Hi Daniele,

here are a few comments/remarks concerning your study.

Attached to this mail you will find a plot showing the MEAN,RMS
and BIAS(=MEAN*RMS) for the MX distribution as a function of
the cut in the missing mass. It is in principal the same plot
send around roughly two weeks ago but now the relevant region in Mmiss
(around zero) is magnified. I hope this presentation is more illustrative.

First of all I assume that you still apply a very hard
cut in the Missing mass of the event (ABS(Mmiss)<0.6 or something similar)
- please correct me If I am wrong.

Such a cut would corresponds to the first few bins around zero (e.g. the
two bins -0.5,0.0 ; 0.0,0.5) in my plot. There it is obvious that MEAN and
RMS for the fitted and raw distribution are not so much different (still
slightly better for the fit thought).
This behavior, however, is easy to understand. Your very tight cut
in Mmiss selects already events that are fulfilling the global
constraints (e.g. Energy conservation) reasonably well.
Hence the improvements from the kinematic fit can not be large for those kinds
of events.
However, as you also learn from the plot, the real improvement from the
fit stems from regions where Mmiss is significantly away from zero. In
this region the fit still gives you an unbiased estimate of the MEAN with
a "stable" RMS.
This is not anymore true for MX raw!

So -to summarize- the improvements from the kinematic fit stems from
region where the global constraints are not perfectly fulfilled
- thats why we need a cfit :-). Therefore, for further studies (please!)
try to soften your cut in Mmiss and figure out where the optimum value
of this cut this is supposed to be.

=> Since you have now set up the "extracting machinery", it probably would
   be a good idea to perform an optimization of the Mmiss cut by just
   scanning the expected error on Vub as function of Mmiss.
   Similar to what I have done for the MEAN and RMS
   of the Mx distribution.

Looking forward to see this results from you.

Regards,

Oliver


On Sun, 23 Dec 2001, Daniele del Re wrote:

>
> Hi all,
>
>  using the last version of recoilNtp and abcFit I started to look at the
> effect of the kinematic fit on the Vub-Vcb separation.
>  In:
>
>  http://www.slac.stanford.edu/~daniele/vub/mx.gif  with kin fit
>
>  http://www.slac.stanford.edu/~daniele/vub/mxfit.gif  without kin fit
>
>  you see the "classic" plot for each component after all cuts
> with and without the kin fit (B0 Cocktail MC). The D/D* peak has more
> events and the Vcb tail at low Mx seems to be less evident after the fit
> but the difference is not dramatic.
>
>  This observation is confirmed by the fit result for the BR(btoulnu)
> (error basically unchanged) and by the plot:
>
>  http://www.slac.stanford.edu/~daniele/vub/mxfitvsmx.gif
>
>  that shows Mxhadfit vs Mxhad after all analysis cuts. Below 1.5 GeV
> Mxhadfit is almost identical to mxhad and this implies that the separation
> Vub-Vcb remains the same.
>
>  Further MC studies are needed to understand the leakage at low Mx for
> Vcb (Guglielmo is studing MC truth for Vcb in Mx<1.5GeV).
>
>  Daniele
>
>
>
>
>
>