Hi,
I have rewritten part of paragraph 5.1 of BAD 347, mainly to understand
the fit myself. Here is a proposal which we might consider as a
replacement.
Ciao, Concezio.

[ 5.1, 2nd paragraph]
$M_{sl}$ is extracted from data by fitting the $m_{es}$ distribution of
events which contain a charged lepton with a momentum above 1 $GeV$,
whereas
$Bg$, i.e. the contribution from cascade and misidentified leptons, is
taken from the MC.

The number of measured $b \rightarrow ul\nu$ events, $M_u$ is determined
with a $cut$
$and$ $count$ technique. Background events consist of three components:
the combinatorial contribution from the fully reconstructed side, $b
\rightarrow cl\nu$ events
and all remaining events (hadronic B decays with either a true lepton
from cascades or a hadron identified as a lepton).

Since the purity of the reconstructed
events depends on the full event and, for instance, on the on
multiplicity
of the recoil, the subtraction of the combinatorial background has to be
performed as a function of the
variable that is being studied. For this reason, the sample is divided
in intervals of the $M_x$
variable and the $m_{es}$ distribution of the reconstructed side is
fitted in
each $M_x$ interval. The value of the yield and its error from the
$m_{es}$ fit is finally
plotted in the correspondent $M_x$ bin.
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 signal-enhanced
and a signal-depleted region.
%
%CB
%=========these equations are perhaps unnecessary================
The amount of events 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}} & = & (1-f_u) M_u + (1-f_c) M_c + (1-f_{oth}) M_{oth} \\
\nonumber
\end{eqnarray}
%=======================================================
%
The amounts of the two background components ($M_c$ and $M_{oth}$) in
the signal-enhanced region are determined from a $M_x$ fit in the
signal-depleted 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 signal-enhanced region, $f_u \approx 1$, is also
taken from simulation. The systematic effects due to these assumption is
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.
...