Hi Sheila,

certainly not a stupid question. A quick answer which certainly does not 
address everything (the experts on the mes fit can certainly give more
insight):
With increasing mX the multiplicity on the signal side increases. This 
should have an impact on the _reconstruction_ of the Breco as there 
are more possibilities for combinatorics. As a consequence, I would expect 
that there is a correlation between the shape of the mes background and mX 
and also between purity and mX. In addition, one can certainly not trust 
the MC to determine the shape of the combinatoric BG. One can use of course
the MC in order to study if these kind of correlations are an issue in
the MC. If yes, one assumes that they are at least as important in data.
If no effect of this kind is observed on the MC you can not exclude that
this will not happen on data. So you need to check on data if this is an
issue.

In other words, if I was a reviewer and one presented a fit which does not 
allow for bin-by-bin differences I would ask for a proof that this assump-
tion is justified and what the related systematic error is.


In principle one should do the same for the signal part. 
In general one should check on MC if there is a systematic change in the 
shape parameters of the signal pdf when varying mX and if this change is 
covered by the errors on the signal shape parameters for the global fit 
averaged over all mX. If this is not the case then one needs to let them 
float in the fit on data or if they are fixed one needs to assign a corre-
sponding systematic error. In my opinion, it is a question of balance 
between statistical and systematic errors.
In the old days (BAD540) there was not much statistics available. As a 
consequence, it was not so much of a problem. With more and more stati-
stics it becomes more and more important to check if the mes fit strategy 
is appropriate.

Cheers,
Heiko


On Sun, 12 Feb 2006, Sheila Mclachlin wrote:

> 
> Hello,
> 
> I have a question.  In VubRecoil studies, 
> like the one in BAD 540, one of the things they 
> do is measure the spectra of variables like 
> mX and pl.  So in order to remove the breco 
> background, they have to sort the events into 
> bins of mX or pl, and perform a separate mes fit 
> in each bin.
> 
> Specifically, for the mX fit, the Crystal Ball 
> parameters are determined from a fit to the full 
> sample, and fixed in the bin-by-bin fits.  
> The Argus parameters are floated in the bin-by-bin fits.  
> 
> * for background, mes varies so much with mX or pl that is is worth 
> the loss of statistics (from the binning) to determine 
> the breco background bin-by-bin.
> 
> * for signal, mes does not vary enough with mX or pl to make it 
> worthwhile to bin the data and incur the loss of statistics.
> OR
> * for signal, we do not have enough faith in the Crystal Ball 
> function to trust it in a bin-by-bin fit.
> OR BOTH.
> 
> So my questions are:
> 
> * Is my interpretation correct?
> * If so, then WHY would mes background vary so much with mX or pl?  
> I can see how mes might vary with the QUALITY of mX, since 
> a badly-reco'd reco-B meson would lead to a badly-reco'd X.  
> But ultimately the two B mesons decay independently, so I don't 
> see why mes should affect the mX or pl distributions very much.  
> And yet they must, or there would be no need for a bin-by-bin 
> fit.
> 
> I hope that's not a stupid question. 
> I'm still kind of new to this stuff.
> 
> Thanks for your help,
> 
> sheila
>