb$^{-1}$ scenario} |
| 147 |
|
\end{table} |
| 148 |
|
|
| 149 |
|
|
