Hi Riccardo,

thanks for all your comments.

I have to admit, that I slightly disagree with your approach
of using the kinematic fit as an selection criteria by it self.
It is fact that a semileptoinc B event - ub or cb - should
fulfill the general requirements of energy and momentum conservation
and also the B mass constraint. The kinematic fit should make
the best job possible in order to provide fitted quantities
which are improved and unbiased estimators of the true underlying
kinematic of the event - "ub or cb" does not matter at this point!
Therefore, the chi^2 distribution for events stem from uc or from ub
are supposed to be equivalent - just reflecting that both are fulfilling
the above mentioned constraints (E,P,MB) equally good. Hence, the chi^2
can  NOT be used to separate ub from cb or vis versa. If it would, you
have set up a biased cfit and you can not expected to get unbiased
quantities out of it.

The right place to separate ub from vub events is AFTER the
fit by using the improved and unbiased kinematic estimators
from the fit (e.g. Plepton(fit) vs Mx(fit) will have higher
discriminating power than Plepton(reco) vs Mx(reco)).

>From a conceptual point of view, a kinematic fit is not an
selection tool by it self. Sometimes the chi^2 can be used
to separate events fulfilling the applied hypotheses (E,P,MB)
from the one which don't. But the main intention is to provide
improved and unbiased estimators of the true underlying event
kinematic.

Let me illustrate this important concept by picking your proposal:

>my naive approach would have been not to try and recover events where we
>have lost something, since this will happen more often in background
>events than in signal ones. I would have said a possible approach is to
treat
>everything as fully reconstructed signal and through away the tails in
the
>global chi^2

Unfortunately, things are not so easy for semileptoinc B events.
You have to keep in mind that we are not talking about fully measured
events. Per definition we have a missing particle creating missing
energy in the event. This quantity is supposed to be determined
from the fit. If the X-system is NOT corrected for missing objects
the whole constraint concept becomes mathematically undetermined
(more unknowns than equations)

NDF=5(Constraints) -3(Neutrino) -4(lost particle) = -2

Of course, the mathematics used for the fit can not handle this
and will automatically transform it to:


NDF=5(Constraints) -3(Neutrino+lost particle) = 2

So all missing momentum and energy from lost particles will be blamed
on the neutrino and you naturally will get biased kinematic
estimators. Even worse is the fact, that the chi^2 will not reflect
this behavior because the neutrino, as unmeasured quantity, does not
enter in the chi^2 definition -> You get a biased kinematic with
a normal chi^2 behavior. No way to separate good from bad events.

The above mentioned problem, was the reason why I have proposed
in my note that, from an experimental point of view, kinematic variables
made out of the (X,neutrino) system are very attractive.
This variables will still represent unbiased and improved kinematic
estimators of the (X,neutrino) system. But If you start to separate
them in X and neutrino you get biased estimators for events
with lost objects.


Looking forward to discuss this with you further!

Cheers,

Oliver





On Wed, 7 Nov 2001, Riccardo Faccini wrote:

> Hi Oliver,
> my naive approach would have been not to try and recover events where we
> have lost something, since this will happen more often in background
> events than in signal ones. I would have said a possible approach is to treat
> everything as fully reconstructed signal and through away the tails in the
> global chi^2 (i.e. tails in M_v^2 if we were not to fit for it).
> After all the real goal is to kill Vcb events with MX<M_D because that is
> the tail that kills us. And those events have missing particles and we do
> not want to recover them...
> As far as the knowledge of the efficiency of such an approach is
> concerned, we are in trouble anyhow because we do not know the
> multiplicity of Vub events...
> 	These are just ramblings, I am very interested in the
> outcome of your approach, but it might be interesting to see both.
> 	ciao
> 	ric
>
> On Tue, 6 Nov 2001, Oliver Buchmueller wrote:
>
> >
> > Well, that's easy to explain. Since we are just summing the four momemta
> > of the measured objects there will be e.g. a costheta dependence for
> > losing objects and hence losing energy. Simple error propagation
> > will not include this in the error definition of the X-system. All missing
> > energy will be blamed on the neutrino ... and that's not what we want.
> > Therefore, we probably will need a (costheta,energy) dependent correction
> > for losing objects on top of the simple sum of cov matrix.
> >
> > Or, if this does not work, we might consider to optimize only the
> > direction measurement of the X-system and assume the energy of X unmeasured
> > in the fit. This will reduce NDF by one and the 2C(3C) will become
> > 1C(2C) but it still should work .... I have already tested this for tau
> > reconstructions where you have similar problems.
> >
> > Anyhow, as I said, that's just the beginning .... .
> >
> >
> > Oliver
> >
> >
> > On Tue, 6 Nov 2001, Riccardo Faccini wrote:
> >
> > > given  we are just taking X to be the sum of the four momemta we can just
> > > add covariance matrices. What is your perplexity?
> > > 	ciao
> > > 	ric
> > >
> > > ______________________________________________________
> > > Riccardo Faccini
> > >  U.C. San Diego, Universita' "La Sapienza" & I.N.F.N. Roma
> > > tel  +39/06/49914338 http://www.slac.stanford.edu/~rfaccini
> > > Univ. La Sapienza. 2,Ple Aldo Moro, I-00100 Roma
> > > Dipartimento di Fisica
> > >
> > > "A voice said to me: 'smile and be happy, things could be worse'. I smiled
> > > and was happy and indeed things got worse" (an office in Ferrara)
> > >
> > >
> > >
> > > On Tue, 6 Nov 2001, Oliver Buchmueller wrote:
> > >
> > > >
> > > > Correct, so far I am using an "overall cov matrix"
> > > > for the event. However, technically the usage of event-by-event errors
> > > > is foreseen and (hopefully) it should improve things even further
> > > > - but not yet sure how to apply the event-by-event
> > > >   stuff to the X-system ... a bit more brain power has to go into
> > > >   this ..thought -
> > > >
> > > > Oliver
> > > >
> > > >
> > > > On Tue, 6 Nov 2001, Riccardo Faccini wrote:
> > > >
> > > > > Great!
> > > > > If I understand correctly you have not yet exploited the candidate by
> > > > > candidate information which is now in the ntuple, that could improve the
> > > > > situation (in particular the tails), correct?
> > > > >
> > > > > I will read the document more carefully later.
> > > > > 	thanks
> > > > > 	ric
> > > > > ______________________________________________________
> > > > > Riccardo Faccini
> > > > >  U.C. San Diego, Universita' "La Sapienza" & I.N.F.N. Roma
> > > > > tel  +39/06/49914338 http://www.slac.stanford.edu/~rfaccini
> > > > > Univ. La Sapienza. 2,Ple Aldo Moro, I-00100 Roma
> > > > > Dipartimento di Fisica
> > > > >
> > > > > "A voice said to me: 'smile and be happy, things could be worse'. I smiled
> > > > > and was happy and indeed things got worse" (an office in Ferrara)
> > > > >
> > > > >
> > > > >
> > > > > On Tue, 6 Nov 2001, Oliver Buchmueller wrote:
> > > > >
> > > > > >
> > > > > > Dear All,
> > > > > >
> > > > > > as promised, the technical development of a
> > > > > > kinematic fit for semileptonic B events is
> > > > > > now finalized. All technical aspects have been
> > > > > > tested successfully (e.g. zero mass for neutrino,
> > > > > > overall constraint fullfillment,...).
> > > > > > The fit uses the whole event information including
> > > > > > not only the leptonic B decay but also the fully
> > > > > > reconstructed B candidate on the "other side".
> > > > > > Hence, not only energy momentum conservation but
> > > > > > also additional mass constraints like Equal Mass
> > > > > > or B Mass hypothesis can be used.
> > > > > >
> > > > > > For those who might be interested in details,
> > > > > > I have made a short node describing the technical
> > > > > > and physical aspects of this tool. Some performance
> > > > > > test are also shown in this note.
> > > > > >
> > > > > > The note can be found in:
> > > > > > http://www.slac.stanford.edu/~buchmuel/B-xlv_kinfit.ps
> > > > > >
> > > > > > This test indicates that's variables build out of
> > > > > > information from X-system AND neutrino (missing momentum)
> > > > > > are the most promising once in terms of "resolution improvements".
> > > > > > The results also suggest that more work has to
> > > > > > invested in the improvement of the X-system reconstruction
> > > > > > because it seems to be the limiting part in the
> > > > > > kinematic reconstruction.
> > > > > >
> > > > > >
> > > > > > I am looking forward to see your reaction/remarks/comments.
> > > > > >
> > > > > > Cheers,
> > > > > >
> > > > > > Oliver
> > > > > >
> > > > > >
> > > > > > By the way,
> > > > > >
> > > > > > this is clearly not the final word concerning kinematic fitting
> > > > > > of the semileptonic events ... it more supposed to be a start ...!
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > >
> > > > >
> > > >
> > > >
> > >
> > >
> >
> >
>
>