Hi Francesca,
let me elaborate a bit more in detail what I wanted to point out.
> First, I think that we need to be consistent within a given theory, but we
> can't apply comments from a group of theorist to another theory. I guess
> it is clear by now to everyone in this mailing list that there are
> two different ways to extract shape parameters from the photon spectrum,
> either fitting the photon spectrum or extracting the information from the
> corresponding photon energy moments.
> We know (although you do not mention explicitely in your email) that Bigi
> and Uraltsev do not agree in fitting the spectrum with their predictions
> but they do only trust the moments.
It's not just Bigi and Uraltsev but also Manohar and Ligeti who raised
their concerns at the CKM workshop. The problem is that you might find a
phenomenological description for the photon spectrum but the associated
parameters might _not_ be those that enter the SF function in b>u decays,
if your photon spectrum is considerably influenced by the K* resonance
(this is more of a general remark and probably not so much an issue for
the used Belle spectrum than for the sum of excl modes spectrum).
Now, for the sum of excl modes spectrum raising Ecut for the moments is
very similar to fitting to the shape. I am still convinced that the result
of the fit to the shape does hardly change if you only fit the spectrum
above 2.26 GeV (or maybe even 2.35) as the upper end of the spectrum is
measured with so much better precision. This becomes clear when you look
at the figure where all the K* region is in one bin. If you keep the total
BR fixed any model that doesn't get the differential BF in the last bin
(K* bin) right will get a rather bad chi2, while I believe the four lowest
points have hardly any weight.
Therefore, for a spectrum where the precision varies so strongly over
Egamma, moment measurements at high Ecut become more and more equivalent
to the fit to the shape (also, there are fewer bins and the shape becomes
more symmetric and so the first two moments determine the shape pretty
well). And indeed the result you obtain from the fit to moments at Ecut =
2.26 GeV is very similar to the one from the fit to the shape.
See also Neuberts reply below (he's talking about the generator notebook):
""""""""""""""
> >From hepph/0504071 and hepph/0408179 I understand that
> w = \Delta + \Lambabar = M_B  2E_min needs to be much larger than Lambda
> _QCD in order to integrate over a large enough region and to be
> insensitive to SF effects, where a value of Emin= 1.8 GeV is considered as
> safe.
Depends what you mean be "safe". I would say "pretty safe". Definitely,
if E0 is much larger, one IS sensitive to SF effects!
> As you know this is very challenging for experimentalists and in fact we
> have measured moments for several minimum photon energy values ranging
> from 1.9  2.25 GeV.
> Is it in your view sensible to use all these measurements to extract SF
> parameters with the help of moment predictions obtained from your
> calculations? And how would we evaluate the associated theoretical errors,
> e.g. would you consider a variation of the SF Ansaetze as sufficient or
> are there other factors to take into account?
For such high cutoff values all you can do is to use the notebook (one
loop precision) and try to play with different functional forms.
Strictly speaking, you will then not learn something about HQET
parameters, but really about how well a functional form is able to fit
the data.
""""""""""""""
So the statement that it is ok to fit the shape but not ok to fit moments
at high Ecut doesn't make much sense to me.
> I think that the current Vub paper is
> perfectly consistent in using the moments for this scheme.
> There is also the BLNP approach that supports the fit to the spectrum and
> the current Vub paper uses the fit to the spectrum within this approach.
> Now, any statement from BBU concerning the fact that the fit to the
> spectrum is not valid, has only to be applied to their own theory. How can
> we tell theorists who do different calculations what they should be
> using?
Moments are an inclusive quantity and don't rely so stronly on the
differential distribution. Of course Neubert supports the fit to the
spectrum (although in my point of view this is contradictory to his own
remarks) and I have no objection to use the result from the fit to the
spectrum and see what comes out for Vub.
The initial question though was about the comment in the paper saying that
"moments are safer than the spectrum" and I believe this is true for the
above mentioned reasons.
Cheers,
Henning
