Hi all,
I've recalculated the parameters for the three ansaetze.
Here are their values:
-- Exponential --
a = 1.32669
0th moment = 1
1st moment = 0
2nd moment = 0.165477
-- Gaussian --
c = 0.3057134
0th moment = 1
1st moment = 0
2nd moment = 0.165495
-- Roman --
rho = 0.2667075
0th moment = 1
1st moment = 0
2nd moment = 0.165480
New plots for the shape functions and their cumulative distributions are
posted at:
http://babar-hn.slac.stanford.edu:5090/hn/aux/petrella/SFplot_new.ps
I would say that now we can trust efficiencies calculated using these
parametrizations.
ciao,
Antonio
Luth, Vera G. wrote:
> Thank you Antonio,
> This clearly explains the problem. As you change the ansatz for the SF,
> the parameters have to be adjusted!
>
> Ciao
> Vera
>
> -----Original Message-----
> From: [log in to unmask]
> [mailto:[log in to unmask]] On Behalf Of Antonio
> Petrella
> Sent: Thursday, July 05, 2007 6:56 AM
> To: vub-recoil
> Subject: Shape Function form
>
> Hi all,
>
> as Kerstin suggested in her message
> http://babar-hn.slac.stanford.edu:5090/HyperNews/get/rev-SemiLep-06-04/1
> 7/2.html,
> I checked the first moments for each shape function ansatz (exponential,
>
> gaussian and roman) that I have implemented in my private version of
> EvtGenModels in order to compute the correct phase space acceptance
> needed for the calculation of tag efficiency when estimating the
> uncertainties due to the different ansateze.
>
> The implementation of the SF formulae has been copied from the package
> VubHybridModel.
>
> For each ansatz the same values for mb (4.6586) and a (1.32669)
> parmeters are used, only the form is changed.
>
> We know that the 0th moment (A0) has to be equal to 1, the 1st moment
> (A1) has to be equal to 0 and the 2nd moment (A2) has to be equal to
> 1/3*mu_pi^2.
>
> Here's what I get:
> -- Exponential form --
> A0=1
> A1=0
> A2=0.165477
>
> Being A2 = (mB-mb)^2/(1+a), I could double check that is correctly
> computed since I provide the masses and the a parmeter from the
> decay.dec file: mB=5.2791, mb=4.6586 and a=1.32669, giving A2=0.165458.
>
> -- Gaussian form --
> A0=1
> A1=0
> A2=0.089637
>
> -- Roman form --
> A0=1
> A1=0
> A2=0.086776
>
> A2 is changing so mu_pi^2 is changing too.
>
> I have also made plots of the shape functions:
> http://babar-hn.slac.stanford.edu:5090/hn/aux/petrella/SFplot.ps
> one can easily see that they're pretty different.
>
> I'm a bit puzzled: should the a parameter be equal for all the forms? It
>
> seems, in this case, that there is no way to have mu_pi^2 unmodified.
>
> Do you have any comment on this?
>
> cheers,
> Antonio
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