Hi
find attached revised versions of paragraph 3 and 5.
In par 3 most mispellings and minor attempts of easy reading.
In par 5 I tried an optimal (at least in my opinion) merge
of the previous versions.
Some (?) indicate needs of further improvement.
Hope can help.
Let me know.
Ciao
Giancarlo
\section{Event Selection}
\label{sec:eventselection}
Events are selected requiring one reconstructed B as described in
the previous section.
\subsection{Track selection}
\subsection{Electron identification}
\subsection{Muon identification}
\subsection{Kaon identification}
\subsection{Event based cuts}
The selection at the event level is made with the following cuts:
\begin{itemize}
\item total charge of the event. The loss of one or more charged particles
affects and in particular reduces the value of the reconstructed $M_x$ in the
recoil. The request of the charge conservation ($Q_{tot} = 0$, where
$Q_{tot} = Q_{breco} + Q_{brecoil}$) rejects the events with missing charged
particles. This is a hard cut (see figure \ref{fig:qtot}). In principle events
with $Q_{tot} = \pm 1$ could still be good as far as the resolution on $M_x$
variable is concerned since the missing particle can have a small momentum
(for instance the soft pion in D* mesons decays) and could not change so much
the value of the reconstructed hadronic mass. Further study (see later)
showed that the increase in statistical power is negligible if we include
events with $Q_{tot} = \pm 1$. Then the cut applied is $Q_{tot} = 0$.
%  qtot
\begin{figure}
\begin{centering}
\epsfig{file=ps/qtotvub.eps,height=5.cm}
\epsfig{file=ps/qtotvcb.eps,height=5.cm}
\caption{Total charge of the event after all analysis cuts. Upper plot: $b \rightarrow ul\nu$. Lower plot: $b \rightarrow cl\nu$ .\label{fig:qtot}}
\end{centering}
\end{figure}
\item missing mass squared. The missing momentum is defined as
$p^{miss} = p^{Y(4S)}  p^{breco}  p^{brecoil}$ and the missing
mass is $p^{miss}^2$. In semileptonic events without cascades
(no semileptonic decays of the D mesons) the only missing particle is
the neutrino. Then the missing mass should be compatible with zero.
A cut on the missing mass is very powerful because it improves
the quality of the event since events with missing particles are rejected.
On the other hand the $b \rightarrow cl\nu$ background can be suppressed
because these events have higher multiplicities and consequently
worse missing
mass resolution. Moreover a cascade semileptonic decay produces an additional
neutrino and then the missing mass has not to be equal to zero.
In figure \ref{fig:mnu2} the $M_{miss}^2$ distribution is plotted both for
signal and background events. After optimization the cut used is
$M_{miss}^2 < 0.5 GeV^2$ (see below).
%  mnu2
\begin{figure}
\begin{centering}
\epsfig{file=ps/mnu2vub.eps,height=5.cm}
\epsfig{file=ps/mnu2vcb.eps,height=5.cm}
\caption{Missing mass squared after all analysis cuts. Upper plot: $b \rightarrow ul\nu$. Lower plot: $b \rightarrow cl\nu$ .\label{fig:mnu2}}
\end{centering}
\end{figure}
\item kaon rejection. This cut is useful to reject $b \rightarrow cl\nu$
background. $b \rightarrow cl \nu$ events contain one D meson. More than
90$\%$ of D decay in kaons. On the other hand $b \rightarrow ul \nu$ events
do not contain kaons in the first order. Then the rejection of the events
with kaons increases a lot the signal over background ratio. There are two
cuts: the number of identified charged kaons and the number of $K_s$ has
to be zero. No cut on $K_L$ is applied since studies showed that IFR and
EMC (?)
information does not permit to identify $K_L$ with the available kinematic
information.
\item number of leptons. Obviously we need at least one lepton in the
event. $b \rightarrow ul\nu$ events cannot have more than on lepton because
$X_u$ system cannot decay semileptonically. The cut applied is N(lepton) = 1.
\item $p^*$ of the lepton. In order to reduce the cascade and fake lepton
contribution, a cut on the momentum of the lepton in the B frame is applied.
The $boost$ in the recoiling B frame is possible since we know the $Y(4S)$ and
the reconstructed B kinematics. The cut is $p^*>1.0GeV$ and the efficiency on
$b \rightarrow ul \nu$ is around $90\%$ (see figure \ref{fig:pstar}).
%  pstar
\begin{figure}
\begin{centering}
\epsfig{file=ps/pstarvub.eps,height=5.cm}
\epsfig{file=ps/pstarvcb.eps,height=5.cm}
\caption{$p^*$ after all analysis cuts. Upper plot: $b \rightarrow ul\nu$. Lower plot: $b \rightarrow cl\nu$ .\label{fig:pstar}}
\end{centering}
\end{figure}
\item sign correlation. In the semileptonic decays of the B meson the lepton
charge is correlated with the flavor of the B. The recoiling B flavor is known
by using the reconstructed B information and therefore we can select only
events with the right sign lepton charge.
The cascade leptons are mostly removed by this cut.
The mixing of the neutral B reverses this correlation in the $17\%$ of the
cases. In the $V_{ub}$ extraction this effect will be properly taken into
account.
\end{itemize}
The total efficiency of these cuts (not including B reconstruction efficiency)
is ... for $b \rightarrow ul\nu$ and ... $b \rightarrow cl\nu$.
The breakdown of all the cut efficiencies are sumarized in the table....
(table with cuts and efficiency on Vcb and Vub events )
\subsection{Optimization of neutral particles contribution}
\label{subsec:neutrals}
%Study motivation
The contribution of neutral particles in reconstructing the invariant mass of the hadronic system (\Mx) has to be carefully studied in order to minimize the impact of the worse reconstruction of such particles with respect to the charged ones.
A specific optimization procedure has been set up in order to find out which are the best cuts to apply when reconstructing neutrals. All the results presented in this section are obtained using quantities from the output of the kinematic fit (see section \ref{sec:kinfit}).
The optimization study has been performed with SP3 and SP4 MC events. The ``vubmix'' and the ``cocktail'' MC samples have been used for the \vub \ study and for the \vcb \ one respectively\footnote{For the MC sample definition see section \ref{sec:datasamples}}.
The quantities considered in the optimization are the sigma and the mean of the \Mx \ residuals distribution and the ratio:
\begin{equation}
r = \frac{S}{\sqrt{S+B}}
\label{optieq}
\end{equation}
where S and B are the number of \vub \ and \vcb \ events, respectively.
The \Mx \ and the \Mx \ residuals distributions are shown in fig. \ref{Mxdisexamp}. A double gaussian fit is superimposed to the \Mx \ residuals distribution. From this fit the mean and the sigma of the core gaussian are extracted and optimized in this study.
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/vub_fit_79.eps,height= 11.0cm}
\end{tabular}
\caption[Mxdisexamp_c]{Fig. a shows the \Mx \ distribution for MC \vub \ events. Fig. b shows the \Mx \ residuals distribution for the same events. A double gaussian fit is superimposed to the \Mx \ residuals distribution. Exclusive $\pi$ and $\rho$ decays are clearly visible. \label{Mxdisexamp}}
\end{center}
\end{figure}
\subsubsection{Optimization of cuts}
\label{subsubsec:neuencut}
Several variables used to reconstruct the neutral particles have been studied in the optimization procedure:
\begin{itemize}
\item Energy, polar ($\theta$) and azimutal ($\phi$) angle of the reconstructed photons
\item The LAT distribution of the $\gamma$s
\item Identity of the $\gamma$ mother
\end{itemize}
Figg.\ref{firexneu}\ref{lasexneu} show the distributions of those quantities.
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/Enspectr_log.eps,height= 8.0cm}
\end{tabular}
\caption[firexneu_c]{Energy spectrum of all reconstructed gammas. \label{firexneu}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/lmomgam.eps,height= 8.0cm}
\end{tabular}
\begin{tabular}{lr}
\epsfig{file=ps/thetagam_E80.eps,height= 8.0cm}
\end{tabular}
\caption[lasexneu_c]{(a) Lateral momentum distribution (LAT) of the $\gamma$s recontructed. (b) Cos($\theta$) distribution of the recontructed $\gamma$s with energy less than 80 \mev . \label{lasexneu}}
\end{center}
\end{figure}
Different cuts have been studied:
\begin{itemize}
\item A photon energy cut ranging from 20 to 110 \mev
\item A combination of cuts on the energy and $\theta$ \ of the $\gamma$
\item Requesting $\gamma$s coming only from \piz s
\end{itemize}
Fig.\ref{vubopstu} shows the behavior of the mean and sigma of the core gaussian fit to the \Mx \ residuals distribution as a function of the various cuts applied. In each plot:
\begin{itemize}
\item The first 10 bins refer to the $\gamma$'s energy cut (first point = 20\mev \ cut, second point 30\mev \ cut, third point 40\mev , etc. etc.)
\item The eleventh bin is obtained by computing the \Mx \ only with $\gamma$s coming from \piz \ mesons
\item The 12$^{th}$ bin corresponds to the requirement that the energy of the $\gamma$ to be greather than 80\mev \ and the LAT to be greather than 0.01
\item The 13$^{th}$ bin is obtained by rejecting gammas in forward (FW) and backward (BW) regions defined in the following way:
\begin{itemize}
\item FW: Energy of the $\gamma$s less than 50\mev \ and cos($\theta$) of the $\gamma$s greather than 0.6
\item BW: Energy of the $\gamma$s less than 30\mev \ and cos($\theta$) of the $\gamma$s less than 0.7
\end{itemize}
\item The 14$^{th}$ bin is obtained by rejecting gammas with E$\leq$80\mev and cos($\theta$) less than 0.7 or greather than 0.6.
\item The 15$^{th}$ bin is obtained by rejecting only those gammas in the FW and BW regions (see the above definition) that have $\phi$ \ less than 2 or greather than 2.5 radiants.
\end{itemize}
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/vub_meandist.eps,height= 8.0cm}
\end{tabular}
\begin{tabular}{lr}
\epsfig{file=ps/vcb_meandist.eps,height= 8.0cm}
\end{tabular}
\caption[vubopstu_c]{Mean and sigma of the core gaussian fit to the \Mx \ residuals distribution as a function of the various cuts applied. The first ten bins are obtained with increasing values of the energy cut on recontructed $\gamma$s. The eleventh bin is obtained accepting only $\gamma$s from \piz. The other bins are obtained applying a combination of energy and angular cuts on recontructed $\gamma$s.
See section \ref{subsubsec:neuencut} for the definition of the various cuts. \label{vubopstu}}
\end{center}
\end{figure}
The same study has been performed for \vcb \ events with the ``Cocktail'' MC and it is shown in fig.\ref{vubopstu}
A plot of the ratio r defined in \ref{optieq} is shown, as a function of the cut applied, in fig \ref{ratiodist}. the normalization of the number of \vub \ and \vcb \ events with respect to the different luminosities is not applied given that the relevant study is about the shape of the distribution and not about it's absolute value.
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/ratiodist9.eps,height= 8.0cm}
\end{tabular}
\caption[ratiodist_c]{Distribution of the ratio r as a function of the cut applied. The first ten bins are obtained with increasing values of the energy cut on recontructed $\gamma$s. The eleventh bin is obtained accepting only $\gamma$s from \piz. The other bins are obtained applying a combination of energy and angular cuts on recontructed $\gamma$s.
See section \ref{subsubsec:neuencut} for the definition of the various cuts. \label{ratiodist}}
\end{center}
\end{figure}
\subsubsection{Testing different backgrounds}
In order to evaluate the impact of the changing background during time the study presented in the previous section (\ref{subsubsec:neuencut}) has been redone for different chunks of SP3 and SP4 MC with different background files. The background files used are shown in table \ref{bkgfiltab}. The effect of the backgrounds changes seems to be negligible in terms of the cut optimization, but the net effect in the \Mx \ residual distribution can be clearly seen in figg. \ref{bkgtime10} and \ref{bkgtime11} which refer to background files x10 and x11, respectively.
%%Add comments???
\begin{table}[htb]
\begin{center}
\begin{tabular}{cccc} \hline \hline
KEY & NEVTS & BKG COLLECTION & CFGALIAS \\ \hline
x2 & 12022 & /groups/bkgtriggers/1999102319991024r1V01 & \\ \hline
x3 & 2200 & /groups/bkgtriggers/1999110619991106r1V01 & \\
x4 & 1 & /groups/bkgtriggers/notused & \\
x5 & 62265 & /groups/bkgtriggers/1999110519991115r1V01 & \\
x6 & 44067 & /groups/bkgtriggers/2000012520000229r1V01 & SP28.6.0 \\
x7 & 44067 & /groups/bkgtriggers/2000012520000229r1V01 & Feb2000Cfg \\
x8 & 92000 & /groups/bkgtriggers/2000030120000331r1V02 & Mar2000Cfg \\
x9 & 102000 & /groups/bkgtriggers/2000040120000430r1V01 & Apr2000Cfg \\
x10 & 60000 & /groups/bkgtriggers/2000050120000531r1V03 & May2000Cfg \\
x11 & 69000 & /groups/bkgtriggers/2000060120000630r1V03 & Jun2000Cfg \\
x12 & 61000 & /groups/bkgtriggers/2000070120000731r1V01 & Jul2000Cfg \\
x13 & 61000 & /groups/bkgtriggers/2000080120000831r1V02 & Aug2000Cfg \\
x14 & 62000 & /groups/bkgtriggers/2000090120000930r1V01 & Sep2000Cfg \\
x15 & 73000 & /groups/bkgtriggers/2000100120001031r1V01 & Oct2000Cfg \\
x16 & 13000 & /groups/bkgtriggers/2001021220010228r1V01 & Feb2001Cfg \\
x17 & 41000 & /groups/bkgtriggers/2001030120010331r1V01 & Mar2001Cfg \\
x18 & 57000 & /groups/bkgtriggers/2001040120010430r1V01 & Apr2001Cfg \\
x19 & 80000 & /groups/bkgtriggers/2001050120010531r1V04 & May2001Cfg \\
x20 & 98000 & /groups/bkgtriggers/2001060120010630r1V02 & Jun2001Cfg \\
x21 & 98000 & /groups/bkgtriggers/2001070120010731r1V01 & Jul2001Cfg \\
x22 & 75000 & /groups/bkgtriggers/2001080120010831r1V01 & Aug2001Cfg \\
x23 & 116000 & /groups/bkgtriggers/2001090120010930r1V01 & Sep2001Cfg \\
x24 & 143000 & /groups/bkgtriggers/2001100120011031r1V01 & Oct2001Cfg \\ \hline
\end{tabular}
\caption[bkgfiltab_c]{Background files used in the SP3 and SP4 MC production in BaBar. Each row shows the ``name'' of the file (as x\#), the number of events generated using that file, the data background collections used to generate the evnts and the period that is covered by the collections.
\label{bkgfiltab}}
\end{center}
\end{table}
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/x10_sigdist.eps,height= 8.0cm}
\end{tabular}
\caption[bkgtime10_c]{\Mx \ residuals sigma distribution for SP3 MC events generated with background file x10. The first ten bins are obtained with increasing values of the energy cut on recontructed $\gamma$s. The eleventh bin is obtained accepting only $\gamma$s from \piz. The other bins are obtained applying a combination of energy and angular cuts on recontructed $\gamma$s.
See section \ref{subsubsec:neuencut} for the definition of the various cuts. \label{bkgtime10}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/x11_sigdist.eps,height= 8.0cm}
\end{tabular}
\caption[bkgtime11_c]{\Mx \ residuals sigma distribution for SP3 MC events generated with backroundg file x11. The first ten bins are obtained with increasing values of the energy cut on recontructed $\gamma$s. The eleventh bin is obtained accepting only $\gamma$s from \piz. The other bins are obtained applying a combination of energy and angular cuts on recontructed $\gamma$s.
See section \ref{subsubsec:neuencut} for the definition of the various cuts. \label{bkgtime11}}
\end{center}
\end{figure}
\subsubsection{Missing momentum direction}
Events with the missing [mass(??)]momentum pointing in the FW and BW noninstrumented cones, and which are therefore more likely to have a worse \Mx \ resolution, can in principle be rejected by a cut on the direction of the missing mass.
The distribution of the cosine of the missing momentum theta angle can be seen in fig. \ref{thetanudist}.
\begin{figure}
\begin{center}
\begin{tabular}{lr}
\epsfig{file=ps/thetanu.eps,height= 8.0cm}
\end{tabular}
\caption[thetanudist_c]{Distribution of the cos($\theta$) of the missing momentum in SP3 MC events. \label{thetanudist}}
\end{center}
\end{figure}
A cut on the cos($\theta$) of the missing momentum has been applied, ranging from 0.55 to 1.0 (forward direction), in order to maximize the ratio r (\ref{optieq}). The cut that results to maximize the ratio is that one at 1.0 (no cut).
(unclear: has to be cleared and phrased).
\subsubsection{Cut selection}
Looking at the plot shown in fig.\ref{ratiodist}, and at the mean and sigma distribution shown in fig. \ref{vubopstu} the 80 \mev \ $\gamma$'s energy cut is chosen: it maximizes the ratio r and minimizes the sigma of the \Mx residuals distribution. The stability of this cut as a funtion of the changing background has been tested (see figg. \ref{bkgtime10} and \ref{bkgtime11}). No cut on the missing mass direction has been applied.
\section{$V_{ub}$ extraction}
\label{subsec:vubextraction}
\subsection{Extraction of the ratio $\frac{BR(b \rightarrow ul\nu)}{BR(b \rightarrow cl\nu)}$}
As mentioned in the introduction, the variable choosen to extract $V_{ub}$ is
the invariant mass of the hadronic system after all cuts. The
ratio of the Branching Ratios
$\frac{BR(b \rightarrow ul\nu)}{BR(b \rightarrow cl\nu)}$ can be written as
shown in \ref{eq:ratioBR}. If we assume that the efficiencies of reconstructed
B tagging ($\epsilon^u_l$ and $\epsilon^c_l$) and of the lepton cut
($\epsilon^u_l$ and $\epsilon^c_l$) are the same for $b \rightarrow ul\nu$
and $b \rightarrow cl\nu$ the formula becomes:
\begin{equation}
\frac{\BR(b \ra u \ell \nu)}{\BR(b\ra c \ell \nu)}=
\frac{N_u}{N_c} =
\frac{M_u /\epsilon_{sel}^u}{(M_{sl}Bg)}
\end{equation}
where $M_u$ is the number $b \rightarrow ul\nu$ events after all the selection
cuts, $\epsilon_{sel}^u$ is the efficiency of selecting $b \rightarrow ul\nu$
in the tagged B sample with a charged lepton with a momentum above 1 $GeV$,
$M_{sl}$ is the total number of events which contain a charged lepton with a
momentum above 1 $GeV$, $Bg$ is the number of non $b \rightarrow cl\nu$ events
in $M_{sl}$.
The determination of $M_u$ is rather simple and basically consists on a $cut$
$and$ $count$ procedure after background subtraction. $b \rightarrow ul\nu$
decays rapresent the signal. The background consists of
$b \rightarrow cl\nu$ events and all remaining events (hadronic B decays
with either a true lepton from cascades or a hadron misidentified as a lepton).
An additional contribution to the background comes from the fact
that the reconstructed B's are not perfectly pure.
A proper subtraction of the background, therefore, is needed even on
the fully reconstructed side. Since the purity of the reconstructed B's
depends on the full event and, in particular, on the multiplicity
of the recoil, the subtraction has to be performed as a function of the
variable under study. We divide, therefore, the sample in intervals of the $M_x$
variable. The $m_{es}$ distribution of the reconstructed side is fitted in
each interval. The value of the yield and its error from the fit is finally
plotted in the correspondent $M_x$ bin.
%  bkg
\begin{figure}
\begin{centering}
\epsfig{file=ps/bkg.eps,height=8.cm}
\caption{Background $M_x$ distributions. Plain histogram is the $b \rightarrow cl\nu$ contribution,
green is the $other$ $events$ component.\label{fig:bkg}}
\end{centering}
\end{figure}

The two other backgrounds are determined by using the $M_x$ distribution
in a region where the signal contribution is negligible. A cut
$M_{cut}$ in $M_x$, where $M_{cut} < M_{D}$, defines a signalenhanced
and a signaldepleted region.
%
%CB
%=========these equations are perhaps unnecessary================
The populations in the two regions are given by
\begin{eqnarray}
N_{M_x<M_{cut}} & = & f_u M_u + f_c M_c + f_{oth} M_{oth} \\ \nonumber
N_{M_x>M_{cut}} & = & (1f_u) M_u + (1f_c) M_c + (1f_{oth}) M_{oth} \\
\nonumber
\end{eqnarray}
%=======================================================
%
The amounts of the two background components ($M_c$ and $M_{oth}$
are determined from a $M_x$ fit in the
signaldepleted region and by taking the background shapes (shown in
Figure \ref{fig:bkg}), hence their relative amounts in the signal region
$f_c$ and $f_{oth}$, from Monte Carlo. The fraction of $b\rightarrow
ul\nu$ events in the signalenhanced region, $f_u \approx 1$, is also
taken from Monte Carlo. The systematic effects due to this procedure,
in particular the effect of the theoretical uncertainty on $f_u$,
will be discussed below. Figure \ref{fig:fitMC} shows the $M_x$ distribution
before and after background subtraction on simulated events,
corresponding to an integrated luminosity of $\sim 230fb^{1}$.
Finally, the efficiency for $b \rightarrow ul\nu$ events after all the
cuts, relative to the tagged B sample with an high momentum lepton,
$\epsilon_{sel}^u$, is taken from the MC.
