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\label{sec:gen} |
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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}, ALPGEN or COMPHEP. To |
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accommodate 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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The goal of the analysis is to study the final state of on-shell $W$ |
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and $Z$ boson, both of them decaying leptonically. The leptonic final |
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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 $l^+ |
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l^-$ invariant mass consistent with $Z$ mass will be considered. CMS |
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detector have a very good energy resolution for electrons and muons, |
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the mass windows will be $\pm 10$ GeV around 91 GeV. |
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> |
are generated with the leading order (LO) event generator |
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> |
{\sl PYTHIA}~\cite{Sjostrand:2003wg}, {\sl ALPGEN} and {\sl COMPHEP}. |
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> |
To accommodate next-to-leading (NLO) effects, constant $k$-factors are applied. |
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> |
Additionally, the cross section calculator {\sl MCFM}~\cite{Campbell:2005} |
| 9 |
> |
is used to determine the NLO differential cross section for the $\WZ$ |
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> |
production. To estimate the uncertainty on the cross-section |
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> |
due to the choice of the PDF, we use NLO event generator |
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> |
{\sl MC@NLO 3.1}~\cite{Frixione:2002ik} together with CTEQ6M PDF set. |
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> |
|
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> |
\subsection{Signal definition} |
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> |
|
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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 |
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> |
following we refer to a lepton to as either a muon or an electron, unless |
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> |
specified otherwise. The leptonic final state $\ell^+ \ell^- \ell^\pm \nu$ also receives a |
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contribution from the $W\gamma^*$ production, where the $\gamma^*$ stands for a |
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> |
virtual photon through the $WW\gamma$ vertex. In this analysis, we |
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restrict this contribution by requiring the $\ell^+\ell^-$ invariant mass to be |
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> |
consistent with the nominal $\Z$ boson mass. As CMS detector has a very |
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> |
good energy resolution for electrons and muons, the mass window |
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> |
is set to be $\pm$ 10 GeV around 91 GeV. |
| 26 |
|
|
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< |
Using MCFM to estimate the total NLO cross section, we found: |
| 27 |
> |
Using {\sl MCFM} we estimate the total NLO $\WZ$ cross-section to be |
| 28 |
|
\begin{equation} |
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< |
\sigma_{NLO} ( pp \rightarrow W^+Z^0; \sqrt{s}=14TeV) = 30.5 pb |
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> |
\sigma_{NLO} ( pp \rightarrow W^+\Z; \sqrt{s}=14~{\rm TeV}) = 30.5~{\rm pb}, |
| 30 |
|
\end{equation} |
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|
\begin{equation} |
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< |
\sigma_{NLO} ( pp \rightarrow W^-Z^0; \sqrt{s}=14TeV) = 19.1 pb |
| 32 |
> |
\sigma_{NLO} ( pp \rightarrow W^-\Z; \sqrt{s}=14~{\rm TeV}) = 19.1~{\rm pb}. |
| 33 |
|
\end{equation} |
| 34 |
|
|
| 35 |
< |
The LO and NLO distribution of \Z transverse momentum are shown of |
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< |
figure~\ref{fig:LOvsNLO} for the case of $W^+$ on the left and $W^-$ |
| 37 |
< |
on the right side. The ratio NLO/LO is also presented on the figure |
| 38 |
< |
and it is increasing as $P_T(Z)$ increased. In the following analysis |
| 39 |
< |
we consider a constant $k-factor$ of 1.84 as we concentrate on the |
| 40 |
< |
first data taking. On the other side, if in the future one wants to |
| 41 |
< |
use such distribution to study the effect of possible anomalous triple |
| 42 |
< |
gauge couplings, it will be necessary to take the $p_T$ dependence of |
| 40 |
< |
this $k-factor$ into account. |
| 35 |
> |
The LO and NLO distributions of the \Z boson transverse momentum are |
| 36 |
> |
shown in Fig.~\ref{fig:LOvsNLO} with the case of $W^+$ on the left and $W^-$ |
| 37 |
> |
on the right side. The NLO/LO ratio, $k$-factor, is also presented on the figure, |
| 38 |
> |
and it is increasing with $p_T(\Z)$. The $p_T$ dependence of the $k$-factor |
| 39 |
> |
becomes important when a proper NLO description of the $\Z$ boson transverse |
| 40 |
> |
momentum must be obtained, $e.g$ to measure the strength of the $WWZ$ coupling. |
| 41 |
> |
As the focus of this analysis is to prepare for the cross-section measurement, |
| 42 |
> |
we take a $p_{T}$-averaged value of the $k$-factor, equal to 1.84. |
| 43 |
|
|
| 44 |
|
\begin{figure}[!bt] |
| 45 |
|
\begin{center} |
| 46 |
|
\scalebox{0.8}{\includegraphics{figs/LOvsNLOZPtWminuns.eps}\includegraphics{figs/LOvsNLOZPtWplus.eps}} |
| 47 |
< |
\caption{$P_T(Z)$ in $W^-Z$ events on the left and $W^+Z$ events on the right |
| 48 |
< |
distribution for LO and NLO calculation. The ratio NLO/LO is also given. |
| 47 |
> |
\caption{$p_T(Z)$ distribution for LO (solid black histogram) and NLO (dashed black histogram) |
| 48 |
> |
in $W^-\Z$ events (left) and $W^+\Z$ events (right). The ratio NLO/LO is also given as a red |
| 49 |
> |
solid line. |
| 50 |
|
} |
| 51 |
|
\label{fig:LOvsNLO} |
| 52 |
|
\end{center} |
| 59 |
|
%# 830x0.173 (== XS x eff.) = 143.59pb |
| 60 |
|
|
| 61 |
|
|
| 62 |
< |
\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. |
| 62 |
> |
\subsection{Signal and background Monte Carlo samples} |
| 63 |
|
|
| 64 |
+ |
The signal Monte Carlo sample is produced using {\sl PYTHIA} |
| 65 |
+ |
generator. The decay for the \W has been forced to $e\nu_e$ or |
| 66 |
+ |
$\mu\nu_{mu}$ or $\tau\nu_{\tau}$ final state, while the \Z decays |
| 67 |
+ |
into electrons or muons only. |
| 68 |
+ |
|
| 69 |
+ |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 70 |
+ |
% YM changes implemented up to here |
| 71 |
|
The main background that we have to consider are all final states |
| 72 |
|
having at least two isolated leptons from the same flavor and with |
| 73 |
|
opposite charge. The third one can be a real isolated lepton or a misidentified |
