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\newcommand{\rb}[1]{\raisebox{1.5ex}[-1.5ex]{#1}}
%\input macros.tex

\def\PL#1#2#3{{Phys. Lett. }{\bf B#1 }(#2) #3}
\def\NIM#1#2#3{{Nucl. Inst. Meth. }{\bf #1 }(#2) #3}
\def\ra{\rightarrow}
\newcommand{\PW}{\mbox{$\mathrm{W}$}}
\newcommand{\PWm}{\mbox{$\mathrm{W}^-$}}
\newcommand{\PWp}{\mbox{$\mathrm{W}^+$}}
\newcommand{\PZz}{\mbox{$\mathrm{Z}$}}
\newcommand{\PMW}{\mbox{$m_{\mathrm{W}}$}}
\newcommand{\PMMW}{\mbox{$m_{\mathrm{W}}^2$}}
\newcommand{\PMMZ}{\mbox{$m_{\mathrm{Z}}^2$}}
\newcommand{\PSW}{\mbox{$\sigma_{\mathrm{WW}}$}}
\newcommand{\PSWv}{\mbox{$\sigma_{\mathrm{WW}}^{\mathrm{vis}}$}}
\newcommand{\PGW}{\mbox{$\Gamma_{\mathrm{W}}$}}
\newcommand{\PGWi}{\mbox{$\Gamma_{\mathrm{W}}^{\mathrm{invis}}$}}
\newcommand{\PGWv}{\mbox{$\Gamma_{\mathrm{W}}^{\mathrm{vis}}$}}
\newcommand{\GEV}{\mbox{$\mathrm{GeV}$}}
\newcommand{\GEVc}{\mbox{$\mathrm{GeV}/{\it c}$}}
\newcommand{\GEVcc}{\mbox{$\mathrm{GeV}/{{\it c}^2}$}}
\newcommand{\MEVc}{\mbox{$\mathrm{MeV}/{\it c}$}}
\newcommand{\MEVcc}{\mbox{$\mathrm{MeV}/{{\it c}^2}$}}
\newcommand{\Pem}{\mbox{$\mathrm{e}^-$}}
\newcommand{\Pep}{\mbox{$\mathrm{e}^+$}}
\newcommand{\Pepem}{\mbox{$\mathrm{e}^+\mathrm{e}^-$}}
\newcommand{\Pee}{\mbox{$\mathrm{ee}$}}
\newcommand{\PWpWm}{\mbox{$\mathrm{W}^+\mathrm{W}^-$}}
\newcommand{\PWW}{\mbox{$\mathrm{W}\mathrm{W}$}}
\newcommand{\PZZ}{\mbox{$\mathrm{Z}\mathrm{Z}$}}
\newcommand{\CCC}{\mbox{$\mathrm{\scriptstyle{CC03}}$}}
\newcommand{\MC}{\mbox{$\mathrm{\scriptstyle{MC}}$}}
\newcommand{\ckm}[1]{\ensuremath{V_\mathrm{#1}}}
\newcommand{\ev}{\mbox{$\mathrm{e}\nu$}}
\newcommand{\mv}{\mbox{$\mu\nu$}}
\newcommand{\tv}{\mbox{$\tau\nu$}}
\newcommand{\lv}{\mbox{$\ell\nu$}}
\newcommand{\qq}{\mbox{$\mathrm{qq}$}}
\newcommand{\qqbar}{\mbox{$\mathrm{q\bar{q}}$}}
\newcommand{\stat}{\ensuremath{\mathrm { (stat.)}}}
\newcommand{\syst}{\ensuremath{\mathrm { (syst.)}}}
\newcommand{\pb}{\ensuremath{\mathrm {pb}}}
\newcommand{\ipb}{\ensuremath{\mathrm {pb}^{-1}}}
\newcommand{\Rs}{\mbox{$\sqrt{s}$}}


\begin{document}


\begin{titlepage}

%{\Large\centerline{EUROPEAN LABORATORY FOR PARTICLE PHYSICS (CERN)}}
{\Large\centerline{P R E L I M I N A R Y }}
\vspace{1cm}
\begin{flushright}
\begin{tabular}{rr}
         & ALEPH 2000-005 \\
         & CONF  2000-002 \\
%         & CERN-EP/99-? \\
         & \today       \\
\end{tabular}
\end{flushright}
\vspace{-2cm}
%\begin{flushleft}
%   EPS-HEP99\\
%   Abstract {\bf 6\_405}\\
%   Parallel sessions: {\bf 6}\\
%   Plenary  sessions: {\bf 6}
%\end{flushleft}
%\begin{flushright}
%{\Huge {\sc {\tt DRAFT 1.}}}
%\end{flushright}

\begin{center}
\vspace{3cm}
\boldmath
{\huge\bf Measurement of W-pair production and W branching 
ratios in  \Pepem{} collisions
%\\ \vspace{0.5cm}
at $\sqrt{s}=$~192 to 202 GeV}\\
{\Large \vspace{7ex} The ALEPH Collaboration}
\unboldmath
\end{center}

\vspace{1cm}
\begin{center}
{\bf Abstract}
\end{center}
The production of $\PWpWm$ pairs is analysed in a data sample
collected by ALEPH between 192 and 202~$\GEV $ centre-of-mass energies,
corresponding to an integrated luminosity of 236.96~$\ipb$. Cross
sections are given for different topologies of W decays into
leptons or hadrons. Combining all final states, the total W-pair
cross section is measured at each LEP centre-of-mass energy. These results, as
well as those obtained with data collected at lower energies, agree
well with newly developed Standard Model
calculations including higher orders. Combining all the W-pair
collected  by ALEPH so far, the decay branching fraction of the W boson
into hadrons is measured to be~$\mathrm{B (W\ra hadrons)} = 67.09
\pm 0.46 \stat \pm 0.32 \syst\%$, allowing a determination of the
CKM matrix element~$|\ckm{cs}|= 0.956 \pm 0.021 \stat \pm 0.015
\syst$.
\\[1.5cm]
{\tt Contact Person: Anne Ealet (ealet@cppm.in2p3.fr), \\
 }\\
\centerline{\large (ALEPH contribution to 2000 Winter conferences)}

\vspace{1cm}
%\centerline{\Huge\bf PRELIMINARY}
%\vfill
%\vbox{
%\hrule width6cm height0.5pt\vskip4pt
%\noindent $^*$contact person :
%%      Patrice Perez (Patrice.Perez@hep.saclay.cea.fr) }
%\centerline{\em (to be Submitted to Physics Letters B)}
\end{titlepage}

\newpage

%\input{authb}
%\setcounter{page}{5}

\section{Introduction}
The W-pair production is studied in \Pepem collisions
using data collected with the ALEPH detector at 
centre-of-mass energies from 192 to 202 ~\GEV, during the 1999 data 
taking period.

The experimental conditions and data analysis follow
those used in the cross section measurement at lower LEP2 energies,
as already described in detail in~\cite{xsecA}.
%attention will be focused on changes in selection procedures
%other than a simple rescaling of cuts with the increased collision energy.

The ALEPH data sample corresponds to an integrated total luminosity of 
236.96~$\pm$~0.25~$\stat~\pm$~0.97~$\syst~\ipb$ and an average centre-of-mass 
energy $\sqrt{s}=$ 197.57~$\pm$~0.10 $\GEV $. The breakdown of the individual
dataset is given in Table~\ref{tab:lumi99}. 

\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Integrated luminosity recorded at each $\sqrt{s}$ energy in 1999
and for the average energy over the year.
}
\label{tab:lumi99}
\begin{tabular} {| c  |  c  |}
\hline 
 Average Energy ($\GEV$) & Integrated Luminosity ($\ipb$) \\ 
\hline \hline
191.58          &   28.93~$\pm$~0.08~$\stat~\pm$~0.12~$\syst$ \\
%\hline
195.52          &   79.86~$\pm$~0.14~$\stat~\pm$~0.33~$\syst$ \\
%\hline
199.52          &   86.28~$\pm$~0.15~$\stat~\pm$~0.35~$\syst$ \\ 
%\hline
201.63           &  41.89~$\pm$~0.11~$\stat~\pm$~0.17~$\syst$ \\
\hline\hline
197.57           & 236.96~$\pm$~0.25~$\stat~\pm$~0.97~$\syst$ \\
\hline 
\end{tabular}
\end{center}
\end{table}

The separation of WW events in all possible W decay channels
allows the determination of the W branching fractions and,
indirectly, the CKM matrix element $V_{\rm cs}$.

In the following, all signal cross sections are defined by the
production of four-fermion final states only through two
resonating W bosons in $t$-channel $\nu_{\mathrm{e}}$ exchange and
$s$-channel $\mathrm{Z/}\gamma$ exchange, referred to as CC03
cross sections~\cite{LEP2workshop}. The measured cross sections
are corrected for the difference, denoted the``4f-CC03
correction'', in the accepted cross sections for CC03 processes
and all Standard Model four-fermion final states consistent with
W-pair decays.

The {\tt KORALW}~\cite{KORALW} version 1.21 Monte Carlo event
generator is used to simulate the signal events. The {\tt
JETSET}~\cite{Jetset} package takes care of hadronisation.
%Comparison samples are generated with {\tt
%EXCALIBUR}~\cite{EXCALIBUR} and {\tt grc4f}~\cite{grc4f} for the
%CC03 and all four-fermion diagrams are used for systematic error
%evaluation. Samples of events are generated with different W
%masses, both for CC03 diagrams and for all WW-like four-fermion
%diagrams, with {\tt KORALW}. 
%{\tt EXCALIBUR} was used to generate
%events with and without colour reconnection effects following the
%ansatz of Ref.~\cite{COLOUR_RECONNECTION}.

The {\tt KORALZ}~\cite{KORALZ} Monte Carlo program
is used to generate background events coming from the~\qqbar~process.
%with a cross-check using {\tt PYTHIA 5.7}~\cite{PYTHIA}.

Other background events are generated with {\tt PYTHIA 5.7}~\cite{PYTHIA}
for \PZZ, \PZz\Pee ~and \PW\ev ~processes, {\tt PHOT02}~\cite{PHOT02}
for $\gamma\gamma$ interactions, {\tt KORALZ} for $\mu$ and $\tau$
pair production and {\tt BHWIDE}~\cite{BHWIDE} 
%and {\tt UNIBAB}~\cite{UNIBAB} 
for Bhabha scattering events.
%For the fully leptonic selections,
%non-WW-like four-fermion background processes with
%two visible leptons (as $\ell'\ell'\nu_{\ell}\nu_{\ell}$)
%are generated with {\tt EXCALIBUR}.
%Care is taken to avoid double counting of backgrounds with
%different generators and to avoid counting as backgrounds
%those WW-like four-fermion processes
%that are part of the 4f-CC03 correction.
%Monte Carlo samples corresponding to integrated luminosities
%fifty times as large as that of the data
%are fully simulated for all background reactions.

The CC03 Standard Model cross section is calculated using the
program~{\tt GENTLE}~\cite{GENTLE} and compared with the recently available
calculations by~{\tt YFSWW3}~\cite{YFSWW}  and 
~{\tt RacoonWW}~\cite{ RacoonWW} with \PMW~= 80.35~\GEVcc~\cite{MWWA}.
%which gives \PSW~= 16.65 pb for
%$\sqrt{s}= 188.63$ GeV 
\boldmath
\section{$ \PWW \ra \ell\nu \ell\nu$ events}
\unboldmath

The selection of fully leptonic W-pair decays follows exactly
the two selections used for the cross section and
branching fraction measurements at lower centre-of-mass energies~\cite{xsecA}.

Beam related background and detector noise that is not simulated
in Monte Carlo events, affect the efficiencies of the cut that
removes $\gamma\gamma$ events depositing energy at angles below
$12^{\circ}$ around the beam. The inefficiency introduced is
measured from random triggers and found to be $7.8 \pm 0.5 \%$.
%The systematic error takes into account the uncertainty on the inefficiencies.

The CC03 efficiencies in the inclusive $\ell\nu\ell\nu$ channels
at each of the four centre-of-mass energies
are given in Table~\ref{tab:lvlv} and are corrected for the beam
related effect. 
%The inclusive combination of the two selections
%has an efficiency of $xx.x \pm 0.x\%$ for the fully leptonic WW
%channels, combined assuming lepton universality. 
The total background 
%amounts to $yyy \pm y.y \stat \pm y.y \syst$ fb and
is dominated by $\gamma\gamma \ra \ell\ell$ and non-WW-like
four-fermion events,
%as $\Pepem\!\ra \ell'\ell'\nu_{\ell}\nu_{\ell}$
%with $\ell'\neq\ell $.
mainly $\mathrm{ZZ} \ra \ell\ell\nu\nu$.
In the data, the inclusive combination selects 294 events.

%The systematic uncertainty on lepton identification amounts to
%0.6\% for electrons and 1.6\% for muons, to cover residual
%discrepancies in identification efficiency and purity between data
%and Monte Carlo. 
The sources of systematic errors are listed in
Table~\ref{tabsys}. 
The values are taken from the 189 $\GEV$ data analysis.
%The effect on the total cross section amounts
%to xx fb and is dominated by the Monte Carlo statistical errors,
%the uncertainties on the background cross sections and the
%uncertainty introduced by the cut on energy detected close to the
%beam axis.

Events are classified into six di-lepton channels making use of
electron and muon identification criteria. A jet or a track is
classified as a tau either if no lepton identification is
fulfilled or if the identified lepton has an energy lower than 25
GeV. A maximum likelihood fit is applied to determine the cross
section for each fully leptonic decay channel using efficiency
matrices for CC03 and backgrounds. The total background amounts, on average for
the four centre-of-mass energies to 114 $\pm$ 8 fb.  
WW-like four-fermion processes are taken into account in the
4f-CC03 correction for each individual channel. 
For all channels together, this correction amounts on average for the
four centre-of-mass energies to +35 $\pm$ 12 fb, 
where the uncertainty comes from Monte Carlo statistics.\\
%, given by $(\epsilon_{\rm 4f}\sigma_{\rm 4f}-
%  \epsilon_{\rm CC03}\sigma_{\rm CC03})^{\lv\lv}$.
\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Efficiencies, number of expected and selected events in the fully leptonic 
channel at each centre-of-mass energy.
     }
\vspace*{0.5cm}
\label{tab:lvlv}
\begin{tabular}{|c|c|c|c|}
\hline 
Energy  &  Average efficiency & Exp. Events & Obs. Events  \\ 
  (GeV) &       (\%)          &             &              \\
\hline \hline
192   &   $63.8 \pm 0.5 \%$       &  37.9  $\pm$ 1  &   32 \\
196   &   $62.6 \pm 0.3 \%$       &  102.8  $\pm$ 2  &   100  \\
200   &   $62.9 \pm 0.3 \%$       &  115.4  $\pm$.2 &  112  \\
202   &   $62.2 \pm 0.2 \%$       &  55.2  $\pm$ 1 &  50  \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Leptonic cross section results at each centre-of-mass energy. The quoted error is statistical only. The systematic error 
is indicated in the last line and is taken from 189 GeV analysis.}
\end{center}
\label{tab:fitlvlv}
\vspace*{0.3cm}
\hspace*{-1.3cm}{
\begin{tabular} {|c|c|c|c|c|c|c|c|}
%\cline{4-4}
\hline 
 Energy  & $\sigma(e\nu e\nu)$ &  $\sigma(e\nu \mu \nu )$  &  $\sigma(e \nu \tau \nu )$  
 &  $\sigma(\mu \nu \mu \nu )$  &  $\sigma( \tau \nu \mu \nu )$   & $\sigma(\tau \nu \tau \nu)$ & $\sigma(l \nu l \nu )$ \\ 
 ($\GEV$) &      (pb)        &      (pb)              &      (pb)           &      (pb)   &      (pb)   &      (pb)   &      (pb)        \\
\hline \hline 
192          &  $ -0.0 \pm 0.10$   & $0.45 \pm 0.18$ &  $0.38 \pm 0.19$ & $0.32 \pm 0.14$ & $0.14 \pm 0.14$ & $0.20 \pm 0.18$ & $1.49 \pm 0.30$ \\
196          &  $ 0.14 \pm 0.07$  & $0.44 \pm 0.11$ &  $0.38 \pm 0.13$ & $0.16 \pm 0.07$ & $0.41 \pm 0.12$ & $0.22 \pm 0.12$ & $1.78 \pm 0.21$ \\
200          &  $ 0.17 \pm 0.08$  & $0.41 \pm 0.10$ &  $0.37 \pm 0.12$ & $0.25 \pm 0.08$ & $0.32 \pm 0.12$ & $0.23 \pm 0.12$ & $1.80 \pm 0.20$ \\ 
202          &  $ 0.23 \pm 0.12$  & $0.38 \pm 0.14$ &  $0.22 \pm 0.16$ & $0.09 \pm 0.10$ & $0.56 \pm 0.19$ & $0.29 \pm 0.18$ & $1.68 \pm 0.27$  \\
\hline  
\syst.       &  $\pm 0.01$        &  $\pm 0.0.1$     &   $\pm 0.02$     &  $\pm 0.01$     &  $\pm 0.01$     &  $\pm 0.02$     & $\pm 0.02$     \\
\hline \hline
\end{tabular}}
\end{table}
%This result agrees with the Standard Model expectation of $1.76 \pm
%0.04$ pb~\cite{therror}.
%The results of the fit for each channel are given in Table~\ref{tab:fitlvlv} at each centre-of-mass energy with the total fully leptonic one, 
The results of the fit for each channel are given in Table 3 at each centre-of-mass energy together with the total purely 
leptonic cross sections extracted from the same fit assuming lepton universality.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\boldmath
\section{$\PWW \ra \ell \nu \qq$ events}
\unboldmath

%\boldmath
%\subsection{Selections}
%\unboldmath
Similarly to the lower energy measurements, three $\ell\nu\qq$
selection procedures are applied. One selection is optimised for
WW events with an  identified electron or muon track. 
The other two are designed to select $\tau\nu\qq$ events, 
based on global variables and topological
properties of events.

The selection of $\ev \qq$ and $\mu\nu \qq$ events
is identical to the previous 189 $\GEV$ analysis~\cite{xsecA}.
The candidate lepton is chosen as the charged track that maximises
$p_l^2 (1-\cos\theta_{lj})$, where $p_l$ is the track momentum and
$\theta_{lj}$ the angle of the track to the closest of the jets
clustered using the remaining charged tracks, with the
Durham-P~\cite{durham} algorithm ($y_{\rm cut}=0.0003$).

The same electron or muon identification criteria as for the fully
leptonic channel are required for this lepton candidate track. 

The probability for an event to come from each of the three
$\ev\qq$, $\mv\qq$ or $\tv\qq$ signal processes is determined from
Monte~Carlo reference samples using the lepton energy, the lepton
isolation and the event total transverse momentum.
%(Fig.~\ref{Plvqq}). 
An event is classified exclusively in the $\ev\qq$
(resp. $\mv\qq$) channel, if its corresponding probability is greater than 0.40
which will exclude it from the $\tv\qq$  search. 
\\
The selection of $\tau\nu \qq$ events is based on global event
variables and is combined with a topological selection attempting
to identify the $\tau$ jet. The selection procedures were described in
detail in previous papers~\cite{xsecA}.
Due to the increasing boost of the W boson, cuts are rescaled with \Rs. 

If an event is selected with this $\tau\nu \qq$ algorithm, it
is kept in the $\tau\nu \qq$ class. If an event is not classified but
contains a well identified electron or muon, 
it is classified in the $\tau\nu \qq$ channel if its probability
to be a $\tau\nu \qq$ event, is greater than 0.40. This
classification reduces the correlation of the measured
cross-section and branching ratio between  $e\ $ and  $\tau $ or
 $\mu $ and  $\tau $  channels (see also section~\ref{branchvcs}).

\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Efficiencies, number of expected and observed events selected 
in the semileptonic channel at each centre-of-mass energy.            
                   }
\vspace*{0.5cm} 
\label{tab:lvqq}
\begin{tabular}{|c|c|c|c|}
\hline 
Energy  &  Average efficiency & Exp. Events & Obs. Events  \\ 
 (GeV) &       (\%)          &          &              \\
\hline \hline
192   &    $81.1 \pm 0.2 \%$       &  182.9  $\pm$ 3    &  179 \\
196   &    $81.0 \pm 0.1 \%$       &  506.3  $\pm$ 6    &  496  \\
200   &    $79.9 \pm 0.1 \%$       &  562.4  $\pm$ 6    &  571  \\
202   &    $79.5 \pm 0.1 \%$       &  272.4  $\pm$ 3    &  267  \\
\hline
\end{tabular}
\end{center}
\end{table}


%\subsection{Results}
%\label{reslvqq}

Table~\ref{tab:lvqq} gives the average efficiencies, 
together with the expected and selected number of events at each
centre-of-mass energy. Expected events are calculated using the CC03 cross section values
from {\tt GENTLE}.  Averaging over the four energies, the inclusive efficiencies for the three semileptonic decay
channels are $85.0 \pm 0.2$\% for the electron channel, $90.6 \pm
0.2$\% for the muon channel and $65.7 \pm 0.3$\% for the tau
channel, giving $80.4 \pm 0.2$\% average efficiency on $\PWW\ra\lv\qq$,
with a total background of $272 \pm$ 10 fb. The overall averaged 4f-CC03 correction is
+28 $\pm$ 48 fb. 
A total of 1513 events are selected in the data.


%are dominated by the Monte Carlo statistical
%error in the 4f-CC03 correction. The uncertainty on the shape of
%the $e^+ e^-$ Bhabha background and the level of the two-photon
%background affect the definition of the electron isolation and
%probability. The uncertainty introduced by the cut on energy
%detected close to the beam axis affects the $\tv\qq$ analyses. A
%model for local energy deposits due to beam background was
%obtained with random trigger events. Such deposits were then added
%to the simulated events to estimate their effect on the
%measurement. Another estimate of this effect was obtained by
%locking out from the analysis all energy deposits below a polar
%angle of 12 degrees.

A similar fit as for fully leptonic events is used here with
the corresponding matrix of efficiencies and backgrounds.
%including the overlaps of the different $\lv\qq$ analyses.
The partial cross sections are then extracted from such a maximum
likelihood fit to the number of events in each selection.
%leading to
%\begin{eqnarray*}
%\sigma (\PWW\ra \ev\qq) & = & 2.41 \pm 0.14 \stat \pm 0.07 \syst ~\pb, \\
%\sigma  (\PWW\ra\mv\qq) & = & 2.39 \pm 0.13 \stat \pm 0.06 \syst ~\pb, \\
%\sigma  (\PWW\ra\tv\qq) & = & 2.23 \pm 0.17 \stat \pm 0.08 \syst ~\pb,
%\end{eqnarray*}
The systematic uncertainties on the cross sections
(Table~\ref{tabsys}) are quoted from the 189 \GEV\ analysis.
%where the systematic errors are obtained by varying all input
%parameters of the fit according to their uncertainties.
%
%The total $\lv\qq$ cross section is extracted by means of the same
%fit, under the assumption of lepton universality:
%
%$$ \sigma  (\PWW\ra\ell\nu \qq) = 7.07 \pm 0.23 \stat \pm 0.11
%\syst~\pb. $$ This result agrees with the Standard Model
%expectation of $7.31 \pm 0.15$ pb~\cite{therror}.
Table~\ref{tab:fitlvqq} summarizes the cross section values for individual 
and inclusive semileptonic final states. 

\begin{table}[h]
\begin{center}
\caption{\protect\footnotesize Semileptonic cross section results at each centre-of-mass energy. The quoted error is statistical only. The systematic error 
is indicated in the last line and is coming from 189 GeV analysis.
}
\vspace*{0.5cm}
\label{tab:fitlvqq}
\begin{tabular} {|c|c|c|c|c|}
\cline{4-4}
\hline 
 Energy  & $\sigma(e\nu qq)$ &  $\sigma(\mu \nu qq)$  & $\sigma(\tau \nu qq)$ & $\sigma(l \nu qq)$ \\ 
 ($\GEV$) &      (pb)        &      (pb)              &      (pb)           &      (pb)           \\
\hline \hline 
192          &  $2.51 \pm 0.36$  & $2.56 \pm 0.34$  &  $2.11 \pm 0.44$  &  $7.28 \pm 0.58$ \\
196          & $2.46 \pm 0.21$   & $2.29 \pm 0.19$  &  $2.79 \pm 0.28$  &  $7.44 \pm 0.35$ \\
200          &  $2.54 \pm 0.21$  & $2.63 \pm 0.20$  &  $ 2.58 \pm 0.28$ &  $7.76 \pm 0.35$ \\ 
202          &  $3.16 \pm 0.34$  & $2.49 \pm 0.28$  &  $1.73 \pm 0.36$  &  $7.55 \pm 0.50$ \\
\hline \hline 
 \syst.        &  $\pm 0.07$       & $\pm 0.06$       &  $\pm 0.08$       &  $\pm 0.12$       \\
\hline \hline 
\end{tabular}
\end{center}
\end{table}



\boldmath
\section{$\PWW \ra \qq\qq$ events}
\unboldmath

The analysis of WW decays to four jets consists of a simple preselection followed
by a fit to the distribution of the output of a neural network
(NN). The preselection and the NN applied are those used for the 189 \GEV\ analysis~\cite{xsecA}. 
Figure~\ref{had:nn} gives the distribution of the NN output values for all
backgrounds and signal Monte Carlo events compared with the data
at each centre-of-mass energy.
%~\cite{mwtampere}.


%\begin{figure}[htb]
%\vspace{-1cm}
%\begin{center}
%\mbox{\epsfig{file=emax.eps,width=140mm}}
%\end{center}
%\vspace*{-0.5cm} \caption{\protect\footnotesize Comparison of the highest jet energy
%distributions for data and Monte Carlo after the four-quark
%preselection. The points are the data and the histograms the Monte
%Carlo predictions. The light shaded histogram shows the expected
%background contribution. \label{had:emax}}
%\end{figure}
\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Summary of results for the fully hadronic channel
  on Monte Carlo and data events. Efficiencies are given in percent of
  CC03~processes and refers to events with a NN output greater than 0.3.
  The expected events include non-qqqq WW decays.
}
\vspace*{0.5cm}
\label{tab:qqqq}
\begin{tabular}{|c|c|c|c|}
\hline 
Energy  &  Efficiency & Exp. Events  & Obs. Events  \\ 
 (GeV) &       (\%)          &           &    \\
\hline \hline
192   &    $91.6 \pm 0.13 \%$       &  253.0  $\pm$ 2  &  283 \\
196   &    $90.4 \pm 0.11 \%$       &  728.4  $\pm$ 3  &  709  \\
200   &    $89.6 \pm 0.12 \%$       &  803.8  $\pm$ 3  &   778  \\
202   &    $89.4 \pm 0.15 \%$       &  391.3  $\pm$ 2  &   361  \\
\hline
\end{tabular}
\end{center}
\end{table}



%At this level of the selection, 3438 events are selected in the
%data while $3593 \pm 7$ events are expected from Standard Model
%processes. This preselection has an efficiency of 98.4\% on CC03
%events and a purity of 35.9\%. The $\PWW \ra \ell \nu \qq$
%processes are considered here as background and amount to 0.99 pb
%at this level.

Table~\ref{tab:qqqq} summarizes the number of selected events, the
efficiencies and the expected number of events at each centre-of-mass  
energy for the fully hadronic final states for a cut 
at 0.3 on the NN output value. Expected events are estimated using the CC03 
cross section from {\tt GENTLE}. For this NN cut, a total of 2131 events are selected
in the data. 


%described in the Appendix and
%are related to the global event properties, the properties of
%jets, WW kinematics and the b-tag probabilities for the four jets.
%The NN is simplified with respect to that used for the analysis of
%the 183 GeV data~\cite{xsecA}, with fewer input variables and a
%slightly improved performance.
%The structure of the NN has 19 inputs, 15 hidden units and 1 output unit.
\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Summary of results for the fully hadronic channel cross sections.
           }
\vspace*{0.5cm}
\label{tab:fitqqqq}
\begin{tabular} {|c|c|}
\hline 
 Energy  ($\GEV$) &  $\sigma(qqqq)$ (pb) \\ 
\hline \hline 
192          &  $8.60 \pm 0.61 \stat \pm 0.13 \syst $  \\
196          & $7.65 \pm 0.35 \stat \pm 0.13 \syst $  \\
200          &  $7.43 \pm 0.34 \stat  \pm 0.13 \syst $  \\
202          &  $6.98 \pm 0.48 \stat  \pm 0.13\syst  $ \\
\hline \hline
\end{tabular}
\end{center}
\end{table}



The cross section is extracted by means of a binned maximum
likelihood fit to the full NN output distribution of data events
where only the normalisation of the Monte Carlo signal is allowed to vary.
The mainly QCD background is kept fixed in shape and
normalisation. The fit result is given in Table~\ref{tab:fitqqqq}.


\begin{table}[htb]
\begin{center}
\caption[]{\protect\footnotesize Systematic error summary in fb, taken from 189 \GEV\ analyses} \vspace{6pt}
\label{tabsys}
\begin{tabular}{|l|c|c|c|}
\cline{2-4} \multicolumn{1}{c|}{} & \multicolumn{3}{|c|}{WW cross
section}  \\ \hline Source &  $\ell\nu\ell\nu$ & $\ell\nu\qq $
&$\qq\qq$ \\ \hline Calibration of calorimeters  & & &  32 \\
\hline Jet energy calibrations  & & & 9 \\ \hline WW generator and
$\PMW$ dependence & & & 25 \\ \hline WW fragmentation    & & &
17\\ \hline QCD generator      & & & 23 \\ \hline background shape
& & & 50\\ \hline Final state Interactions & & & 38
\\ \hline Background normalisation & 13 & 30& 84 \\ \hline
Luminosity & 9 & 35 & 39 \\ \hline Monte Carlo statistics & 15 &
61 & 36
\\ \hline Beam background & 11 & 30 & 40 \\ \hline Lepton
identification    & 2 & 45 &
\\ \hline Lepton isolation & & 56 & \\ \hline Probability
discrimination & & 46 & \\ \hline
 \hline Total & 24 &  118 &  134
\\ \hline
\end{tabular}
\end{center}
\end{table}


The sources contributing to the systematic error are summarised in
Table~\ref{tabsys} and correspond to the determination for the 189 \GEV\
data. 
Several cross checks have been performed on the fit result to
search for possible biases arising in the selection and full
simulation of the WW events: a previous version of the
NN~\cite{xsecA}, which has a different preselection, 
%gives $6.81 \pm 0.23~\pb$. Another estimate with a preselection 
%based mostly on charged tracks and 
a NN using only charged tracks to construct six input variables 
%gives $6.83 \pm 0.25~\pb$. Along the same line,
and a selection based on calorimeter measurements with six input
variables to a linear discriminant 
%gives $6.80 \pm 0.27~\pb$. A variety of linear discriminant analyses 
%using from 4 up to 14 variables give results which vary from 6.65 to 6.80 pb.
give consistent results.

\begin{figure}[htb]
\vspace{-1cm}
\begin{center}
\begin{picture}(200,550)
\put(-150,240){
\epsfxsize85mm\epsfbox{nn192.eps}
}
\put(80,240){
\epsfxsize85mm\epsfbox{nn196.eps}
}
\put(-150,0){
\epsfxsize85mm\epsfbox{nn200.eps}
}
\put(80,0){
\epsfxsize85mm\epsfbox{nn202.eps}
}
\end{picture}
\end{center}
\vspace*{-0.5cm} 
\caption{\protect\footnotesize Comparison of NN output distributions at each centre-of-mass energy
for data and Monte Carlo in the four-quark channel after the
preselection. The points are the data and the shaded histograms the background Monte
Carlo predictions. The unshaded histogram is the WW CC03 signal 
expectation and the curve shows the binned maximum likelihood fit to
the data. \label{had:nn}}
\end{figure}

\clearpage
\section{Total cross section}
The total cross section is obtained from a fit assuming the
Standard Model branching fractions, the only unknown being the total
cross section. The result would not be significantly different if the
branching fractions of the Standard Model decay modes were left free,
as long as no new decay mode is present in W decays.
 The fit is applied at each centre-of-mass energy to all data 
selected as described in the previous sections and uses the matrices of
efficiencies and backgrounds of the various analyses. 

Figure~\ref{fig:wwxs} shows the total cross
section measured as a function of the centre-of-mass energy. The results of the fits
are given in Table~\ref{tab:fit}.
New calculations with the Double Pole Approximation
(DPA)~\cite{Beenakker} have recently appeared and two Monte Carlo programs,
{\tt YFSWW3}~\cite{YFSWW} and {\tt
RacoonWW}~\cite{RacoonWW}, are being developed.
The predictions from {\tt RacoonWW} also include soft-photon exponentiation
and LL ISR corrections beyond  $\mathcal{O}\rm(\alpha)$
 in addition to the calculations described in~\cite{RacoonWW} ; moreover, the hadronic channels 
are multiplied with the naive QCD correction factors in accordance 
with the QCD correction included in the W width.
Table~\ref{tab:fit} summarizes
expectations from these models: The {\tt GENTLE} results~\cite{GENTLE} are indicated,
together with results from {\tt YFSWW3}~\cite{YFSWW} and {\tt RacoonWW}~\cite{RacoonWW}.
% The predictions from {\tt RacoonWW}
%also include corrections for ISR and naive QCD correction, even if not mentioned in~\cite{RacoonWW}.
The systematic uncertainty of 2\% is assigned for {\tt GENTLE} whereas errors quoted for
{\tt RacoonWW} and {\tt YFSWW3} are
MC statistics only. The expected uncertainty is of the order of  0.5\%~\cite{MCLEP2}. 
The predictions of these two new calculations are presented with   {\tt GENTLE} expectations 
on Figure~\ref{fig:wwxs}. On average over data from 172 to 202 GeV, the measured
cross section is lower than the {\tt GENTLE} calculation by -3.6 $\pm$ 1.4\% where the
error is experimental only. However, it agrees well with
 the more complete {\tt YFSWW3} and  {\tt RacoonWW} expectations which are respectively -2\% and -2.5\%
lower than {\tt GENTLE}. 

\begin{table}[htbp]
\begin{center}
\caption{\protect\footnotesize Summary of results of the fit for the total cross section at all centre-of-mass energies 
and predictions from three calculations. A systematic uncertainty of 2\% is
 assigned for {\tt GENTLE}
 whereas errors quoted for {\tt RacoonWW} and {\tt YFSWW3} are
MC statistics only. }
\vspace*{0.5cm}
\label{tab:fit}
\begin{tabular}{|l|c|c|c|c|c|} 
\hline
& Energy  &  $\sigma(WW)$ & {\tt GENTLE} & {\tt RacoonWW} & {\tt YFSWW3} \\ 
& ($\GEV$) &   (pb)        &  (pb)  &  (pb)    &  (pb)  \\
\hline \hline
\cline{2-6}
&172          &   $11.71 \pm 1.23 \pm 0.28 \syst $ & 12.39 $\pm 0.34  $  &  12.09 $\pm$ 0.01 & 12.15 $\pm$  0.01\ \\
&183          &   $15.57 \pm 0.62 \pm 0.29 \syst $ & 15.71 $\pm 0.34  $  &  15.37 $\pm$ 0.01 & 15.43 $\pm$  0.01\ \\
\rule{0.5cm}{0pt}
\begin{rotate}{90}%
\end{rotate}\rule{0.5cm}{0pt}
&189          &   $15.71 \pm 0.34 \pm 0.18 \syst $ & 16.64 $\pm 0.34  $  &  16.24 $\pm$ 0.01 & 16.33 $\pm$  0.01\ \\
\hline \hline
&192          &   $17.23 \pm 0.89 \pm 0.18 \syst $ & 16.95 $\pm 0.34  $  &  16.52 $\pm$ 0.01 & 16.63 $\pm$  0.01 \\
&196          &   $17.00 \pm 0.54 \pm 0.18 \syst $ & 17.25 $\pm 0.35  $ &  16.79 $\pm$  0.01 &  16.92 $\pm$ 0.01 \\
\rule{0.5cm}{0pt}
\begin{rotate}{90}NEW%
\end{rotate}\rule{0.5cm}{0pt}
&200          &   $16.98 \pm 0.53 \pm 0.18 \syst $ & 17.45 $\pm 0.35  $ &  16.97 $\pm$  0.01  & 17.11 $\pm$ 0.01 \\ 
&202          &  $16.16 \pm 0.74 \pm 0.18 \syst $  & 17.52 $\pm 0.35  $ & 17.03 $\pm$  0.01   & 17.16 $\pm$ 0.01 \\
\hline
\hline
\end{tabular}
\end{center}
\end{table}
\section{Branching fractions and $V_{\rm cs}$}
\label{branchvcs} The same fit as for the total cross section is
performed combining the data samples collected from 161 to 202 
~\GEV~centre-of-mass energies.

Without assuming lepton coupling universality, the eleven
unknowns are the three individual leptonic branching fractions
and the eight total
cross sections at 161, 172, 183, 189, 192, 196, 200 and 202~\GEV.
The hadronic branching fraction is set to
$1 - {\rm B}_{\mathrm e} - {\rm B}_{\mu} - {\rm B}_{\tau}$.
The fitted leptonic branching fractions are

\begin{eqnarray*}
%{\rm B}_{\mathrm e}&=&
{\rm B}(\PW\ra\ev)&=&11.26\pm 0.32\stat\pm 0.17\syst\%,\\
%{\rm B}_{\mu}&=&
{\rm B}(\PW\ra \mv)  &=& 10.99\pm 0.30\stat\pm 0.16\syst\%, \\
%{\rm B}_{\tau}&=&
{\rm B}(\PW\ra \tv)  &=&  10.63\pm 0.39\stat\pm 0.22\syst\%,
\end{eqnarray*}
and are consistent with lepton universality and the Standard Model
expectations. 

The QCD part of the systematic error is defined as
coming from the effect of different QCD generators for the
background and for the signal fragmentation as well as from final
state interactions. It amounts to 0.04\% in each channel. Due to
cross-contaminations in the identification of W decays to
\tv~versus \ev~or \mv , the measured ${\rm B}(\PW\ra \tv)$ is
28\% anticorrelated with ${\rm B}(\PW\ra\ev)$ and
25\% anticorrelated with ${\rm B}(\PW\ra\mv)$.
The ${\rm B}(\PW\ra\ev)$ is
4.5\% anticorrelated with ${\rm B}(\PW\ra\mv)$.

If lepton universality is assumed
(${\rm B}_{\mathrm e} = {\rm B}_{\mu} ={\rm B}_{\tau}=
 (1-{\rm B}_{\rm q})/3$),
a fit to
${\rm B}(\PW\ra \qq)$
and the four total cross sections as unknowns
yields the measurement of the hadronic branching fraction
%(see the correlation matrix in Table~\ref{tabcor2}):
$$ {\rm B}(\PW\ra \qq) = 67.09 \pm 0.46 \stat\pm 0.32   \syst\%.
$$ The QCD part of the systematic error is 0.10\%.

This result can be expressed in terms of
the individual couplings of the
W to quark-antiquark pairs:
\begin{eqnarray*}
   \frac{{\rm B}(\PW\ra \qq)}{1-{\rm B}(\PW\ra \qq)} & = &
 ( |\ckm{ud}|^2 + |\ckm{cd}|^2 +
|\ckm{us}|^2 + |\ckm{cs}|^2 + |\ckm{ub}|^2 + |\ckm{cb}|^2 )
 (1+\alpha_{s}(\PMMW )/\pi).
\nonumber \\
\end{eqnarray*}
The world average value of $\alpha_{s}$(\PMMZ ) evolved to \PMMW\
is taken as $\alpha_{s}$(\PMMW ) = $0.121 \pm 0.002$. The other
measured CKM matrix elements~\cite{pdg98} give a squared sum of
$1.049 \pm 0.008$. The measured hadronic branching fraction is then
interpreted as $$ |V_{\rm{cs}}| = 0.956\ \pm 0.021 \stat\pm 0.015
\syst. $$
\begin{figure}[htb]
\begin{center}
\mbox{
 \epsfig{file=plot_ww_paper14.eps,width=140mm}
}
\end{center}
\vspace*{-0.5cm} 
\caption{\protect\footnotesize Measurements of the W-pair production
cross section at eight centre-of-mass energies, compared to the
Standard Model predictions from {\tt GENTLE}, {\tt YFSWW3} and
{\tt RacoonWW}, for the world average
value of the W mass~\cite{MWWA}. 
\label{fig:wwxs}}
\end{figure}



\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Conclusions}
The W-pair production cross section at $\sqrt{s}$ =  192 to 202 GeV
has been measured in all decay channels with an integrated
luminosity of 236.96~$\ipb$. The determination of individual
branching fractions has been performed. 
The total cross sections have been measured at the four new centre-of-mass energies and,
as the previously reported measurements~\cite{xsecA},
are in agreement with the recent expectations of {\tt RacoonWW} and {\tt YFSWW3}.
After inclusion of the data
taken at centre-of-mass energies of 161, 172, 183 and 189 GeV, the
hadronic decay branching fraction is found to be $ 67.09 \pm 0.46
\stat \pm 0.32 \syst$\% which is used to determine the CKM matrix
element $|V_{\rm{cs}}| = 0.956 \pm 0.021\stat \pm 0.015\syst$.


\section*{Acknowledgements}
We would like to thank S. Dittmaier and W. Placzek for invaluable discussions
on DPA. It is a pleasure to congratulate our colleagues
from the CERN accelerator divisions
for the successful operation of LEP in 1999 above 190 GeV.
We are indebted to the engineers and technicians in all our institutions for
their contributions to the excellent performance of ALEPH.
Those of us from non-member
countries thank CERN for its hospitality.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


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\end{document}
