text:
\subsection{Background in the four-lepton channel}
The main backgrounds that contribute to the 4$\ell$-2SFOS and 4$\ell$-1SFOS
SRs are diboson processes,
dominated by $ZZ^{\ast}$ with \met\ from $\Ztau$ decay,
and triboson processes,
in particular $ZWW^{\ast}$, which has the same signature as the signal.
These processes respectively account for about 85\% and 15\% of the total background
contamination.
To normalise $ZZ^{\ast}$ a dedicated CR, the 4$\ell$-$ZZ$ CR, is defined by inverting the requirement on the invariant mass of dileptons from the Higgs boson candidate.
All the other minor background processes, listed in table~\ref{tab:CRs}, are modelled by simulation.

\subsection{Background in the three-lepton channel}
Three classes of backgrounds contribute to the 3$\ell$ channel.
The first class comprises diboson processes: $WZ/W\gamma^{\ast}$,
$ZZ^{\ast}$ with an undetected lepton mainly due to its low-$\pt$, and $Z\gamma$, in which the photon converts to electron--positron pairs.
The $ZZ^{\ast}$ contribution in this channel is mainly due to single-resonant $ZZ^{\ast}$ production
where the three-lepton invariant mass is just below the $Z$ boson mass.
The second class includes triboson processes, mainly $WWW^{\ast}$.
The last class of backgrounds are processes with a misidentified lepton, mainly $Z$+jets and top-quark pair production.

In the 3$\ell$-3SF and 3$\ell$-1SFOS SRs, $WZ/W\gamma^{\ast}$ and $ZZ^{\ast}$ represent the leading background contributions accounting for about 80\%
of the total background yields, with 65\%  from $WZ/W\gamma^{\ast}$ and 15\% from $ZZ^{\ast}$.
Production of $Z\gamma$, $VVV$, $Z$+jets and top-quarks share the remaining background fraction equally.
The 3$\ell$-0SFOS SR  contains contributions of similar size from $WZ/W\gamma^{\ast}$, $VVV$ and top-quark production. In this SR
the total background event yield is about eight times lower than in the 3$\ell$-3SF and 3$\ell$-1SFOS SRs.

A 3$\ell$-$WZ$ CR is defined by reversing the $Z$-veto requirement,  in order to select events with a $Z$ boson decay.
The 3$\ell$-$ZZ$ CR and 3$\ell$-$Z\gamma$ CR are defined by requiring low
\met\ values
to reflect the absence of final-state neutrinos in the background process
under study.
For these control regions, the invariant mass of the three leptons must be consistent with the
$Z$ boson mass.
These regions are further distinguished according to the flavour combination of the three leptons, namely
$eee$ or $\mu{\mu e}$ for the 3$\ell$-$Z\gamma$ CR, and
$\mu\mu\mu$ or $ee\mu$ for the 3$\ell$-$ZZ$ CR.

The 3$\ell$-$Z$jets CR is defined by reversing the \met\ and the $Z$-veto selections.
The properties of misidentified electrons and muons are different;
therefore the 3$\ell$-$Z$jets CR is further split
into the misidentified-electron component ($eee+\mu\mu e$
events) and misidentified-muon component ($\mu\mu\mu+ee\mu$ events) and
an
NF is assigned to each component.
In the 7~\tev\ data sample, the predicted $Z$+jets event yield with misidentified muons in the $\ensuremath{{\rm 3}{\ell}}$ SRs is negligible.
Furthermore, the number of events in the $3\ell$-$Z$jets CR with such a lepton flavour combination is too small
to reliably extract the NF.
Therefore the estimation of the misidentified-muon component is taken directly from simulation.

The 3$\ell$-Top CR is defined by requiring at least one $b$-tagged jet.
The $Z$+jets contribution is difficult to isolate from other processes that include $Z$ bosons.
Thus the NF for this process is constrained not only by the
3$\ell$-$Z$jets CR, but also in part by the 3$\ell$-$WZ$ CR and the
3$\ell$-$ZZ$ CR, as indicated in table~\ref{tab:CRs}.

\subsection{Background in the opposite-sign two-lepton channel}

The dominant background in this channel is top-quark production, which accounts for about 50\% of the total contamination.
The 2$\ell$-OSTop CR is defined by requiring a high invariant mass of the lepton pair in the final state.
As the $b$-jet rejection criteria are the same in the CR and SR,
the systematic uncertainties related to $b$-tagging largely cancel between the two regions.
The second dominant background is $\Ztau$, which accounts for 20\% of the total
background in the SR.
A dedicated control region, 2$\ell$-$Z\tau\tau$ CR, is defined by requiring a large opening angle between the two leptons.
The $WW$ process constitutes the third largest background, accounting for 10\% of the total.
Due to a difficulty in separating this process from $\ttbar$ events over a wide kinematic region,
no dedicated CR is defined, and this process is modelled purely by MC simulation.

The contribution of backgrounds with misidentified leptons, $W$+jets and multijet, accounts for 10\% of the total background.
The misidentified-lepton background rate has an uncertainty of  40\%.
Due to this large uncertainty, the misidentified-lepton background contributes significantly to this channel.
The $WZ/W\gamma^{\ast}$ production and the ggF production followed by $\ensuremath{H{\rightarrow\,}WW^{\ast}}$ decay, each representing 5\%  of the total background, are modelled with MC simulation.

\subsection{Background in the same-sign two-lepton channel}

The  $WZ/W\gamma^{\ast}$ and $W$+jets processes each account for one third of the total background.
Some of the
$WZ/W\gamma^{\ast}$ events with three leptons enter the selection when
one of the leptons escapes detection.
To normalise this process, the 2$\ell$-$WZ$ CR is defined by selecting events with three leptons.
The contamination from $W$+jets events with one misidentified lepton
is estimated by using the same data-driven method used in the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel.

The remaining background processes contribute at the 10\% level or less.
The normalisation of $W\gamma$
is based on the 2$\ell$-$W\gamma$ CR, defined
by requiring at least one electron consistent with a conversion, including a requirement that the electron does not have a hit in the innermost pixel layer.
The background contribution to the \ensuremath{{\rm 2}{\ell}}-SS channel
due to lepton charge misidentification, in otherwise charge-symmetric
processes, is found to be relevant only for electrons and affects
top-quark production, opposite-sign $WW$ and $Z$+jets.
It represents 10\% of the total background in the \ensuremath{{\rm 2}{\ell}}-SS1jet SR and
3\% of the total background in the \ensuremath{{\rm 2}{\ell}}-SS2jet SR.
The 2$\ell$-SSTop CR, 2$\ell$-$WW$ CR and 2$\ell$-$Z$jets CR are defined selecting opposite-sign leptons to normalise these contributions.
Moreover, in  2$\ell$-SSTop CR at least one $b$-tagged jet is selected.
Due to the small production rate, no control region is defined to normalise
the $WW$ events  from vector boson scattering with same charge, whose rate is taken directly from simulation.

\subsection{Normalisation factors and composition of control regions}

NFs are computed through the signal extraction fit explained in section~\ref{sec:interpretation}.
Table~\ref{tab:CRs} lists
the main background processes, along with the CRs that contribute to the determination of their NFs.
The NFs, which are specific to each signal region, are fitted taking into account only the total
number of expected and observed events in each CR, separately for the
8~\tev\ and 7~\tev\ data samples, and are summarised in table~\ref{tab:NFs}.
The numbers of observed and expected events from simulation in the
  8~\tev\ and 7~\tev\ data analysis are summarised
in table~\ref{table:CR34}.

Background spectra and the expected composition of the CRs in 8~\tev\ collisions are shown in figures~\ref{Figure:CR-3lep}--\ref{Figure:CR-SS}.
The $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ component is
shown on top of the background to demonstrate that
there is no significant signal leakage in the CRs.
The exact amount of signal leakage in each CR is presented in table~\ref{table:CR34}.

In these tables and figures, each background process normalised using CRs is presented separately,
while backgrounds that are not normalised using CRs are grouped together as ``Others''.
The ggF and VBF production of Higgs bosons,
and the $VH(H \rightarrow \tau\tau)$ process
are included in the ``Others'' category, assuming $\mH = 125\gev$ and
the SM value for the
cross sections and for the branching fraction.

\begin{table}[h!]
\begin{center}
\begin{tabular}{l||c|c|cc}
 \multicolumn{5}{l}{(a) 8 \tev\ data sample} \\
\hline
Channel & \ensuremath{{\rm 4}{\ell}}\ & \ensuremath{{\rm 3}{\ell}}\ & \multicolumn{2}{c}{ \ensuremath{{\rm 2}{\ell}}\ } \\
\hline
Category       & 2SFOS, 1SFOS & 3SF, 1SFOS, 0SFOS & DFOS & SS2jet, SS1jet \\
\hline
\hline
Process      &   &  &  &  \\
~~$WZ/W\gamma^{\ast}$  & ---                  & $1.08^{+0.08}_{-0.06}$              & ---                  & $0.94 \pm 0.10$\\
&&&&\\
~~$ZZ^{\ast}$          & $1.03^{+0.11}_{-0.10}$ & $1.28^{+0.22}_{-0.20}$             & ---                  & ---          \\
~~OS $WW$             & ---                  & ---                               & ---                  & $0.80 \pm 0.33$ \\
~~$W\gamma$           & ---                  & ---                               & ---                  & $1.06 \pm 0.12$ \\
~~$Z\gamma$           & ---                  & $0.62^{+0.15}_{-0.14}$              & ---                  & ---          \\
&&&&\\
~~$Z/\gamma^{\ast}$    & ---                  & $0.80^{+0.68}_{-0.53}$ ($\mu$-misid) & $0.90^{+0.18}_{-0.16}$ & $0.86 \pm 0.30$  \\
&&&&\\
                      &                      & $0.33^{+0.12}_{-0.11}$ ($e$-misid)   && \\
&&&&\\
~~Top                 & ---                  & $1.36^{+0.34}_{-0.30}$              & $1.05^{+0.16}_{-0.14}$ & $1.04 \pm 0.08$  \\
&&&&\\
\hline
 \multicolumn{5}{l}{} \\
 \multicolumn{5}{l}{(b) 7 \tev\ data sample} \\ \cline{1-4}
Process      &   &  &  &  \\
~~$WZ/W\gamma^{\ast}$  & ---                  & $1.02^{+0.12}_{-0.11}$
                                 & ---           & \\
&&&&\\
~~$ZZ^{\ast}$          & $1.59^{+0.36}_{-0.31}$ & $1.78^{+0.51}_{-0.42}$            & ---           & \\
&&&&\\
~~OS $WW$             & ---                  & ---                             & ---           & \\
~~$W\gamma$           & ---                  & ---                             & ---           & \\
~~$Z\gamma$           & ---                  & $0.45^{+0.09}_{-0.09}$            & ---           & \\
&&&&\\
~~$Z/\gamma^{\ast}$    & ---                  & $0.68^{+0.16}_{-0.15}$ ($e$-misid) & $1.11^{+0.38}_{-0.34}$ & \\
&&&&\\
~~Top                 & ---                  & $1.25^{+0.66}_{-0.52}$            & $0.93^{+0.16}_{-0.14}$ & \\
&&&&\\
\cline{1-4}
\cline{1-4}
\end{tabular}

\caption{Summary of background normalisation factors in the (a) 8~\tev\ and (b) 7~\tev\ data samples.
         The uncertainties include both the statistical and systematic components (see section~\ref{sec:systematics}).
         ``---'' denotes that the background process,
               when considered, is normalised by MC simulation.}
\label{tab:NFs}
\end{center}
\end{table}

\begin{table}[h!]
\begin{center}
\scalebox{0.58}{
\begin{tabular}{l|| D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1}}
\multicolumn{9}{l}{ (a) 8~\tev\ data sample}                       \\
\hline
Channel            & \multicolumn{1}{c|}{ \ensuremath{{\rm 4}{\ell}}\ } &
                                                        \multicolumn{5}{c|}{ \ensuremath{{\rm 3}{\ell}}\ } & \multicolumn{2}{c}{ DFOS \ensuremath{{\rm 2}{\ell}}\ }     \\
\hline
CR                 & \multicolumn{1}{c|}{$ZZ$} & \multicolumn{1}{c}{$WZ$} & \multicolumn{1}{c}{$ZZ$} & \multicolumn{1}{c}{$Z$jets} & \multicolumn{1}{c}{Top} & \multicolumn{1}{c|}{$Z\gamma$} & \multicolumn{1}{c}{$Z\tau\tau$} & \multicolumn{1}{c}{OSTop}\\
 \hline
Observed events           & \multicolumn{1}{c|}{122} & \multicolumn{1}{c}{578} & \multicolumn{1}{c}{60} & \multicolumn{1}{c}{251} & \multicolumn{1}{c}{55} & \multicolumn{1}{c|}{156} & \multicolumn{1}{c}{328} & \multicolumn{1}{c}{1169}\\
MC prediction             & 121 , 16 & 576 , 63  & 60 , 10     & 249 , 46 & 55 , 12     & 155 , 31 & 326 , 55 & 1160 , 150\\
\multicolumn{1}{l||}{MC (no NFs)}    & 118 , 10 & 543 , 50  & 48 , 4  & 351 , 40 & 48 , 6  & 188 , 17 & 354 , 56 & 1120 , 140\\
\hline
Composition ($\%$)        &&&&&&&&\\
$~~WZ/W\gamma^{\ast}$     &   \multicolumn{1}{c|}{---} & 89.3 , 1.5
                                                                                & 5.5 , 1.0   & 25.9 , 3.5   & 20 , 4  &  1.68 , 0.31   &\multicolumn{1}{c}{---}&\multicolumn{1}{c}{---}\\
$~~ZZ^{\ast}$             &   99.49 , 0.17               & 6.7 , 1.2    & 90.1 , 2.1   & 38 , 5   & 3.6 , 1.2   &  47 , 6  &\multicolumn{1}{c}{---}&\multicolumn{1}{c}{---}\\
$~~Z\gamma$               &   \multicolumn{1}{c|}{---} & 0.54 , 0.17
                                                                                & 0.6 , 0.5    & 5.5  , 1.5   & 2.4 , 0.9   &  43 , 7  &\multicolumn{1}{c}{---}&\multicolumn{1}{c}{---}\\
$~~Z$+jets                &   \multicolumn{1}{c|}{---} & 1.1 , 0.5  & 2.1 , 1.5    & 29 , 7   & 5.50 , 3.34   &  8.3 , 3.4   &78.2 , 2.8 &0.7 , 0.4\\
$~~$Top                   &    0.019 , 0.012             & 0.66 , 0.18  & 0.27 , 0.13  & 0.081 , 0.034  & 64 , 6  &  0.13 , 0.06 &10.5 , 1.6 &71.3 , 3.3\\
$~~$Others                &   0.49 , 0.17              & 0.80 , 0.16  & 1.16 , 0.20    & 0.87 , 0.13  & 3.6 , 0.6   &  0.33 , 0.06 &11.2 , 1.9 &27.8 , 3.2\\
$~~VH~(H\rightarrow WW^{\ast})$    &   0.026 , 0.006     & 0.93 , 0.16  & 0.26 , 0.11  & 0.37 , 0.09  & 0.52 , 0.13 &  0.052 , 0.011 &0.100 , 0.018&0.21 , 0.04\\
\hline
\end{tabular}
}
\end{center}

\begin{center}
\scalebox{0.58}{
\begin{tabular}{l|| D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} }
\hline
Channel       & \multicolumn{5}{c}{SS \ensuremath{{\rm 2}{\ell}}\ } \\
\hline
CR            & \multicolumn{1}{c}{$W\gamma$} & \multicolumn{1}{c}{$WZ$} & \multicolumn{1}{c}{$WW$} & \multicolumn{1}{c}{SSTop}& \multicolumn{1}{c}{$Z$jets} \\
\hline
\hline
Observed events           & \multicolumn{1}{c}{228} & \multicolumn{1}{c}{331} & \multicolumn{1}{c}{769} & \multicolumn{1}{c}{5142} & \multicolumn{1}{c}{39731} \\
MC prediction             & 229 , 41  & 311 , 66   & 742 , 63    & 5080 , 350   & 41000 , 14000\\
\multicolumn{1}{l||}{MC (no NFs)}    & 218 , 35  & 335 , 68   & 787 , 58    & 4930 , 330   & 47000 , 16000\\
\hline
Composition (\%)       &&&&& \\
$~~W\gamma$                    &85.0 , 2.4  &\multicolumn{1}{c}{---}  &0.46 , 0.14  &0.049 , 0.018 &0.022 , 0.007 \\
  $~~WZ/W\gamma^{\ast}$    &1.02 , 0.27 &85 , 4            &2.34 , 0.24  &0.200 , 0.029 &0.38 , 0.09\\
$~~WW$                   &0.37 , 0.08 &0.028 , 0.014&23.9, 2.3   &1.43 , 0.21   &0.57 , 0.15 \\
$~~Z$+jets               &4.2,1.6     &7.0, 3.5                 &7.0 , 2.0  &2.2 , 0.7   &97.7 , 0.5 \\
$~~$Top                  &0.68,0.20   &1.50, 0.29   &62.7 , 2.8   &95.5 , 0.8  &0.86 , 0.21 \\
$~~$Others               &8.7 , 1.2   & 5.3, 1.2  &3.2 , 0.4  &0.63 , 0.11   &0.44 , 0.11 \\
$~~VH~(H\rightarrow WW^{\ast})$   &\multicolumn{1}{c}{---}   &0.77, 0.17  &0.32 , 0.04  &0.036 , 0.005 &0.0077, 0.0020 \\
\hline
\end{tabular}
}
\end{center}

\begin{center}
\scalebox{0.58}{
\begin{tabular}{l|| D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1}}
 \multicolumn{9}{l}{(b) 7~\tev\ data sample}                       \\
\hline
Channel          & \multicolumn{1}{c|}{ \ensuremath{{\rm 4}{\ell}}\ } &
                                                      \multicolumn{5}{c|}{ \ensuremath{{\rm 3}{\ell}}\ }  & \multicolumn{2}{c}{ DFOS \ensuremath{{\rm 2}{\ell}}\ }     \\
\hline
CR               & \multicolumn{1}{c|}{$ZZ$} & \multicolumn{1}{c}{$WZ$} & \multicolumn{1}{c}{$ZZ$} & \multicolumn{1}{c}{$Z$jets} & \multicolumn{1}{c}{Top} & \multicolumn{1}{c|}{$Z\gamma$} & \multicolumn{1}{c}{$Z\tau\tau$} & \multicolumn{1}{c}{OSTop}\\
\hline
 Observed events          & \multicolumn{1}{c|}{24} & \multicolumn{1}{c}{101} & \multicolumn{1}{c}{18} & \multicolumn{1}{c}{68} & \multicolumn{1}{c}{9} & \multicolumn{1}{c|}{123} & \multicolumn{1}{c}{55} & \multicolumn{1}{c}{137}\\
 MC prediction            & 24 , 8  & 101 , 16    & 18 , 5  & 67 , 15     & 8 , 4   & 123 , 26      & 55 , 15    & 137 , 20\\
 \multicolumn{1}{l||}{MC (no NFs)}   & 15 , 5  & 99 , 10  & 10.7 , 0.6  & 81 , 7 & 8.1 , 1.4   & 208 , 12      & 51 , 12    & 145 , 18\\
\hline
 Composition  ($\%$)    & &&&&&&&\\
 $~~WZ/W\gamma^{\ast}$   &  \multicolumn{1}{c|}{---} & 87.5 , 2.5  & 3.1 , 1.1   & 6.9 , 1.4  & 14 , 5 & 0.61 , 0.15    &\multicolumn{1}{c}{---}&\multicolumn{1}{c}{---}\\
 $~~ZZ^{\ast}$           &  99.71 , 0.12  & 7.4  , 2.1  & 92.7 , 2.3  & 26 , 6  & 4.2 , 2.5   &  32 , 7               &\multicolumn{1}{c}{---}&\multicolumn{1}{c}{---}\\
 $~~Z\gamma$             &  \multicolumn{1}{c|}{---} & 1.8 , 0.8   &
                                                                     0.5 , 0.4   & 48 , 7  & 6 , 4   & 59 , 7    &\multicolumn{1}{c}{---}&\multicolumn{1}{c}{---}\\
 $~~Z$+jets              &  \multicolumn{1}{c|}{---} & 1.5 , 0.8   & 3.0 , 1.4   & 19 , 5  & 0.4 , 2.2   & 8.2 , 2.1     &76 , 6  & 0.14 , 0.15   \\
 $~~$Top                 &  0.031 , 0.015 & 0.7 , 0.4 & 0.01, 0.20 & 0.07 , 0.13 & 71, 10      & 0.03 , 0.04   &13 , 5  & 75.2 , 3.2\\
 $~~$Others              &  0.23 , 0.11 & 0.56 , 0.11 & 0.44 , 0.11  & 0.115 , 0.021 & 4.2 , 1.4  &  0.05 , 0.17 &11 , 4  & 24.7 , 3.2\\
 $~~VH~(H\rightarrow WW^{\ast})$  &  0.02 , 0.31 & 0.53 , 0.08 & 0.106 , 0.030 & 0.044, 0.008 & 0.41 , 0.17  &  0.0154 , 0.0027  &0.048 , 0.017 & 0.135 , 0.030 \\
\hline
\end{tabular}
}
\caption{Number of observed and predicted events and background
  composition in the CRs for the $\ensuremath{{\rm 4}{\ell}}$,  $\ensuremath{{\rm 3}{\ell}}$ and
  $\ensuremath{{\rm 2}{\ell}}$ channels in the (a) 8~\tev\ and (b) 7~\tev\ data samples.
         Normalisation factors are taken into account in the calculation of the composition.
The uncertainties on event yields include both the statistical and
systematic components (see section~\ref{sec:systematics}).
}
\label{table:CR34}
\end{center}
\end{table}

\begin{figure}[htp]
\begin{center}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_WZCR_ALL_Mll02_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_ZZCR_ALL_Mll02_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_ZCR_ALL_Mll02_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_TopCR_ALL_Mll02_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_ZgCR_ALL_Mll02_mh125_lin.pdf}}
\caption{
Distributions of the invariant mass of leptons $\ell_0$ and $\ell_2$, defined in secton~\ref{sec:analysis}, in the five CRs defined in the 3$\ell$ channel:
(a) 3$\ell$-$WZ$ CR, (b) 3$\ell$-$ZZ$ CR, (c) 3$\ell$-$Z$jets CR, (d) 3$\ell$-Top CR and (e) 3$\ell$-$Z\gamma$ CR.
Data (points) are compared to the background plus $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation
(stacked filled histograms),
where the background contributions are normalised by applying the normalisation factors
shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents total uncertainty, both statistical and systematic (see section~\ref{sec:systematics}), on the total background estimate.
The last bin includes overflows.
}
\label{Figure:CR-3lep}
\end{center}
\end{figure}

\begin{figure}[htp]
\begin{center}
\includegraphics[width = 0.48\textwidth]{quadlep_ZZCR_Cut_OR_ALL_m4l_mh125_log.pdf}
\caption{
Distribution of the 4-lepton invariant mass $m_{4\ell}$ in the 4$\ell$-$ZZ$ CR control region.
Data (points) are compared to the background plus $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation
(stacked filled histograms),
where $ZZ^{\ast}$ events are normalised by applying the normalisation factor
shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents total uncertainty, both statistical and systematic (see section~\ref{sec:systematics}), on the total background estimate.
The last bin includes overflows.
}
\label{Figure:CR-4lep}
\end{center}
\end{figure}
\begin{figure}[htp]
\begin{center}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{emme_CutFailVBFHighMllTopCR_2jetincl_DYjj_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{emme_CutZtautauControl_2jetincl_DYjj_mh125_lin.pdf}}
\caption{
Distributions of the difference in rapidity between the two leading jets $\Delta y_{jj}$ (a) in the 2$\ell$-OSTop CR and (b) in the 2$\ell$-$Z\tau\tau$ CR.
Data (points) are compared to the background plus $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation
(stacked filled histograms),
where the background contributions are normalised by applying the normalisation factors
shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents total uncertainty, both statistical and systematic (see section~\ref{sec:systematics}), on the total background estimate.
The last bin includes overflows.
}
\label{Figure:CR-DFOS}
\end{center}
\end{figure}

\begin{figure}[htp]
\begin{center}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{CutWGCR_DPhill_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{CutWZCR_lepPtLead_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{CutWWCR_MT_STVF_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{CutTOPCR_MET_STVF_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{CutZCR_DPhill_mh125_lin.pdf}}
\caption{
Distribution of relevant variables in the control regions in the 2$\ell$-SS channel:
(a) azimuthal angle between the two leptons $\Delta \phi_{\ell_1\ell_2}$ in the 2$\ell$-$W\gamma$ CR,
(b) transverse momentum of the leading lepton in the 2$\ell$-$WZ$ CR,
(c) transverse mass $\ensuremath{m_{\rm T}}$ in the 2$\ell$-$WW$ CR,
(d) missing transverse momentum $\met$ in the 2$\ell$-SSTop CR and
(e) $\Delta \phi_{\ell_1\ell_2}$, in the 2$\ell$-$Z$jets CR.
Data (points) are compared to the background plus $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation
(stacked filled histograms),
where the background contributions are normalised by applying the normalisation factors shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents total uncertainty, both statistical and systematic (see section~\ref{sec:systematics}), on the total background estimate.
The last bin includes overflows.
}
\label{Figure:CR-SS}
\end{center}
\end{figure}

\clearpage
\newpage

\subsection{Event reconstruction}
\input{Reconstruction}
\label{sec:reconstruction}

\subsection{Event selection}\label{sec:eventselection}
Events are required to contain a primary vertex.
The four channels are further split into eight
signal regions, designed to optimise the sensitivity to the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ process,
with a specific set of selections applied to define each signal region.
The selection criteria rely on the number of leptons
and their properties such as charge, flavour, $\pt$,
and on the number of jets and $b$-tagged jets and on the magnitude of the missing transverse momentum.
Leptons with $\pt{} > 15\gev$ are selected and their number is used to divide the analysis in the
various channels. Similarly the analysis channels are subdivided in categories according the number of selected jets.
Of particular importance are the invariant masses and opening angles among the selected objects,
most notably those of  opposite-sign  lepton pairs.
The spin-0 property of the Higgs boson, in conjunction with the $V\mbox{-}A$ structure of the weak interaction,
results in a preference for a small opening angle of lepton pairs from the
$H \rightarrow WW^{\ast} \rightarrow \ell\nu\ell\nu$ decays.
On the other hand, as described in section~\ref{sec:analysis},
major backgrounds
often contain $Z$ boson production or $\ttbar$ production which give rise to opposite-sign lepton pairs
with a large opening angle.
In the $\ensuremath{{\rm 2}{\ell}}$-SS channel, the lepton originating from  the Higgs boson decay is selected by minimising
the invariant mass of the lepton and jet(s);
cuts are then applied to the opening angle between this lepton and the closest jet in the transverse plane.
The definitions of the signal regions used for each channel are summarised
in table~\ref{tab:event_selection} and further detailed in sections~\ref{subs:4l}--\ref{subs:2lss}.

\begin{sidewaystable}[hp!]
\begin{center}
\scalebox{0.85}{
\begin{tabular}{r||cc|ccc|ccc}
\hline
Channel &  \multicolumn{2}{c|}{\ensuremath{{\rm 4}{\ell}}} & \multicolumn{3}{c|}{\ensuremath{{\rm 3}{\ell}}}& \multicolumn{3}{c}{\ensuremath{{\rm 2}{\ell}}}    \\
\hline
Category &  2SFOS & 1SFOS  & 3SF & 1SFOS & 0SFOS & DFOS & SS2jet & SS1jet \\
\hline
Trigger & \multicolumn{2}{c|}{single-lepton triggers} & \multicolumn{3}{c|}{single-lepton triggers}& \multicolumn{3}{c}{single-lepton \& dilepton triggers} \\
\hline
Num.  of leptons & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2  \\
$p_{\rm T,leptons}$ [\gev] & $>25,20,15$ & $>25,20,15$ & $>15$ &$>15$ & $>15$ & $>22,15$ & $>22,15$ & $>22,15$ \\
Total lepton charge & 0 & 0 & $\pm 1$ & $\pm 1$ & $\pm 1$ & 0 & $\pm 2$ & $\pm 2$  \\
Num.  of SFOS pairs  & 2& 1 & 2 & 1 & 0 & 0 & 0 & 0   \\
Num.  of jets & $\le 1$ & $\le 1$ & $\le 1$ & $\le 1$ & $\le 1$ & $\ge 2$ & 2 & 1  \\
$p_{\rm T,jets}$ [\gev] &$>25~(30)$ &$>25~(30)$ &$>25~(30)$ &$>25~(30)$ &$>25~(30)$ &$>25~(30)$ &$>25~(30)$&$>25~(30)$\\
Num.  of $b$-tagged jets & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\met\ [\gev] & $>20$ & $>20$ & $>30$ & $>30$ & --- & $>20$ & $>50$ & $>45$   \\
\ptmiss\ [\gev] & $>15$ & $>15$ & $>20$ & $>20$ & --- & --- & --- & ---  \\
$|m_{\ell\ell} - m_{Z}|$ [\gev] & $<10~(m_{\ell_{2}\ell_{3}})$ & $<10~(m_{\ell_{2}\ell_{3}})$ & $>25$ & $>25$ & --- & --- & $>15$ & $>15$ \\
Min. $m_{\ell\ell}$ [\gev] & $>10~(m_{\ell_{0}\ell_{1}})$ & $>10~(m_{\ell_{0}\ell_{1}})$&  $>12$ & $>12$ & $>6$ & $>10$ & $>12~(ee,\mu\mu)$ & $>12~(ee,\mu\mu)$ \\
                        & & & & & & & $>10~(e\mu)$ & $>10~(e\mu)$\\
Max. $m_{\ell\ell}$ [\gev] & $<65~(m_{\ell_{0}\ell_{1}})$ & $<65~(m_{\ell_{0}\ell_{1}})$ &$<200$ & $<200$ & $<200$ & $<50$ & --- & ---  \\
$m_{4\ell}$ [\gev] & $>140$ & --- & --- & --- & --- & --- & --- & ---  \\
$p_{\rm T,4\ell}$ [\gev] & $>30$& --- & --- & --- & --- & --- & --- & ---  \\
$m_{\tau\tau}$ [\gev] & --- & --- & --- & --- & --- & $<(m_{Z} - 25)$ & --- & ---  \\
$\Delta R_{\ell_{0}\ell_{1}}$ & --- & ---& $<2.0$ & $<2.0$ & --- & --- & --- & --- \\
$\Delta \phi_{\ell_{0}\ell_{1}}$ [rad] & $<2.5~(\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost})$ & $<2.5~(\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost})$ & --- & --- & --- & $<1.8$ & --- & --- \\
$\ensuremath{m_{\rm T}}$ [\gev] & --- & --- & --- & --- & --- & $<125$ &  ---&$>105~(\ensuremath{m_{\rm T}^{\rm lead}})$  \\
Min. $m_{\ell_{i}j(j)}$ [\gev] & --- & --- & --- & --- & --- & --- & $<115$ & $<70$ \\
Min. $\phi_{\ell_{i}j}$ [rad] & --- & --- & --- & --- & --- & --- & $<1.5$ & $<1.5$ \\
$\Delta y_{jj}$ & --- & --- & --- & --- & --- & $<1.2$ & --- & --- \\
$|m_{jj} - 85|$ [\gev] & --- & --- & --- & --- & --- & $<15$ & --- & --- \\
\hline
\end{tabular}
}
\caption{
Definition of each signal region in this analysis. $\ensuremath{m_{\rm T}^{\rm lead}}$ is the transverse mass of the leading lepton and the $\vecmet$ (see section \ref{subs:2lss} for the definition of $\ensuremath{m_{\rm T}^{\rm lead}}$). For $p_{\rm T,leptons}$ in the \ensuremath{{\rm 4}{\ell}}\ channel the three
values listed above refer to the leading, sub-leading, and to the two remaining leptons, respectively. For $p_{\rm T,leptons}$ in the \ensuremath{{\rm 2}{\ell}}\ channel the two values listed above refer to the leading and  sub-leading leptons, respectively. For $p_{\rm T,jets}$ the value in parentheses refers to forward jets ($|\eta| > 2.4$).
}
\label{tab:event_selection}
\end{center}
\end{sidewaystable}

In all the  $\ensuremath{{\rm 4}{\ell}}$ and $\ensuremath{{\rm 3}{\ell}}$ signal regions, events are recorded using inclusive single-lepton triggers,
which are fully efficient for high lepton multiplicity signatures.
For the $2\ell$ channels in 8~\tev\ data taking, dilepton triggers are also used.
In all channels at least one lepton must match a candidate reconstructed at trigger level.
This requires the leading lepton in an event to have $\pt$ greater than 24~\gev\ in the 8~\tev\ data sample, and greater than 18~\gev\ and 20~\gev\ for muons and electrons respectively in the 7~\tev\ data sample.
Single lepton trigger efficiencies are measured with respect to
offline reconstructed leptons using leptonic \Zboson\ decays. The
measured values are approximately  95\% for electrons, 90\% for muons in the endcap and 70\%
for muons in the barrel.

\subsubsection{Four-lepton channel}\label{subs:4l}
Events in the $\ensuremath{{\rm 4}{\ell}}$ channel are required to have exactly four leptons.
The $\pt$ of leading and sub-leading leptons must be above 25~\gev\ and 20~\gev, respectively,
and the \pt\ of each of the remaining two leptons must exceed 15~\gev.
The total charge of the four leptons is required to be zero.
Only events with at least one SFOS lepton pair are accepted, and events are assigned to the 4$\ell$-2SFOS and 4$\ell$-1SFOS SRs according to the number of such pairs.

In order to select final states with neutrinos, \met{} and \ptmiss\ are required to be above 20~\gev\ and above 15~\gev, respectively.
In order to reduce the $\ttbar Z$ background, events are vetoed if they contain more than one jet.
Top-quark production is further suppressed by vetoing events with any $b$-tagged jet with \pt~above 20~\gev.
The invariant mass of $\ell_2$ and $\ell_3$, $m_{\ell_2\ell_3}$, is required to satisfy
$|m_{\ell_2\ell_3}- m_{Z}| < 10 \gev$ (where $m_{Z}$ is the mass of the $Z$ boson),
and the invariant mass of $\ell_0$ and $\ell_1$, $m_{\ell_0\ell_1}$, is required to be between 10~\gev\ and 65~\gev.
This requirement on  $m_{\ell_0\ell_1}$  greatly reduces the contamination from $ZZ^{(\ast)}$ production in events with two pairs of SFOS leptons.

The sensitivity is improved by exploiting two additional variables.
The variable $\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost}$ denotes the difference in azimuthal angle
between the two leptons from the Higgs boson candidate in
the frame where
the Higgs boson's \pt\ is zero.
The Higgs boson transverse momentum is approximated with
$\vecptmissH \sim - \vecptmissZ - \vecptmissjet$, or with
$\vecptmissH \sim - \vecptmissZ$ if no jet is present.
The angular separation $\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost}$ is
required to be below 2.5~rad.
The magnitude of the vector sum of the lepton transverse momenta, \pt$_\mathrm{4\ell}$, can discriminate against
the main background, $ZZ^{(\ast)}$, which has no neutrinos.
A cut requiring \pt$_\mathrm{4\ell}>$ 30~\gev\ is introduced for the 4$\ell$-2SFOS SR.
In this signal region the invariant mass of the four leptons is required to be above 140~\gev\ to remove
events from the $H\to ZZ^{\ast} \to 4\ell$ decay, which are the target of another analysis~\cite{Aad:2014eva}.
In the signal extraction through the fit explained in section~\ref{sec:interpretation}, the 4$\ell$-2SFOS  and 4$\ell$-1SFOS SRs enter as two separate signal regions.

\subsubsection{Three-lepton channel}\label{subs:3l}
For the $\ensuremath{{\rm 3}{\ell}}$ channel, exactly three leptons with  $\pt > 15\gev$  are required with a total charge of $\pm1$.
After this requirement, contributions from
background processes that include more than one misidentified lepton,
such as  $W$+jet production and inclusive $b{\bar b}$ pair production, are negligible.
Events are then separated into the 3$\ell$-3SF, 3$\ell$-1SFOS and 3$\ell$-0SFOS SRs,
requiring three SF leptons, one SFOS lepton pair and zero SFOS lepton pairs, respectively.

In order to reduce the background from $t{\bar t}$
production, events are vetoed if they contain more than one jet.
The background from top-quark production is further suppressed by vetoing events if they contain any $b$-tagged jet with \pt~$> 20\gev$.
In order to select final states with neutrinos, \met{} is required to be above 30~\gev\ and \ptmiss\ above 20~\gev\ in the 3$\ell$-3SF and 3$\ell$-1SFOS SRs.
In the 3$\ell$-0SFOS SR, \met\ or \ptmiss\ selections are not imposed because the main backgrounds also contain neutrinos.
The invariant mass of all SFOS pairs in the 3$\ell$-3SF and 3$\ell$-1SFOS SRs is required to satisfy $|m_{\ell\ell}- m_{Z}| > 25 \gev$.
This requirement suppresses $WZ$ and $ZZ^{*}$ events, and increases the $Z$+jets rejection.

A lower bound is set on the smallest invariant mass of pairs of oppositely charged leptons at 12~\gev\  in the 3$\ell$-3SF and 3$\ell$-1SFOS SRs, and
at 6~\gev\ in the 3$\ell$-0SFOS SR.
In addition, an upper bound on the invariant mass of oppositely charged leptons is set at 200~\gev\ in the three signal regions.
These selections reject  backgrounds from HF and reduce the number of combinatorial lepton pairs from the $WZ/W\gamma^{\ast}$ process.
The latter could indeed give larger mass values with respect to the  $WH$ process since it can proceed through the t- and u-channels, in addition to the s-channel, which is also present in $WH$ production.

The angular separation $\Delta R_{\ell_0\ell_1}$ is required to be smaller than 2 in the 3$\ell$-3SF and 3$\ell$-1SFOS SRs.
This cut favours the Higgs boson decay topology relative to that of $WZ/W\gamma^{\ast}$ events.

In the 3$\ell$-3SF and 3$\ell$-1SFOS SRs, the shape of a  multivariate
discriminant based on a Boosted Decision Trees
(BDT)~\cite{Hoecker:1019880}, which produces a multivariate classifier (``BDT Score''), is used to achieve a further separation
between  signal and background.
The main purpose of the multivariate classifier is to distinguish between the
signal and the dominant $WZ/W\gamma^{\ast}$  and $ZZ^{\ast}$ backgrounds, and the BDT is trained against these two background processes.
The BDT parameters are chosen in order
to ensure that there is no overtraining, i.e. that the BDT is robust
against statistical fluctuations in the training samples.
The BDT input discriminating variables
which provide the best separation between signal and background are
the \pt\ of each lepton, the magnitude of their vector sum,
the invariant masses of the two opposite-sign lepton pairs ($m_{\ell_0\ell_1}$,  $m_{\ell_0\ell_2}$),
$\Delta R_{\ell_0\ell_1}$, $\met$, and \ptmiss.
In the fit, the shape of the distribution of the ``BDT Score'', divided into six bins,
is used  to extract the number of observed events in the 3$\ell$-3SF and 3$\ell$-1SFOS SRs,
while the shape of the distribution of $\Delta R_{\ell_0\ell_1}$, divided into four bins,
is used to extract the number of observed events in the 3$\ell$-0SFOS SR.
In the other channels only the event yield in each signal and control
region is used without shape information.

\subsubsection{Opposite-sign two-lepton channel}\label{subs:2los}
In the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel, exactly two leptons with $\pt$ larger than 22~\gev\ and 15~\gev\ are required.
Only opposite-sign $e\mu$ final states are considered in order to reduce the background from $Z$+jets, $WZ$ and $ZZ$ events.
A cut on the invariant mass of the lepton pair, $m_{\ell_0\ell_1} > 10\gev$, is applied to reject combinatorial dilepton backgrounds.
In order to select final states with neutrinos, \met{} is required to be above 20~\gev.
These selections reduce the
background processes that contain jets faking leptons.
The presence of at least two jets with $\pt > 25\gev$
is required.
The background from top-quark production is reduced
by vetoing events if they contain any $b$-tagged jets with $\pt > 20 \gev$.
To reject the $Z$+jets production that leads to $e \mu$ final states through \Ztau ~decay,
a requirement of $m_{\tau\tau} < (m_{Z} -25\gev)$ is applied, where $m_{\tau\tau}$ is the  dilepton invariant mass reconstructed using the collinear approximation~\cite{HWWllpaper}, namely under the assumptions that the lepton pair originates from $\tau$ lepton decays, the neutrinos are the only source of ${E_{\T}^{\miss}}$ and they are collinear with the charged leptons.

Upper bounds
on the invariant mass of the lepton pair, $m_{\ell_0\ell_1} < 50 \gev$, and the azimuthal angular separation of the lepton pair, $\Delta\phi_{\ell_0\ell_1} < 1.8$ rad,
are applied to enhance the Higgs boson signal relative to the $WW$, $\ttbar$ and $W$+jets backgrounds.
Requirements on the rapidity separation between the two leading jets, $\Delta y_{jj} < 1.2$, and the invariant mass of the two leading jets,
$|m_{jj}-85\gev| < 15 \gev$, are introduced to select jets from the associated $W/Z$ bosons.
The central value of the $m_{jj}$ selection interval
is larger than the $W$ boson mass
in order to retain the acceptance for $ZH$ production with $Z \rightarrow \qqbar$ decay.

The selection $\ensuremath{m_{\rm T}} < 125$~\gev\ is applied, where $\ensuremath{m_{\rm T}}$
is the transverse mass of the dilepton system and $\met$, defined as
  $\ensuremath{m_{\rm T}} = \sqrt{(E_{\rm T}^{\ell\ell}+\met)^{2} - |{\bf \pt}^{\ell\ell}+{\bf \met}|^{2}}$,
where $E_{\rm T}^{\ell\ell} = \sqrt{|{\bf \pt}^{\ell\ell}|^{2}+m_{\ell\ell}^{2}}$.
The selections on $\Delta y_{jj}$ and $m_{jj}$ make this channel orthogonal to the ggF-enriched $n_{j} \ge 2$ category in ref.~\cite{HWWllpaper}, while orthogonality with respect to the VBF category is ensured by explicitly vetoing the BDT signal region of the VBF analysis~\cite{HWWllpaper}.
In the fit the 2$\ell$-DFOS channel enters as a single signal region.

\subsubsection{Same-sign two-lepton channel}\label{subs:2lss}
In the $\ensuremath{{\rm 2}{\ell}}$-SS channel, exactly two leptons with the same charge are required.
Lower bounds on lepton \pt{} are set to 22~\gev\ and 15~\gev\ and
both the same-flavour and different-flavour combinations are considered.
A lower bound on $m_{\ell_1\ell_2}$ is applied at 12~\gev\ for same-flavour lepton pairs and at
10~\gev\ for different-flavour lepton pairs.
Despite the same-charge requirement, a wrong-charge assignment may allow background contributions
from $Z$ boson decays. Therefore
a veto on same-flavour lepton pairs with $|m_{\ell_1\ell_2}- m_{Z}| < 15 \gev$
is introduced.

The 2$\ell$-SS2jet and 2$\ell$-SS1jet SRs require the number of jets to be exactly two or
exactly one, respectively.
Events with $b$-tagged jets having $\pt > 20~\gev$ are discarded.
The \met\ is required to be larger than 50~\gev\ in the 2$\ell$-SS2jet SR and larger than 45~\gev\ in the 2$\ell$-SS1jet SR.
Additional cuts are applied to events in the 2$\ell$-SS2jet and 2$\ell$-SS1jet SRs, on the following variables (see table~\ref{tab:event_selection} for details):
the minimum invariant mass of a lepton and the jet(s) in the event,
$m_{\ell_i {\rm j}}^{\rm min}$ ($m_{\ell_i {\rm jj}}^{\rm min}$);
the smallest opening angle between the lepton which minimises the above variable and a jet,
$\Delta\phi_{\ell_i {\rm j}}^{\rm min}$; the transverse mass of the leading lepton and the $\vecmet$, $\ensuremath{m_{\rm T}^{\rm lead}} = \sqrt{2 \times p_{\rm T, lead} \times \met \times (1 - \cos(\phi_{\rm lead} - \phi_{\met}))}$,
where $p_{\rm T, lead}$ and $\phi_{\rm lead}$ are respectively the transverse momentum and $\phi$ angle of the leading lepton.
Lower values of $m_{\ell_i {\rm j}}^{\rm min}$ ($m_{\ell_i {\rm jj}}^{\rm min}$)
and of $\Delta\phi_{\ell_i {\rm j}}^{\rm min}$
favour Higgs boson decays relative to the
major backgrounds. High values of  $\ensuremath{m_{\rm T}^{\rm lead}}$ help in reducing $W$+jets background.
The \pt\ threshold for the sub-leading muon in the $\mu\mu$ channel is increased to 20~\gev\ in both the SRs to suppress misidentified muons from $W$+jets and multijet production.

In the fit, the 2$\ell$-SS2jet and 2$\ell$-SS1jet SRs
are further split into four signal regions according to the combination of lepton flavours in each event:
$ee$, $e\mu$, $\mu e$ and $\mu \mu$, where $e\mu$ refers to the case in which the electron has
leading $\pt$ while $\mu e$ refers to the case in which the muon has leading $\pt$.
This splitting is motivated by the expected differences in the background contributions, for example $W\gamma$,
which is expected to be zero in the $\mu\mu$ channel but not in the other channels.

\subsubsection{Signal acceptance}\label{subs:signal}
The number of expected $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ events surviving the event selections
is presented for each channel in table~\ref{tab:signal}.
The total acceptance for $WH(H \rightarrow WW^{\ast} \rightarrow \ell\nu\ell\nu)$,
$WH(H\rightarrow  WW^{\ast} \rightarrow \ell\nu q q)$ and
$ZH(H\rightarrow  WW^{\ast} \rightarrow \ell\nu\ell\nu)$ is 3.7\%, 0.3\% and 1.9\%, respectively.
The analysis acceptance for the $ZH(H\rightarrow  WW^{\ast} \rightarrow \ell\nu q q)$ process is negligible.
The acceptance is defined as the ratio of the number of events in the SRs to the number of events expected according to the branching fractions for the various processes.
Associated Higgs boson production followed by the decay  $H\rightarrow\tau\tau$
cannot be completely isolated from the selected final states.
Therefore the results presented in this paper, with the exception of
 Section \ref{sec:couplings} for consistency of the analysed model,  include this process as part of the background,
with the production cross section ($\sigma_{VH}$) and ${\rm Br}(H\rightarrow\tau\tau)$ fixed to the SM value.

\clearpage
\begin{table}[h!]
\begin{center}
\scalebox{0.93}{
\begin{tabular}{r||cc|ccc|ccc}
 \multicolumn{9}{l}{(a) 8~\tev\ data sample}                       \\
\hline
Channel &  \multicolumn{2}{c|}{\ensuremath{{\rm 4}{\ell}}} & \multicolumn{3}{c|}{\ensuremath{{\rm 3}{\ell}}}& \multicolumn{3}{c}{\ensuremath{{\rm 2}{\ell}}}    \\
\hline
Category &  2SFOS & 1SFOS  & 3SF & 1SFOS & 0SFOS & DFOS & SS2jet & SS1jet \\
\hline
$WH~(H\rightarrow WW^{\ast})$&---                  &---                 & 0.56   & 1.4  & 1.3   & 1.5   & 1.0   & 1.8  \\
$ZH~(H\rightarrow WW^{\ast})$& 0.21   & 0.24  & 0.17  & 0.18 & 0.15 & 0.67 & 0.02 & 0.19  \\
\hline
\multicolumn{1}{c||}
{$VH~(H\rightarrow WW^{\ast})$}& 0.21 & 0.24 & 0.73 & 1.6 & 1.4  & 2.2 & 1.0 & 2.0  \\
\cline{2-9}
(all categories)  & \multicolumn{8}{c}{9.4 }\\

\hline
 \multicolumn{9}{c}{}                       \\
 \multicolumn{9}{l}{(b) 7~\tev\ data sample} \\
\cline{1-7}
$WH~(H\rightarrow WW^{\ast})$&---                   &--                   & 0.12 & 0.29 & 0.26 & 0.21 \\
$ZH~(H\rightarrow WW^{\ast})$&  0.023 & 0.021 & 0.013 & 0.033 & 0.028 & 0.075 \\
\cline{1-7}
\multicolumn{1}{c||}
{$VH~(H\rightarrow WW^{\ast})$}& 0.023 & 0.021 & 0.13 & 0.32 & 0.29 & 0.29 \\
\cline{2-7}
(all categories) & \multicolumn{6}{c}{1.1 } & &\\
\cline{1-7}
\cline{1-7}
\end{tabular}
}
\caption{Number of expected $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ events in the signal regions, for $\mH = 125\gev$, in the (a) 8~\tev\ and (b) 7~\tev\ data samples.}
\label{tab:signal}
\end{center}
\end{table}

\section{Introduction                                             \label{sec:introduction}        }
\input{Introduction}
\section{Analysis overview                                        \label{sec:analysis}            }
\input{Overview}
\section{The ATLAS detector                              \label{sec:atlas}               }
\input{Detector}
\section{Data samples                           \label{sec:DataMC}               }
\input{Samples}
\section{Event reconstruction and selection                                          \label{sec:selection}           }
\input{EventSelection}
\section{Background modelling                                      \label{sec:bkg}                 }
\input{Background}
\clearpage
\newpage
\section{Systematic uncertainties                             \label{sec:systematics}         }
\input{Systematics}
\section{Results                              \label{sec:results}              }
\input{Results}
\section{Conclusions                              \label{sec:conclusions}              }
\input{Conc}
\clearpage
\section*{Acknowledgements}
\input{Acknowledgements}

\subsection{Statistical method \label{sec:stat_formalism} }
The signal extraction is performed using the profile likelihood ratio
method~\cite{asymptotics}, which consists of maximising a binned likelihood function \makebox{$\mathcal{L}(\mu,
\boldsymbol{\theta}\mid\boldsymbol{n})$}.
The likelihood is the product of  Poisson distributions for each SR and CR.
The mean
values of the distributions are the sum of the  expected yields  of signal and background. The
symbol $\boldsymbol{n}$ represents the observed events in each SR
and CR. The signal and background expectations are functions of the
signal-strength parameter, $\mu$, and a set of nuisance parameters, $\boldsymbol{\theta}$.
The signal strength $\mu$ multiplies the SM predicted signal event yield
in all categories, while background normalisation factors, included as
nuisance parameters, represent corrections for  background
sources normalised to data.
Signal and background predictions are affected by systematic uncertainties
that are described by nuisance parameters.
The normalisation factors are left free in the fit, while the constraints on the systematic uncertainties are chosen to be log-normal distributions.

The test statistic $q_{\mu}$  is defined as
\begin{equation}
q_{\mu} = -2{\rm
  ln}\frac{\mathcal{L}(\mu,\boldsymbol{\hat{\theta}_{\mu}})}{\mathcal{L}_{\rm
    max}} = -2{\rm
  ln \Lambda}.
\label{eq:q_mu}
\end{equation}
The symbol $\boldsymbol{\hat{\theta}_{\mu}}$  indicates the nuisance parameter values at the maximum of the
likelihood function for a given $\mu$.
The denominator is the maximum value of $\mathcal{L}$
obtained with both $\mu$ and $\theta$ floating.
When the denominator is maximised, $\mu$ takes the value of $\hat{\mu}$.
The $p_0$ value is computed for the test statistic $q_0$ evaluated at $\mu=0$ in eq.~(\ref{eq:q_mu}), and is defined to be the
probability to obtain a value of $q_0$ larger than the observed value
under the background-only hypothesis. There are no bounds on
$\hat{\mu}$, although $q_0$ is defined to be negative if $\hat{\mu}
\le 0$.
The equivalent formulation, expressed in terms of the number of standard deviations $\sigma$, is
referred to as the local significance $Z_0$.
The signal acceptance for all production
modes and decays are computed
assuming $\mH=125.36\gev$, which is the mass measured in $H \to \gamma \gamma$ and $H \to 4 \ell$ decays by ATLAS~\cite{Aad:2014aba}.
The acceptance for this mass is obtained  interpolating  between the values computed at $\mH = 125$ and $130 \gev$.
\clearpage
\subsection{Characterisation of the excess and $VH$ signal region splitting                       \label{sec:characterization}
}

Table~\ref{tab:split} shows the expected sensitivity to the SM Higgs boson with mass $\mH=125.36\gev$,
the observed signal significance $Z_0$ for \ensuremath{H{\rightarrow\,}WW^{\ast}}\ decays and the measured $\mu$ value using the categories described in section~\ref{sec:selection}.
The 3$\ell$-3SF and 3$\ell$-1SFOS SRs are further split in the likelihood function according to the value of the ``BDT Score'',
while the 3$\ell$-0SFOS SR is split into intervals of $\Delta R_{\ell_0,\ell_1}$, as discussed in section~\ref{subs:3l}.
The intervals are shown in figures~\ref{Figure:SR_3lep}(a)--\ref{Figure:SR_3lep}(c).
Each of the 2$\ell$-SS2jet and 2$\ell$-SS1jet SRs is further split into four sub-categories according to the flavour of the leading and sub-leading leptons.
For the 2$\ell$-DFOS a single SR is considered.
The numbers in table~\ref{tab:split} are computed by adding the contributions from the ggF and VBF production to the signal component, and the relative strengths of $VH$,
ggF and VBF production are fixed to the SM values and constrained with their theoretical uncertainties.

\input{table_mu_magda}

\subsection{Signal significance extraction and determination of signal strengths                             \label{sec:interpretation}
}

The $VH$-targeted categories are then combined with the categories of the ggF and VBF analysis
using $H\to WW^{\ast} \to \ell \nu \ell \nu$ decays described in ref.~\cite{HWWllpaper}.
The combination is again performed by building a likelihood
function that includes the SRs and CRs of the ggF, VBF and $VH$ analyses.
The experimental and theoretical uncertainties affecting the same sources
are correlated among different production modes.
The $\mu$ values for each production mode ($\mu_{\rm ggF}$, $\mu_{\rm
  VBF}$, $\mu_{VH}$) are correlated in all categories and fitted together while the
background NFs are uncorrelated among the different
analyses as they cover different phase-space regions. Therefore, when
extracting $\mu_{VH}$, $\mu_{WH}$ and $\mu_{ZH}$, the ggF and VBF
productions are treated as background and their yields determined by
the global fit.

\noindent The fit results for the $\mu$ values for the $WH$, $ZH$ and $VH$
production
are:

\[
\mu_{WH} = 2.1^{+1.5}_{-1.3}{\,{(\rm stat.)}}^{+1.2}_{-0.8}{\,{(\rm sys.)}} , \, \,
\mu_{ZH} = 5.1^{+3.8}_{-3.0}{\,{(\rm
    stat.)}}^{+1.9}_{-0.9}{\,{(\rm sys.)}} , \, \, \\
\]
\[
\mu_{\small{VH}} = 3.0^{+1.3}_{-1.1}{\, {(\rm stat.)}}^{+1.0}_{-0.7}{\,{(\rm sys.)}}.
\]

The uncertainties on the $\mu_{VH}$ value are shown in
table \ref{table:sys_mu_VH} (see section \ref{sec:systematics} for
their description). The derivative of $\mu_{VH}$ with $m_{H}$ has
been evaluated to be -5.8 \%/\gev\ at $m_H = 125.36$~\gev.

\begin{table}[h!]
\begin{center}
\scalebox{0.75}{
\begin{tabular}{l||cc}
\multicolumn{2}{l}{ Uncertainties on the signal strength $\mu_{VH}$ (\%)}    \\
\hline
Signal theoretical uncertainties  &     \multicolumn{2}{c}{$\Delta \mu_{VH}/\mu_{VH}$} \\
                                               & + & - \\
~~~$VH$ acceptance             & 11 & 7 \\
~~~Higgs boson branching fraction & 7 & 4 \\
~~~QCD scale                     & 1.6 & 0.7 \\
~~~PDF and $\alpha_{\rm S}$            & 3.2 & 1.5  \\
~~~$VH$ NLO EW corrections         & 2.5 & 1.2 \\
\hline
Background theoretical uncertainties  &      \\
~~~  QCD scale                  & 10 & 9 \\
~~~  PDF and $\alpha_{\rm S}$         & 2.3 & 2.0 \\
~~~  $VVV$ $K$-factor               & 3.0 & 3.0 \\
~~~  MC modelling               & 7.5 & 6.9  \\
\hline
\\
\hline
Experimental uncertainties       &      \\
~~~Jet                           & 14 & 9  \\
~~~${E_{\T}^{\miss}}$ soft term              & 3.4 & 2.3 \\
~~~Electron                      & 4.8 & 2.9   \\
~~~Muon                          & 4.8 & 3.2   \\
~~~Trigger efficiency            & 1.7 & 0.9  \\
~~~$b$-tagging efficiency          & 4.7 & 3.2  \\
~~~Fake factor                  & 14 & 12 \\
~~~Charge mis-assignment        & 1.1 & 1.0 \\
~~~Photon conversion rate       & 0.8 & 0.7 \\
~~~Pile-up                       & 3.0 & 1.9  \\
~~~Luminosity                    & 5.4 & 3.3 \\
MC statistics & 8 & 8 \\
CR statistics              & 18 & 15  \\
ggF SR statistics        & 5.5 & 4.4 \\
VBF SR statistics        & 1.9 & 1.5 \\
ggF+VBF CR statistics        & 10 & 9 \\
\hline
\end{tabular}
}
\end{center}
\caption{Percentage theoretical and experimental uncertainties on the
  observed $VH$ signal strength $\mu_{VH}$. The contributions from signal-related and
  background-related theoretical uncertainties are specified. The ``VH
  acceptance'' is evaluated using both the $qq \to (W/Z)H$ and the
  $gg \to ZH$ production. The
  statistical uncertainty due to the ggF and VBF subtraction
  measured in the categories of the ggF and VBF analysis are indicated with ``ggF SR
  statistics'' and ``VBF SR statistics'', for the contribution from
  the signal regions, and ``ggF+VBF CR statistics'' for the
  contribution from the control regions. The row ``MC statistics''
  shows the uncertainty due to the statistics of the simulated samples.
The values are obtained from the combination of the 8~\tev\ and 7~\tev\ data samples.
}
\label{table:sys_mu_VH}
\end{table}
Figure \ref{fig:muvh_muzh} shows the value of the test statistic as a function of
$\mu_{WH}$ and $\mu_{ZH}$; as shown, the correlation between
the two parameters is weak.
\begin{figure}
\begin{center}
\includegraphics[width=0.6\textwidth]{mu_WH_mu_ZH.pdf}
\end{center}
\caption{The value of the test statistic as a function of $\mu_{WH}$ and
  $\mu_{ZH}$, for $\mH=125.36\gev$. The contours
correspond to the
  values of $(\mu_{WH},\mu_{ZH})$ associated with
the  68\%,
  90\% and 95\% confidence levels.
  The black cross indicates the best fit to the data and the open circle represents the SM expectation ($\mu_{WH}$, $\mu_{ZH}$)=(1,1).} \label{fig:muvh_muzh}
\end{figure}

 Table~\ref{tab:summary} summarises the signal strengths for each
production mode and their combination at a value of
$\mH = 125.36\gev$, together with the observed and the expected
$Z_0$. The combined signal strength is $\mu = 1.16^{+0.16}_{-0.15}
{\rm (stat.)}^{+0.18}_{-0.15} {\rm (sys.)}$,
and the significance of the excess respect to the background only
hypothesis is 6.5  $\sigma$, while the expected significance in the
presence of a Higgs boson decaying to $WW^{*}$ is 5.9 $\sigma$.
Figure \ref{fig:mu_s} shows the value of the test statistic
as a function of the signal strength of each production mode ($\mu_{\rm
  ggF}, \mu_{\rm VBF}, \mu_{VH}$) and as a
function of the combined signal strength $\mu_{HWW}$.

\begin{figure}
\begin{center}
\begin{tabular}{cccc}
\includegraphics[width=0.45\textwidth]{scan_folder_nott_mu_ggF.pdf} &
\includegraphics[width=0.45\textwidth]{scan_folder_nott_mu_VBF.pdf} \\
(a) & (b) \\
\includegraphics[width=0.45\textwidth]{scan_folder_nott_mu_VH.pdf} &
\includegraphics[width=0.45\textwidth]{scan_folder_nott_mu_glob.pdf} \\
(c) & (d) \\
\end{tabular}
\end{center}
\caption{The
value of the test statistic as a function of the $\mu$ value from the
different production modes (a) ggF, (b) VBF, (c) $VH$ and (d) all
combined. All values are extracted from the combined fit.
The best fit values are represented by the markers at the likelihood minima, with the $\pm 1 \sigma$ and $\pm 2 \sigma$  uncertainties given by the green and yellow shaded bands.
}\label{fig:mu_s}
\end{figure}

The obtained values are all compatible with the SM expectation within
1.4 standard deviations. Figures~\ref{fig:correlation}(a) and \ref{fig:correlation}(b)  show
the two-dimensional dependence of the likelihood on $\mu_{VH}$ and $\mu_{\rm ggF}$, and on $\mu_{VH}$ and $\mu_{\rm VBF}$.
The $\mu$ values not displayed are kept as free unconstrained parameters in the fit.
The correlation between the parameters shown in figure~\ref{fig:correlation} is small.
The central values obtained for $\mu_{\rm ggF}$ and $\mu_{\rm VBF}$ are slightly
different from those reported in ref.~\cite{HWWllpaper}.
The shift represents a few percent of the quoted errors
and is pulled up by the presence of a small contamination by $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ events
in the 1-jet and 2-jets categories of the ggF and VBF analysis.

\input{table_mu_summary.tex}
\clearpage
\begin{figure}[h]
\subfigure[]{\includegraphics[width=0.49\textwidth]{mu_ggF_mu_VH.pdf}}
\subfigure[]{\includegraphics[width=0.49\textwidth]{mu_VBF_mu_VH.pdf}}
\caption{Likelihood as a function of the production mode signal
  strengths in two-dimensional planes of (a)  $\mu_{VH}$  vs $\mu_{\rm ggF}$ and
(b) $\mu_{VH}$ vs $\mu_{\rm VBF}$.
  The black cross indicates the best fit to the data and the open circle represents the SM expectation (1,1).
}
\label{fig:correlation}
\end{figure}
\subsection{Measurement of the couplings to vector bosons and fermions}
\label{sec:couplings}

The values of $\mu_{\rm ggF}$, $\mu_{\rm VBF}$ and $\mu_{VH}$ can be used to test the compatibility of the bosonic
and fermionic couplings of the Higgs boson with the SM prediction using
the formalism developed in ref.~\cite{Heinemeyer:2013tqa}.
Assuming the validity of the SU(2) custodial symmetry and a universal
scaling of the fermion couplings relative to the SM prediction, two
parameters are defined: the scale factor for the SM coupling to the vector bosons ($\kappa_V$)
and the scale factor for the coupling to the fermions ($\kappa_F$).
Loop-induced processes are assumed to scale as in the
SM. The $H \to \tau \tau$ contribution is treated
as signal and its yield is parameterised as a function of $\kappa_V$ and
$\kappa_F$.
The total width of the Higgs boson can be expressed as the sum of the different
partial widths, each one rescaled by the square of the appropriate scaling
factor. Neglecting the small contribution from $\Gamma(H \to\gamma\gamma)$ and rarer decay modes,
the $\ensuremath{H{\rightarrow\,}WW^{\ast}}$ decay branching fraction is expressed as:

\begin{equation*}
{\small
{\mathrm{Br}}(\ensuremath{H{\rightarrow\,}WW^{\ast}}) = \frac{\kappa_V^2 \Gamma_{\rm SM} (\ensuremath{H{\rightarrow\,}WW^{\ast}})}{\kappa_F^2\Gamma_{\rm SM} (H \to
  f\overline{f}) +
  \kappa_F^2\Gamma_{\rm SM}(H \to gg) +  \kappa_V^2\Gamma_{\rm SM}(H\to VV)},
}
\end{equation*}

\noindent where $\Gamma_{\rm SM}(H\to f\overline{f})$,  $\Gamma_{\rm SM} (H\to gg)$ and $\Gamma_{\rm SM} (H\to VV)$ are the SM partial decay
widths to fermions, gluons and weak bosons, respectively.

The ggF ($gg \to H$) process depends directly on the fermion scale factor $\kappa_F^2$ through the top and bottom quark loops, while the VBF ($qq \to Hqq$) and $VH(qq \to VH)$ production cross sections are proportional to
$\kappa_V^2$, as expressed by the following relations:

\begin{equation*}
{\small
\sigma(gg \to H) = \kappa_F^2\sigma_{\rm SM}(gg \to H), \quad \sigma(qq \to H qq) =
\kappa_V^2\sigma_{\rm SM}(qq \to Hqq),
}
\end{equation*}
\begin{equation*}
\sigma(qq \to WH,ZH) = \kappa_V^2\sigma_{\rm SM}(qq \to WH,ZH).
\end{equation*}
where the $\sigma$ without subscript indicates the $(\kappa_V$, $\kappa_F)$-dependent cross sections
and $\sigma_{\rm SM}$ represents the SM cross sections.
The $gg \to ZH$ production cross sections are more complex functions of both $\kappa_V$ and $\kappa_F$~\cite{CombinationNote}:
\begin{equation*}
\sigma(gg \to ZH)_{\,8\tev} = (0.37\times \kappa_F^2 - 1.64\times \kappa_F\times \kappa_V + 2.27\times \kappa_V^2)\,\sigma_{\rm SM}(gg \to ZH)_{\,8\tev},
\end{equation*}
\begin{equation*}
\sigma(gg \to ZH)_{\,7\tev} = (0.35\times \kappa_F^2 - 1.58\times \kappa_F\times \kappa_V + 2.24\times \kappa_V^2)\,\sigma_{\rm SM}(gg \to ZH)_{\,7\tev},
\end{equation*}
The signal event yield is
expressed as $ \sigma \cdot {\rm Br}(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ using the narrow-width
approximation.
Only the relative sign between $\kappa_V$ and $\kappa_F$ is observable and hence
in the following only $\kappa_V>0$ is considered, without loss of
generality.

Sensitivity to the sign results from negative interference, in the $gg \to ZH$ process, between the
box diagram in which both the $Z$ and $H$ bosons are produced directly
from the heavy-quark loop and the triangle diagram in which only the
$Z^{*}$ is produced and subsequently radiates a Higgs boson~\cite{Englert:2013vua}.
Because the relative weights of such processes depend on the
$\sqrt{s}$ of the interaction, different coefficients appear in the
expression for 8 and 7~\tev.

\begin{figure}[t!]
\begin{center}
\includegraphics[width=\textwidth]{overlayKvKf-tweaks.pdf}%
\end{center}
\caption{
The likelihood scan as a function of $\kappa_V$ and $\kappa_F$ both with and without the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$
contribution.~Both the expected and observed contours corresponding to the 68\%,
and 95\% C.L. are shown.
The yellow star and circles indicate the best fit values to the data, and the white cross represents the SM expectation ($\kappa_V$, $\kappa_F$)=(1,1).
}
\label{fig:couplings}
\end{figure}

The likelihood dependence on $\kappa_V$ and $\kappa_F$ is shown in figure~\ref{fig:couplings}.
The product $\sigma(gg \to H)\cdot {\rm Br}(\ensuremath{H{\rightarrow\,}WW^{\ast}})$, which is measured with good accuracy, does not depend on $|\kappa_F|$ in the limit $|\kappa_F| \gg \kappa_V$.
This explains the
low sensitivity to high values of $\kappa_F$.

On the other hand $\mu_{\rm VBF}$ and $\mu_{VH}$, as measured for the $\ensuremath{H{\rightarrow\,}WW^{\ast}}$ decay, should vanish in the limit
$|\kappa_F| \gg \kappa_V$ due to the increased value of the Higgs boson total width and the consequent reduction of the $\ensuremath{H{\rightarrow\,}WW^{\ast}}$ branching fraction.
The observation of significant excesses in the VBF and $VH$ production modes therefore leads to an exclusion of the $|\kappa_F| \gg \kappa_V$ region.

The fit to the data results in two local minima and, although the negative $\kappa_F$ solution is preferred to the positive solution at $0.5\sigma$, the observed results are compatible with the SM expectation, and the best fit values are:
\begin{eqnarray*}
|\kappa_F| = 0.85^{+0.26}_{-0.20}, \quad |\kappa_V| = 1.06^{+0.10}_{-0.10},
\end{eqnarray*}
and their correlation is $\rho = 0.54$.

\subsection{Theoretical uncertainties}
The theoretical uncertainties on the total Higgs boson production cross section and branching fraction are evaluated by following the recommendation of the LHC Higgs cross-section working group~\cite{Dittmaier:2011ti,Dittmaier:2012vm,Heinemeyer:2013tqa}. Uncertainties concerning QCD renormalisation and factorisation scales, which are hereafter collectively referred to as QCD scales, PDF, the value of $\alpha_{\rm S}$ and branching fraction are estimated.

The main uncertainty on the $VH$($\ensuremath{H{\rightarrow\,}WW^{\ast}}$) process, shown in the ``$VH$ Acceptance'' row in table~\ref{table:sys_sign_bck}(a),
accounts for the uncertainties in the acceptance of the signal
processes and it is evaluated with MINLO-$VH$j {\sc
  Powheg-Box1.0}~\cite{Luisoni:2013cuh} simulation.
The leading contributions are the missing next to leading order QCD
contributions in $qq\rightarrow VH$  simulated with {\sc Pythia8} and
the parton shower uncertainty. The first is evaluated by comparing the
{\sc Pythia8} prediction with the MINLO-$VH$j  interfaced with {\sc
  Pythia8} and amounts to 7\%. The second is computed  by comparing
 MINLO-$VH$j interfaced with {\sc Pythia8}
with MINLO-$VH$j interfaced with {\sc Herwig} and accounts for a further 7\%.

The cuts on the number of jets are found to be the  main
source of such uncertainties. The uncertainty on the acceptance of the $gg\rightarrow ZH$
process is estimated to be  5\%  in the \ensuremath{{\rm 4}{\ell}}\ channel, the only channel where this process is relevant.

Uncertainty on the Higgs boson branching fraction to $WW^{\ast}$, which is particularly important for the $VH$ and VBF production modes, amounts to 4\%.
The QCD scale uncertainty is 1\% for $WH$ production and 3\% for $ZH$ production.
This uncertainty is larger for $ZH$ production due to the $gg\rightarrow ZH$ contribution.
The ``VH NLO EW corrections''
refers to additional uncertainties on the corrections~\cite{Denner:2011rn} to the NLO differential cross section,
applied as a function of the
\pt\ of the associated weak bosons in the LO $WH$ and $ZH$ production modes generated by {\sc Pythia8}.
 The size of this uncertainty is 2\%.

The uncertainties on ggF production are due to the inclusive cross section dependence from QCD scales, the  PDF choice
and $\alpha_{\rm S}$, they range  from 7\% to 8\%.
In the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel, an additional uncertainty due to the
jet multiplicity cut is computed with {\sc MCFM}
\cite{Campbell:2010ff} and amounts to about 12\%.

The uncertainties from the QCD scales of backgrounds are estimated
by varying the scales up and down independently by a factor of two.
{\sc MCFM} is used to estimate this uncertainty in
the $\ensuremath{{\rm 4}{\ell}}$, $\ensuremath{{\rm 3}{\ell}}$ and $\ensuremath{{\rm 2}{\ell}}$-SS channels.
In the \ensuremath{{\rm 4}{\ell}}\ channel the uncertainty on $ZZ^{\ast}$ is 4\% in the SRs and CR.
However, due to the cancellation between the SRs and CR, the resultant effect becomes negligible.
In the 3$\ell$-3SF and 3$\ell$-1SFOS SRs the QCD scale uncertainty on $WZ/W\gamma^{\ast}$
is determined in each bin of the ``BDT Score'' and ranges between 3\% and 6\%.
In  the $\ensuremath{{\rm 2}{\ell}}$-SS channel, due to cancellations, the QCD scale uncertainties on $WZ/W\gamma^{\ast}$ and $W\gamma$
are found to be negligible with the exception of the 2$\ell$-SS2jet SR, in which
 100\% uncertainty is assigned to $W\gamma$.
The QCD scale uncertainty on the same-sign $WW$+2jet, estimated using  {\sc VBF@NLO}~\cite{Campanario:2008yg},  is of the order of 40\%.
In the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel, QCD scale uncertainties on top-quark and $WW$+2jet production with at least two QCD couplings, referred to as QCD $WW$ in the following, are estimated as 9\% and 17\%
by using {\sc MC@NLO} and {\sc MadGraph}, respectively.

The PDF uncertainties on backgrounds are calculated
by following the PDF4LHC recipe~\cite{Botje:2011sn}
using the envelope of predictions from MSTW2008, CT10 and NNPDF2.3 PDF sets
with the exception of top-quark production in the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel,
which is evaluated with the same technique used in the ggF-enriched $n_{j} \ge 2$ category in ref.~\cite{HWWllpaper}.
The uncertainties range from 1\% to 6\%, depending on the background process and the
categories.
An uncertainty of 33\% on the NLO $K$-factor for the triboson process is evaluated by using {\sc VBF@NLO};
in the 3$\ell$-0SFOS SR this uncertainty is estimated in bins of $\Delta R_{\ell_0,\ell_1}$ and ranges from 1\% to 6\%.

The ``MC modelling'' row in table~\ref{table:sys_sign_bck}(b) takes
the yield variation observed between predictions of different MC generators.
In the \ensuremath{{\rm 3}{\ell}}\ and $\ensuremath{{\rm 2}{\ell}}$-SS channels, the uncertainties on the $WZ/W\gamma^{\ast}$ event yield
due to the modelling of the underlying event, parton shower and matching of the matrix element to the
parton shower are evaluated by comparing the predictions of    {\sc Powheg-Box+Pythia} and {\sc MC@NLO+Herwig}.
In the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel, an  uncertainty  due to  underlying event and parton shower modelling
is assigned to top-quark production and $\Ztau$ by comparing the expectations from {\sc Powheg-Box+Pythia} and {\sc Powheg-Box+Herwig},
and {\sc Alpgen+Pythia} and {\sc Alpgen+Herwig}, respectively.
The QCD $WW$ event yield in the $\ensuremath{{\rm 2}{\ell}}$-DFOS channel is estimated using {\sc Sherpa}. The uncertainty from the
underlying event, parton shower modelling and matrix element implementation is evaluated through a comparison with {\sc MadGraph+Pythia}.
The uncertainty on the main background in the \ensuremath{{\rm 4}{\ell}}\ channel, $ZZ^{\ast}$, is dominated by the statistical component;
a systematic uncertainty from the different models, underlying event and parton shower is assigned through a comparison between
{\sc Powheg-Box+Pythia} and {\sc Sherpa}.

\subsection{Experimental uncertainties}
One of the dominant experimental uncertainties, labelled ``Jet'' in table~\ref{table:sys_sign_bck},
derives from the propagation of the jet energy scale calibration and resolution uncertainties.
They were derived from a combination of simulation, test-beam data, and in situ measurements~\cite{Aad:2014bia}.
Additional uncertainties due to differences between quark and gluon jets, and between light- and heavy-flavour jets,
as well as the effect of pile-up interactions are included.
For jets used in this analysis, the jet energy scale uncertainty
ranges from 1\% to 7\%, depending on \pt\ and \eta.
The relative uncertainty on the  jet energy resolution
ranges from 2\% to 40\%, with the largest value of
the resolution and relative uncertainty occurring at the
\pt\ threshold of the jet selection.

The ``Muon'' and ``Electron''  uncertainties include those from lepton reconstruction, identification and isolation,
 as well as lepton energy and momentum measurements. The ``Trigger efficiency'' uncertainty in table~\ref{table:sys_sign_bck}
refers to the uncertainty on the lepton trigger efficiencies. The uncertainties on the lepton and trigger
efficiencies are of the order of 1\% or smaller.

The changes in jet,  electron and muon energy scale uncertainties due to
varying them by their systematic uncertainties are propagated
to the \met\ evaluation and included in the   ``Jet'',  ``Electron'' and  ``Muon'' rows in table~\ref{table:sys_sign_bck}.
An additional ``${E_{\T}^{\miss}}$ soft term'' uncertainty is associated with the contribution of calorimeter energy deposits
not assigned to any reconstructed objects in the ${E_{\T}^{\miss}}$
reconstruction~\cite{ATLAS-CONF-2012-101,ATLAS-CONF-2010-020,ATLAS-CONF-2014-019}.

The ``$b$-tagging efficiency'' row refers to the uncertainties on the efficiency of tagging of $b$-jets and
 include contributions from $b$-jet identification and charm and light-flavour jet rejection factors~\cite{CONF-2014-046,CONF-2014-004}.  The uncertainties related to $b$-jet identification
range from $<$1\% to 8\%. The uncertainties
on the misidentification rate for light-quark jets depend
on \pt\ and \eta, and have a range of 9--19\%. The uncertainties
on $c$-jets reconstructed as $b$-jets range between 6\%
and 14\% depending on \pt.

The uncertainty labelled as ``Fake factor'' is associated with the
 data-driven estimates of the $W$+jets and multijet backgrounds in the $\ensuremath{{\rm 2}{\ell}}$ channels; it ranges between 35\% and 45\% depending on the sample
and on categories.
A ``Charge mis-assignment'' systematic uncertainty is estimated to account for the mismodelling of the charge
flip effect by
comparing the number of lepton pairs with same charge and opposite charge under the $Z$ boson mass peak in data and MC simulation,
resulting in a 16\% relative uncertainty. The uncertainty is assigned to $WZ/W\gamma^{\ast}$ in the 3$\ell$-0SFOS SR,
and top-quark production, $Z$+jets and $WW$ in the $\ensuremath{{\rm 2}{\ell}}$-SS channel.

The uncertainty labelled as ``Photon conversion rate''  is assigned to $W\gamma$ in the $\ensuremath{{\rm 2}{\ell}}$-SS channel,
and is evaluated by comparing the yield in  data and in  MC simulation for events with
two muons and one electron with no hit on the innermost pixel detector layer. It is relevant only for the
$\ensuremath{{\rm 2}{\ell}}$-SS channel and has a size of 6.5\% for $W\gamma$.

The ``Pile-up'' field in table~\ref{table:sys_sign_bck} includes
the uncertainty on the weights applied to all simulated events to match the distribution of the number of  pile-up interactions to that of data.
The uncertainty on the integrated luminosity for the 2012 data is $\pm$ 2.8\%
 and it is derived following the same methodology as that detailed in ref.~\cite{Aad:2013ucp}.
For the 2011 data the uncertainty on the integrated luminosity is $\pm$ 1.8\%~\cite{Aad:2013ucp}.
The  backgrounds normalised with CR data are not affected by the luminosity uncertainty.

The dominant systematic uncertainties on the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ process in the
$\ensuremath{{\rm 4}{\ell}}$ and $\ensuremath{{\rm 3}{\ell}}$ channels are due to uncertainties on lepton reconstruction and on the
jet energy scale and resolution.
In the $\ensuremath{{\rm 2}{\ell}}$ channels, the jet energy scale and resolution uncertainties are the most important.

\subsection{Event yields and distributions} \label{sec:yields}
The number of events in each category is summarised in
table~\ref{table:SR8} and in table~\ref{table:SR7} for the 8~\tev\ and
7~\tev\  data sample, respectively.
In the  \ensuremath{{\rm 2}{\ell}}-DFOS and \ensuremath{{\rm 2}{\ell}}-SS1jet categories the numbers of observed
events are slightly larger than the expectation.
The lepton flavour composition of the events in the \ensuremath{{\rm 2}{\ell}}-SS channel is shown in
table~\ref{table:SR_SSBD}, in which the high event yield of the \ensuremath{{\rm 2}{\ell}}-SS1jet SR mainly
originates from  the $\mu\mu$ and $\mu e$ channels. The behaviour of the
observed data yield as a function of the data period was studied. The
events were uniformly distributed according to the acquired luminosity as
expected, excluding temporary failures of the detector subsystems as an explanation
of the excess. Moreover it was checked that known detector defects were not
increasing the rate of particular background sources.
Finally, the kinematic distributions of the events were analysed in
order to look for striking features pointing to some particular
missing background contribution. Because no particular problem was
found, the data excesses were attributed
to statistical fluctuations.

Distributions of some of the relevant variables after the event selection
are presented for 8~\tev\ data in figure~\ref{Figure:SR_4lep}
for the 4$\ell$ analyses, in figure~\ref{Figure:SR_3lep} for the 3$\ell$ analyses and in figure~\ref{Figure:SR_twolep}
for the 2$\ell$ analyses.
Figures~\ref{Figure:SR_4lep}(a) and~\ref{Figure:SR_4lep}(c)
show the opening angle between the leptons in
the frame where the \pt\ of the Higgs boson is zero,
$\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost}$, in 4$\ell$-1SFOS events.
Figures~\ref{Figure:SR_4lep}(b) and~\ref{Figure:SR_4lep}(d)
show the $\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost}$ in
4$\ell$-2SFOS events.
Figures~\ref{Figure:SR_3lep}(a) and~\ref{Figure:SR_3lep}(b) present the ``BDT Score'' distribution
in  the 3$\ell$-3SF and 3$\ell$-1SFOS SRs, respectively, and figure~\ref{Figure:SR_3lep}(c) shows the distribution of $\Delta R$ between the leptons
from the Higgs boson candidate, $\Delta R_{\ell_{0}\ell_{1}}$, in the
3$\ell$-0SFOS SR.
Figures~\ref{Figure:SR_4lep}(a) and~\ref{Figure:SR_4lep}(b) are obtained by applying
the selections in table~\ref{tab:event_selection} only down to the cuts on the $\pt^{\mathrm{miss}}$, in order to maximise the number of events,
while the full selection is applied
to produce the distributions in figures~\ref{Figure:SR_4lep}(c) and~\ref{Figure:SR_4lep}(d).
The distributions in figures~\ref{Figure:SR_3lep}(a)--\ref{Figure:SR_3lep}(c) are shown with all the selections applied except for the one on the displayed variable.
Figure~\ref{Figure:SR_twolep}(a) presents the transverse mass, $\ensuremath{m_{\rm T}}$,
in the 2$\ell$-DFOS SR, while figure~\ref{Figure:SR_twolep}(b) and  figure~\ref{Figure:SR_twolep}(c) show
the smallest opening angle in the transverse plane between a lepton and a jet, $\Delta \phi_{\ell_{i},j}^{\mathrm{min}}$, in the
 2$\ell$-SS1jet SR  and  the 2$\ell$-SS2jet SR, respectively.
The distributions in figure~\ref{Figure:SR_twolep} are shown with all the selections applied except for the one on the displayed variable.
No data populates figure~\ref{Figure:SR_4lep}(d).
In all distributions, good agreement
between data and the MC prediction is observed.

\begin{sidewaystable}[h!]
\begin{center}
\scalebox{0.86}{
\begin{tabular}{l|| D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} }
 \multicolumn{9}{l}{8~\tev\ data sample}                       \\
 \hline
Process &  \multicolumn{2}{c|}{\ensuremath{{\rm 4}{\ell}}} & \multicolumn{3}{c|}{\ensuremath{{\rm 3}{\ell}}}& \multicolumn{3}{c}{\ensuremath{{\rm 2}{\ell}}}    \\
\hline
Category &  \multicolumn{1}{c}{2SFOS} & \multicolumn{1}{c|}{1SFOS} & \multicolumn{1}{c}{3SF} & \multicolumn{1}{c}{1SFOS} & \multicolumn{1}{c|}{0SFOS} & \multicolumn{1}{c}{DFOS} & \multicolumn{1}{c}{SS2jet} & \multicolumn{1}{c}{SS1jet} \\
\hline
Higgs boson &&&&&&&\\
$~VH~(H\rightarrow WW^{\ast})$   &0.203 , 0.030   &0.228 , 0.034   &0.73 , 0.10   &1.61  , 0.18  &1.43 , 0.16   &2.15  , 0.30            &1.04 , 0.18     &2.04  , 0.30 \\
$~VH~(H\rightarrow \tau\tau)$    &0.0084 , 0.0032 &0.012 , 0.004 &0.057 , 0.011 &0.152 , 0.023 &0.248 , 0.035 &\multicolumn{1}{c}{---} &0.036 , 0.008 &0.27 , 0.04 \\
~ggF                 &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &0.076,0.015&0.085,0.018 &\multicolumn{1}{c|}{---}  &2.4,0.5              &\multicolumn{1}{c}{---}  & \multicolumn{1}{c}{---}          \\
~VBF                 &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} & 0.180,0.025            & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---}  \\
~ttH                 &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---}  \\
\hline

Background    &&&&&&& \\
$~~V$                  &\multicolumn{1}{c}{---}     &\multicolumn{1}{c|}{---}      &0.22,0.16 &1.9,0.6 &0.37,0.15&  14,4& 8 , 4 &15 , 5  \\
$~~VV$                 &1.17,0.20&0.31,0.06 &19,3&28,4&4.7,0.6&10.1,1.6& 11.2 , 2.1& 26 , 4   \\
$~~VVV$                &0.12,0.04&0.10,0.04 &0.8,0.3 &2.2,0.7 &2.93,0.29&\multicolumn{1}{c}{---}         & \multicolumn{1}{c}{---} & 0.47 , 0.05 \\
$~~$Top                &0.014,0.011&\multicolumn{1}{c|}{---}      &0.91,0.26 &2.4,0.6 &3.7,0.9&24,4& 0.75 , 0.19 & 1.3 , 0.5   \\
$~~$Others             &\multicolumn{1}{c}{---}     &\multicolumn{1}{c|}{---}   &\multicolumn{1}{c}{---}      &\multicolumn{1}{c}{---}      &\multicolumn{1}{c|}{---}    & 2.3,0.9 & 0.71 , 0.30 & 0.60 , 0.24  \\
$~~$Total              &1.30,0.23&0.41,0.09&22,4&34,6&11.7,1.8&50,5& 21 , 5 & 44 , 6   \\
\hline
Observed events         & \multicolumn{1}{c}{0} & \multicolumn{1}{c|}{3} & \multicolumn{1}{c}{22} & \multicolumn{1}{c}{38} & \multicolumn{1}{c|}{14} & \multicolumn{1}{c}{63} & \multicolumn{1}{c}{25} & \multicolumn{1}{c}{62} \\
\hline
 \end{tabular}
}
\caption{Number of observed and predicted events in the SRs and their composition in the 8~\tev\ data sample. Background
processes that contribute less than 1$\%$ of the total background, and Higgs boson production modes that contribute less than 1$\%$ of the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ process, are not included in the table. The uncertainties on event yields include both the statistical and systematic components (see section~\ref{sec:systematics}).}
\label{table:SR8}
\end{center}
\end{sidewaystable}

\begin{sidewaystable}
\begin{center}
\scalebox{0.90}{
\begin{tabular}{l|| D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} }
\multicolumn{7}{l}{7~\tev\ data sample}                       \\
\hline
Process &  \multicolumn{2}{c|}{\ensuremath{{\rm 4}{\ell}}} & \multicolumn{3}{c|}{\ensuremath{{\rm 3}{\ell}}} & \multicolumn{1}{c}{\ensuremath{{\rm 2}{\ell}}} \\
\hline
Category &  \multicolumn{1}{c}{2SFOS} & \multicolumn{1}{c|}{1SFOS} & \multicolumn{1}{c}{3SF} & \multicolumn{1}{c}{1SFOS} & \multicolumn{1}{c|}{0SFOS} & \multicolumn{1}{c}{DFOS} \\
\hline
Higgs boson &&&&&&\\%&& \\
$~V(H\rightarrow WW^{\ast})$          &0.0226 , 0.0033  &0.0208 , 0.0031 &0.129 , 0.013 &0.325 , 0.034  &0.291 , 0.031 &0.28,0.05 \\
\hline
$~V(H\rightarrow \tau\tau)$    &0.0031 , 0.0012  &0.0014, 0.0008 &0.0163 , 0.0035 &0.041, 0.006 &0.067, 0.010 &0.0075 , 0.0032 \\
~ggF                  &\multicolumn{1}{c}{---}     &\multicolumn{1}{c|}{---}    &0.0045,0.0015     &0.0045,0.0019  &0.0048,0.0027   &0.32,0.09 \\
~VBF                  &\multicolumn{1}{c}{---}     &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---}   &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---}   &0.021,0.004 \\%        &&  \\
~$\ttbar$H                  &\multicolumn{1}{c}{---}     &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---}   &0.006,0.004 & 0.0041,0.0032   &\multicolumn{1}{c}{---} \\

\hline \\
\hline
Background    &&&&&&\\
$~~V$                 &\multicolumn{1}{c}{---}               &\multicolumn{1}{c|}{---}                 &0.36,0.30   &0.59,0.34   &0.36,0.22   &3.4,1.3\\
$~~VV$                &0.37,0.14     &0.031,0.013     &4.1,0.6   &5.7,1.0     &1.3,0.2   &0.89,0.27 \\
$~~VVV$               &0.014,0.005 &0.0095,0.0033 &0.082,0.028 &0.21,0.07 &0.338,0.031 &\multicolumn{1}{c}{---}           \\
$~~$Top               &0.006,0.004 &\multicolumn{1}{c|}{---}                 &0.12,0.14   &0.4,0.3   &0.44,0.29   &3.2,0.8 \\
$~~$Others            &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c}{---}&\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---}\\
$~~$Total             &0.39,0.15     &0.041,0.016     &4.6,1.1     &7.0,1.9     &2.5,0.7   &7.5,1.7   \\
\hline
Observed events       & \multicolumn{1}{c}{1} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c}{5} & \multicolumn{1}{c}{6} & \multicolumn{1}{c|}{2} & \multicolumn{1}{c}{7} \\
\hline
\end{tabular}
}
\caption{Number of observed and predicted events in the SRs and their
  composition in the 7~\tev\ data sample. Background
processes that contribute less than 1$\%$ of the total background, and Higgs boson production modes that contribute less than 1$\%$ of the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ process, are not included in the table. The uncertainties on event yields include both the statistical and systematic components (see section~\ref{sec:systematics}).}
\label{table:SR7}
\end{center}
\end{sidewaystable}

\begin{sidewaystable}[h!]
\begin{center}
\scalebox{0.82}{
\begin{tabular}{l|| D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} | D{,}{\pm}{-1} D{,}{\pm}{-1} }
 \multicolumn{9}{l}{8~\tev\ data sample}                       \\
 \hline
Process &  \multicolumn{2}{c|}{SS \ensuremath{{\rm 2}{\ell}}\ ($ee$)} &\multicolumn{2}{c|}{SS \ensuremath{{\rm 2}{\ell}}\ ($e\mu$)}&\multicolumn{2}{c|}{SS \ensuremath{{\rm 2}{\ell}}\ ($\mu e$)}&\multicolumn{2}{c}{SS \ensuremath{{\rm 2}{\ell}}\ ($\mu\mu$)}    \\
\hline
Category & \multicolumn{1}{c}{SS2jet} & \multicolumn{1}{c|}{SS1jet} & \multicolumn{1}{c}{SS2jet} & \multicolumn{1}{c|}{SS1jet} & \multicolumn{1}{c}{SS2jet} & \multicolumn{1}{c|}{SS1jet} & \multicolumn{1}{c}{SS2jet} & \multicolumn{1}{c}{SS1jet} \\
\hline
Higgs boson &&&&&&&\\
$~VH~(H\rightarrow WW^{\ast})$      & 0.15 , 0.07    & 0.39 , 0.08   & 0.36 , 0.08   & 0.50 , 0.12   & 0.24 , 0.08   & 0.69 , 0.14   & 0.28 , 0.06   & 0.46 , 0.11 \\

$~VH~(H\rightarrow\tau\tau)$ & 0.009 , 0.004 & 0.063 , 0.013   & 0.012 , 0.004 & 0.081 , 0.018 & 0.0040 , 0.0020 & 0.080 , 0.014 & 0.012 , 0.004 & 0.046 , 0.010 \\
$~$ggF                      & 0.0028 , 0.0021 & 0.0011 , 0.0011  &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c}{---} \\
~VBF                        &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c}{---} \\
~$\ttbar$H                        &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c}{---} \\
\hline
Background    &&&&&&& \\
$~~V$                       & 2.9 , 2.8       & 5.0 , 2.0       & 2.5 , 1.0       & 6.6 , 2.3     & 1.4 , 0.6     & 2.1 , 0.7   & 1.1 , 0.8     & 1.1 , 0.8 \\
$~~VV$                      & 2.8 , 0.9     & 6.3 , 1.3       & 4.7 , 1.3       & 10.9 , 1.8    & 2.3 , 0.7     & 5.6 , 1.1     & 1.3 , 0.4     & 3.5 , 0.8 \\
$~~VVV$                     &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} &\multicolumn{1}{c|}{---} &\multicolumn{1}{c}{---} & 0.13 , 0.02 &\multicolumn{1}{c}{---} & 0.11 , 0.03 \\
$~~$Top                     & 0.12 , 0.08   & 0.49 , 0.14     & 0.36 , 0.15     & 0.48 , 0.23   & 0.24 , 0.08   & 0.39 , 0.13 & 0.035 , 0.032   &\multicolumn{1}{c}{---} \\
$~~$Others                  & 0.07 , 0.04   &\multicolumn{1}{c|}{---}                  & 0.26 , 0.12     & 0.44 , 0.17   & 0.32 , 0.15     &\multicolumn{1}{c|}{---}                & 0.061 , 0.031   & 0.056 , 0.029 \\
Total                       & 5.9 , 3.1       & 11.9 , 2.4      & 7.9 , 1.7       & 18.6 , 3.0    & 4.3 , 0.9     & 8.2 , 1.3     & 2.6 , 0.9      & 4.8 , 1.2 \\
\hline
Observed events             & \multicolumn{1}{c}{4} & \multicolumn{1}{c|}{12} & \multicolumn{1}{c}{8} & \multicolumn{1}{c|}{25} & \multicolumn{1}{c}{7} & \multicolumn{1}{c|}{14} & \multicolumn{1}{c}{6} & \multicolumn{1}{c}{11} \\
\hline
\end{tabular}
}
\caption{Number of observed and predicted events in the \ensuremath{{\rm 2}{\ell}}-SS channel in the 8~\tev\ data sample with different lepton flavour combinations: $ee$, $e\mu$, $\mu e$ and $\mu\mu$.
Background processes that contribute less than 1$\%$ of the total background, and Higgs boson production modes that contribute less than 1$\%$ of the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ process, are not included in the table. The uncertainties on event yields include both the statistical and systematic components (see section~\ref{sec:systematics})}
\label{table:SR_SSBD}
\end{center}
\end{sidewaystable}

\begin{figure}[h!]
\begin{center}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{quadlep_Cut4_1_ALL_DPhi_H_boosted_mh125_log.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{quadlep_Cut4_2_ALL_DPhi_H_boosted_mh125_log.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{quadlep_Cut10_1_ALL_DPhi_H_boosted_mh125_log.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{quadlep_Cut11_2_ALL_DPhi_H_boosted_mh125_log.pdf}}
\caption{Distributions of the angular separation in $\phi$ between the opposite-sign lepton pair
from the Higgs boson decay candidate in the frame where the \pt\ of the Higgs boson is zero, $\Delta \phi_{\ell_{0}\ell_{1}}^{\rm boost}$, in
the 4$\ell$ analyses using the 8~\tev\ data sample:
(a) and (c) with 4$\ell$-1SFOS events, and (b) and (d) with 4$\ell$-2SFOS events.
Figures (a) and (b) are
obtained by applying the cuts in table~\ref{tab:event_selection} down to the track missing \pt\ ($\pt^{\mathrm{miss}}$) selection,
removing the other selections in order to increase the otherwise very limited number of events,
while the distributions in (c) and (d) have all the selections applied.
Data (points) are compared to the background plus the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation (stacked filled histograms),
where the background components are normalised by applying the normalisation factors shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents the total uncertainty on the background estimate including the statistical and systematic uncertainties added in quadrature.
}
\label{Figure:SR_4lep}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_Cut8_ALL_isEEE_MMM_mva_weight_varbin_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zenri_Cut8_ALL_isEEM_MME_mva_weight_varbin_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{trilep_Zdefi_Cut8_ALL_DRll01_varbin_mh125_lin.pdf}}
\caption{Distributions of relevant quantities for the
3$\ell$ analyses using the 8~\tev\ data sample:
(a) ``BDT Score'' in the 3$\ell$-3SF and (b) in the 3$\ell$-1SFOS SRs, and
(c) the angular separation in $R$ of the two opposite-sign leptons with smaller $\Delta R$ distance, $\Delta R_{\ell_{0}\ell_{1}}$, in the 3$\ell$-0SFOS SR.
The distributions are shown with all
the selections applied except for the one on the displayed variable.
Data (points) are compared to the background plus the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation (stacked filled histograms),
where the background components are normalised by applying the normalisation factors shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents the total uncertainty on the background estimate including the statistical and systematic uncertainties added in quadrature.
}
\label{Figure:SR_3lep}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{emme_CutFailVBFTopoMjj_2jetincl_MT_STVF_papv6_mh125_lin.pdf}}\\
\subfigure[]{\includegraphics[width = 0.48\textwidth]{Cut1jetSubLeadPt_NoDPhi_DeltaPhiljMin_mh125_lin.pdf}}
\subfigure[]{\includegraphics[width = 0.48\textwidth]{Cut2jetSubLeadPt_NoDPhi_DeltaPhiljMin_mh125_lin.pdf}}
\caption{Distributions of relevant quantities for the  2$\ell$ analyses using the 8~\tev\ data sample:
(a) transverse mass $\ensuremath{m_{\rm T}}$ in the 2$\ell$-DFOS SR,
the smallest azimuthal opening angle between a lepton and a jet, $\phi_{\ell_{i}j}^{\mathrm{min}}$, (b) in the 2$\ell$-SS1jet and (c) 2$\ell$-SS2jet SRs.
The distributions are shown with all
the selections applied except for the one on the displayed variable.
Data (points) are compared to the background plus the $VH(\ensuremath{H{\rightarrow\,}WW^{\ast}})$ (\mH=125~\gev) signal expectation (stacked filled histograms),
where the background components are normalised by applying the normalisation factors shown in table~\ref{tab:NFs}.
The hatched area on the histogram represents the total uncertainty on
the background estimate including the statistical and systematic
uncertainties added in quadrature.
}
\label{Figure:SR_twolep}
\end{center}
\end{figure}

redpajama_set_name: RedPajamaArXiv


adenocarcinoma a malignant tumor formed in the glandular epithelium.
adenoma a usu. benign tumor that starts in a gland or has a glandlike arrangement of cells.
adenosine an organic compound that is made up of adenine and ribose and found in nucleic acids, and that may be obtained as a white crystalline powder through the hydrolysis of yeast.
adenovirus any of a group of viruses that causes disease of the upper respiratory tract.
adequacy the state of being adequate.
à deux (French) of or for two, esp. in an intimate or private manner.
ADHD abbreviation of "attention deficit hyperactivity disorder"; a mental disorder, usually beginning in childhood, characterized by impulsiveness and excessive activity.
adhesive bandage a small piece of cloth or plastic with a sticky material on one side. You use an adhesive bandage to cover a wound and keep it clean.
adhesive tape a strip of cotton, plastic, or other tape coated with a sticky material on one side, used esp. for attaching bandages.
ad hoc for this particular case, occasion, or purpose only; with respect only to this.


Abuse survivors are usually wary of new relationships for extremely good reasons that are not their fault. Almost always, the cycle of abuse starts out as something that appears wonderful. The new guy or gal is interested in them. Not only interested, but infatuated. They too-quickly claim they are "the one." They study their target, quick to note all their likes and dislikes, which feels like manna from heaven for someone who has been emotionally neglected. They are quick to become intimate, physically, mentally, and emotionally. Abusers hook their victims fast, always under some romantic guise of "fate" or "true love." Just when the victim believes it's real, the trouble starts.
This initial stage of love bombing is how an abuser manipulates their prey into a false attachment. Everyone needs to be seen, heard, loved, and cared for, and this is the ammunition an abuser uses to target their victims. When someone feels loved, they relax. They bond. They become emotionally dependent, believing *at last* they can entrust their heart to another. In a healthy relationship, all of this is beautiful, necessary, and true for the relationship to grow and evolve. In a toxic relationship, this bond becomes the stuff of nightmares.
Because of the trauma bond this initial love bombing experience creates, the victim becomes confused. They struggle to reason and reconcile why their lover suddenly changed. "He's just having a bad day." "She didn't mean it." "He really loves me, deep down. I remember how it used to be. We can get back to that." In the cycle of abuse, love bombing turns to emotional neglect, which causes the victim to shift to minimization and denial in order to make sense of it. Emotional and psychological abuse begins, and in some cases, an abuser can become physically violent. If an abuser is challenged, the gaslighting begins. Suddenly, the victim is "selfish" and "crazy." The abuser will rage, manipulate, and blame their victim of everything they are actually doing. If their victim does not break out of the minimization and denial, they will succumb and feel like they really are going crazy.
The cycle of abuse can de-escalate quickly, but when a victim of abuse decides it's time to leave, the abuser will quickly switch back to the love-bombing stage in order to keep them. 'Round and 'round it goes, and it's pure hell.
Long after a survivor has left and done a fair amount of healing after an abusive relationship, panic can set in when meeting anyone new. The remedy for healing is not to isolate oneself and swear off all future love interests, but to learn how to open one's heart to another again in an intimate relationship. Healing from relational abuse requires being in healthy relationships with others. I can't think of anything more legitimately terrifying for someone who has experienced this form of abuse, to have to open up and rely on another to heal.
So, how does one approach a new relationship after a toxic one? Very slooooowly, and extremely cautiously. Boundaries are the key word. Tattoo it on your forehead if you must. In a healthy relationship, the love interest will respect and appreciate your boundaries. Set more boundaries than you think you need to start, and see how your candidate handles them. If you feel any pressure, manipulation, or guilt to relax those boundaries, this person is not the one for you. Perhaps they are not abusive, but a survivor of abuse needs someone who respects all boundaries in order for things to work. Look for empathy. Fallout from a toxic relationships are easy to understand (if you're not a narcissist), so look for understanding and compassion. Someone who genuinely wants to get to know you and love you deeply will not be "put off" by a trauma history. They will want to weep with you when you are grieving, and get angry with you when you are angry. So give them the opportunity, slowly.
Love after abuse is possible. Healthy, healing relationships are possible. Abuse survivors are worthy and deserving of loving and connected relationships, and they often make the very best partners. When they are paired with those who truly love them, all of the positive aspects of their personality that once made them a target for an abuser finally get to shine.
Previous Previous post: Who Am I, and What Do I Want?


This track she wrote for Little Big Town has her country vibe all over it!
Taylor Swift may have changed her style from country music to a more modern pop kind of tune, but it seems like she hasn't forgotten her roots since we can still see the old Taylor written all over the song "Better Man" by Little Big Town. After all, she wrote it!
In a press conference, Little Big Town's singer, Karen Fairshild, said that Tay sent them the song, "and it was very special to her." The decision to keep the credits private for a while is because of Tay's words where she says, "That's the greatest honor as a songwriter that you could ever give me is that you don't want anyone to know I wrote it." The band knew that they would tell the credits eventually, saying that "it was a hard question to dodge for a while."
After the big reveal, Taylor posted this on Instagram, wishing the band good luck for their performance at the CMA Awards.
Who do you think this song is about? Tell us in the comments!