| 4 |
|
The signal and background samples for the full detector simulation |
| 5 |
|
are generated with the leading order (LO) event generators |
| 6 |
|
{\sl PYTHIA}~\cite{Sjostrand:2003wg}, {\sl ALPGEN} and {\sl COMPHEP}. |
| 7 |
< |
To accommodate next-to-leading (NLO) effects, constant $k$-factors are applied. |
| 8 |
< |
Additionally, the cross section calculator {\sl MCFM}~\cite{Campbell:2005} |
| 9 |
< |
is used to determine the NLO differential cross section for the $\WZ$ |
| 10 |
< |
production. To estimate the uncertainty on the cross-section |
| 11 |
< |
due to the choice of the PDF, we use NLO event generator |
| 12 |
< |
{\sl MC@NLO 3.1}~\cite{Frixione:2002ik} together with CTEQ6M PDF set. |
| 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 |
< |
\subsection{Signal definition} |
| 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}~\cite{Frixione:2002ik} NLO event generator |
| 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. The leptonic final state $\ell^+ \ell^- \ell^\pm \nu$ also receives a |
| 20 |
< |
contribution from the $W\gamma^*$ production, where the $\gamma^*$ stands for a |
| 21 |
< |
virtual photon through the $WW\gamma$ vertex. In this analysis, we |
| 22 |
< |
restrict this contribution by requiring the $\ell^+\ell^-$ invariant mass to be |
| 23 |
< |
consistent with the nominal $\Z$ boson mass. As CMS detector has a very |
| 24 |
< |
good energy resolution for electrons and muons, the mass window |
| 25 |
< |
is set to be $\pm$ 10 GeV around 91 GeV. |
| 20 |
> |
specified otherwise. |
| 21 |
|
|
| 22 |
|
Using {\sl MCFM} we estimate the total NLO $\WZ$ cross-section to be |
| 23 |
|
\begin{equation} |
| 28 |
|
\end{equation} |
| 29 |
|
|
| 30 |
|
The LO and NLO distributions of the \Z boson transverse momentum are |
| 31 |
< |
shown in Fig.~\ref{fig:LOvsNLO} with the case of $W^+$ on the left and $W^-$ |
| 32 |
< |
on the right side. The NLO/LO ratio, $k$-factor, is also presented on the figure, |
| 33 |
< |
and it is increasing with $p_T(\Z)$. The $p_T$ dependence of the $k$-factor |
| 34 |
< |
becomes important when a proper NLO description of the $\Z$ boson transverse |
| 35 |
< |
momentum must be obtained, $e.g$ to measure the strength of the $WWZ$ coupling. |
| 36 |
< |
As the focus of this analysis is to prepare for the cross-section measurement, |
| 37 |
< |
we take a $p_{T}$-averaged value of the $k$-factor, equal to 1.84. |
| 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{$p_T(Z)$ 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 |
< |
} |
| 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; bottom plot: k factor } |
| 46 |
|
\label{fig:LOvsNLO} |
| 47 |
|
\end{center} |
| 48 |
|
\end{figure} |
| 62 |
|
into electrons or muons only. |
| 63 |
|
|
| 64 |
|
The background to the \WZ final state can be divided in physics and |
| 65 |
< |
instrumental. Physics background includes the contributions from |
| 66 |
< |
either converted photons that produce isolated leptons misidentified |
| 72 |
< |
as a decay products of $\W$ or $\Z$ bosons, or genuine leptons from |
| 73 |
< |
diboson processes. The only non-negligible physics backgrounds are |
| 74 |
< |
$\Z\gamma$ and $\Z\Z$ processes officially produced with {\sl PYTHIA} |
| 75 |
< |
generator. |
| 65 |
> |
instrumental. The only physics background is from $Z^0Z^0$ production |
| 66 |
> |
where one of the leptons is either mis-reconstructed or lost. |
| 67 |
|
|
| 68 |
< |
The instrumental backgrounds are all include jets that are misidentified |
| 69 |
< |
as isolated leptons. These include production of $\W$ and $\Z$ bosons |
| 70 |
< |
with jets and $t\bar{t}$ processes. We summarize the instrumental background |
| 71 |
< |
processes below. |
| 68 |
> |
The instrumental backgrounds are all due to mis-identified electron candidates |
| 69 |
> |
from either jets or photons. These backgrounds include production of $\W$ and $\Z$ bosons |
| 70 |
> |
with jets and $t\bar{t}$ processes and $Z^0\gamma$ process. The background from $W\gamma$ |
| 71 |
> |
production, where the $\gamma$ converts and produces a dielectron system is neglected |
| 72 |
> |
due to a requirement on the $\ell^+\ell^-$ invariant mass to be consistent with the nominal \Z boson mass. |
| 73 |
|
|
| 74 |
+ |
All non-negligible instrumental backgrounds are summarized below. |
| 75 |
|
\begin{itemize} |
| 76 |
|
\item $\Z + jets$: this background is one of the dominant to the \WZ final state. Although |
| 77 |
|
the misidentification rate for a jet to be misidentified as a lepton is quite small, the |
| 96 |
|
this background further. We use the officially produced sample of $\W+jets$ processes |
| 97 |
|
for different number of jets in the final state generated by the {\sl ALPGEN} |
| 98 |
|
generator. |
| 99 |
+ |
\item $Z^0\gamma$: this process is calculated with {\sl PYTHIA}. |
| 100 |
|
\end{itemize} |
| 101 |
+ |
The background sources that have \Z bosons described above are simulated with the |
| 102 |
+ |
contribution from the virtual photon. |
| 103 |
|
|
| 104 |
|
All the samples we use in this study are a part of the CSA07 production and |
| 105 |
|
are generated using $\mathrm{CMSSW}\_1\_4_\_6$ using the full {\sl GEANT} |
