Hi Concezio,

On Wed, 5 Jul 2006, Concezio Bozzi wrote:

> Hi all,
> 
> I think there is another issue to be addressed. Up to now, we have been 
> worrying about fixing the signal/peaking background components in our 
> mES fits, to deal with instabilities in bin of kinematic variables with 
> low statistics. We implemented constraints on the signal/peaking 
> background components for mES distributions as a function of the bins of 
> the kinematical (mx, p+, q2) variables, but only for DATA.
> 
> However, our final mx, p+, mx/q2 fits need also distributions for 
> Vcb+other MC and Vub(IN+OUT) signal MC. These MC components have been 
> and are currently being determined by performing mES fits as usual, e.g. 
> by leaving the signal, peaking and combinatorial backgrounds floating 
> and without any constraint applied. There are plenty of mES fits on MC 
> with low statistics. Recall also that every single bin in the kinematic 
> variable under study results from an appropriate sum of mES fits 
> performed separately on charged B, neutral B opposite flavor and same 
> flavor to correct for BBbar mixing.  If you look  e.g. at Antonio's 
> latest VVF fits in
> 
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/
> 
> you see that mES fits on data
> 
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_data3.eps 
> (charged B)
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_data4.eps 
> (neutral B opposite flavor)
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_data5.eps 
> (neutral B same flavor)
> 
> have the peaking/signal fixed (only signal S, combinatorial background B 
> and argus shape ar are floating in the fits), whereas the peaking 
> background component P is also floating in the MC mES fits:
> 
> Vcb+other
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vcboth3.eps
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vcboth4.eps
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vcboth5.eps
> 
> VubIN
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vubin3.eps
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vubin4.eps
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vubin5.eps
>  
> VubOUT
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vubout3.eps
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vubout4.eps
> http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedmES_vubout5.eps
> 
> The bottom line is: we need to constraint somehow the signal/peaking 
> background components in the mES fits also for these MC samples. The 
> question is: how?
> 
> One possible solution is to use the full (charged + neutral B) MC sample 
> which has been used to correct for the  data, but Antonio showed in his 
> previous posting that the fits are not stable for high mx values (signal 
> and peaking background are swapped), and are not good for intermediate 
> mx values. Grouping several high mx bins seems not to give more stable 
> results.
This is of course rather annoying as I would have thought that such a 
grouping would help.
A way out could be that we fit the sig/peakBG ratio on the MC-enriched
sample e.g. with a polynomial of order 2 and take this function for the 
correction.
BTW: Antonio, does the fit for the second bin which has by far the
     smallest error have a good chi^2?

> Another possibility (which can also be applied when constraining S/P = 
> signal/peaking on data) is to determine separately S and P, by e.g. 
> counting or fitting for S in events with truebrecomode==recobrecomode, 
> and fitting ony P and the combinatorial background in events with 
> truebrecomode!=recobrecomode. This latter solution should give more 
> robust estimates.
This sounds to be a good idea.

Cheers,
Heiko

> In any case, any S/P constraint would be determined on the entire 
> (charged+neutral B) sample, and it should be dependent perhaps only on 
> the kinematical variables.

> Any comments?
> Ciao, Concezio.
> 
> 
> Antonio Petrella wrote:
> > Hi,
> >
> > we also computed a correction factor for the signal/peaking bkg using 
> > the entire mx distribution, not a bin by bin.
> >
> > In this case the fit looks better, with respect to the bin by bin one:
> >
> > http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fix129/test_fix129fitresults.eps 
> >
> > http://www.slac.stanford.edu/~petrella/tmp/scra/Ibutest_fixed/test_fixedfitresults.eps 
> >
> >
> > cheers,
> >   Antonio
>