Hi all,
as Kerstin suggested in her message
http://babar-hn.slac.stanford.edu:5090/HyperNews/get/rev-SemiLep-06-04/17/2.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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