Hi Heiko et al.,
I add a few remarks that hopefully clarify some of the points.
Bob
On Tue, 21 Dec 2004, Heiko Lacker wrote:
> Hi,
>
> since I could not attend the workshop I'm relying on the written summary
> and try to digest this.
>
> Below I'm trying to set-up a list of action items but have also questions.
> Please correct me if I did not understand correctly or missed an
> important point.
>
> Cheers,
> Heiko
>
> >1) The ideal set of measurements for inclusive decays which experiments
> >should attempt to publish are, in general:
> >
> > a) computed in the B rest frame or otherwise corrected for the B
> > momentum
> This becomes relevant if we are quoting results with a cut on the lepton
> energy. So it turn out to be important for the mX-unfolding.
This point should be thought of as a "best practices" suggestion
> > b) unfolded with respect to detector resolution effects
> We are on the right track concerning the one-bin unfolded mX-q^2 partial BF.
> Concerning the unfolded mX spectrum, moments and branching fraction see
> below.
>
> > c) include differential branching fractions (ie a spectrum) for as wide
> > a range as possible (even for bins which are not significant or are
> > not included in an optimal integrated branching fraction measurement)
> >
> > d) include partial branching fractions with respect to a cut threshold
> > (minimum lepton momentum, photon energy, etc.) for as many cut values
> > as is possible (even those values for which duality is expected to be
> > violated or the inclusive prediction is expected to fail).
> This has just been started before the WS.
>
> > e) include as many orders of moments as possible (even if predictions
> > do not exist) integrated with respect to as many cut values as is
> > possible, as in d).
> >
> > f) computed for B+ and B0 together and separately, where possible.
> I suggest to tackle this once all the dirty work is behind us:
> production, evaluation of systematic uncertainties, ...
Again, best practice....
> > g) partial widths, since these are directly comparable to theory and
> > are the same for B+ and B0 up to isospin-breaking effects (but the
> > partial BFs are not).
> Why should the rates neccessarily the same? If WA is playing a substantial
> role then also the rates will significantly different unless the difference
> in the B+ and B0 is only due to WA effects is compensating this.
> I always thought it was Pauli Interference making the main part of the
> lifetime difference though ...
The point here is fairly trivial - the BF are NEVER the same due to the
lifetime difference. The partial widths are the same up to WA effects.
> > 2) We can use moments from b->clnu, b->ulnu and b->sg to constrain the
> > SF parameters. There are two paths to extracting Vub from this
> > information that seem to be agreed upon:
> >
> > a) fit the shape function parameters on b-->s gamma events and then
> > apply them to Vub, eventually adding the information from the Vub
> > moments themselves.
> >
> > b) use the results of the b-->c lnu fit to extract the b-->ulnu
> > moments on the full phase space and then use the generator to fit SF
> > parameters out of them. In taking this approach we should
> Just to be sure that I understand correctly here:
> The precision of the OPE parameters extracted in b-->c lnu
> would then constrain the SF parameter variation in our MC?
The 1st and 2nd moments of the SF would be constrained. One would then
have to use different SF ansatz imposing these constraints on the moments.
> > i) use a variety of functional forms for the SF, since only
> > the 1st and 2nd moments are constrained at present
> We need to implement the Roman SF (wherever the name is coming
> from) and the Gaussian SF by a reweighting the DFN SF.
Yes - this has to be done in all our analyses. Dominique is looking into
this for q2-Ee.
> > ii) use fits to the b->sg spectrum to reduce the range of SF
> > functional forms that need be considered. (We should provide
> > fully unfolded b->sg spectra if possible, so that SF fits can
> > be done by 3rd parties.)
> >
> > iii) implement the new Neubert et al. formulas for b->ulnu and b->sg
> > in our MC generators
> I'm not sure if this is already taken care of by somebody.
> Any insight here?
Ric and Masahiro will look into the b->ulnu part, although I'm sure they
could use help. I think the RadPen group is supplying someone to
implement the new b->sg generator. We still need some information from
Neubert for all this.
> > 3) We should use the mathematica notebooks from Neubert et al. to
> > extract Vub from our partial rates for q2-Ee and the Ee endpoint
> > (and Mx, if the new MC generator is not ready in time). The notebooks
> > should be used with the error ellipses derived from the Belle b-->s gamma
> > moments themselves that are going to be published (allegedly) in two
> > weeks by Neubert&co themselves.
> >
> > 4) We should use the updated numbers from Ligeti et al. for extracting
> > Vub from the q2-Mx measurement, and use Neubert et al. as a
> > cross-check, since the latter is not (yet) fully to 2nd order in
> > alpha_S. In the coffee break Zoltan and Christian (on the phone)
> > offered to redo the calculations with whatever SF and corresponding
> > uncertainty we believe is necessary. They did not seem interested in
> > writing things in such a way that we can do this correction ourselves.
> Would/Should we publish then only the partial BF for q2-Mx or also a
> partial BF for mX (maybe depending on the mX cut)?
Remove the "only" from your sentence. We will of course interpret our
partial width using whatever viable theoretical approaches are available
at the time.
> > 5) Relating b->sg integrals directly to b->ulnu integrals is no longer
> > met with great enthusiasm (although one of the potential proponents
> > of this method wasn't there)
> >
> > 6) We should build our hybrid model in a way that preserves the
> > inclusive values for the <Mx^2> and <Mx^4-<Mx^2>^2> moments
> That would be a nice feature. Is the procedure already clear how to build
> the hybrid in this case?
No - ideas here would be welcome.
> > 7) We got no new information on duality, but it isn't considered a major
> > concern at present
> >
> > 8) We got no new suggestion on how to better quantify the WA uncertainty;
> > just the usual comparison of B+/B0 rates in b->ulnu at high
> > q2 / high Ee / low Mx. Neubert said: "until you have better information
> > take 3% as the relative error in the B+/B0 semileptonic widths and
> > assume the full difference is contained in your signal region."
> > Nobody objected to this. Note that 3% on the difference in total
> > rates means 1.5% on the average rate, which is more relevant to our
> > inclusive measurements (except in cases where tagging results in a
> > significant B+/B0 acceptance asymmetry).
> Hm, where does the 3% actually come from?
> E.g. Macro has been playing around with errors of O(20-30%).
> In this context: where does this large error come from?
If you go back to the original paper by Voloshin (to which nobody seems to
have added anything of substance) he quote (eqn 9) DBF = 3.9|Vub|^2 =
1*10^-4, where DBF = BF(B+->Xlnu) - BF(B0->Xlnu). The sign of the effect
is unknown. For analyses accepting equal fractions of B+ and B0, the
effect is 1/2 DBF divided by the average BF(b->ulnu) or roughly
(1*10^-4)/2 / 25*10^-4 = 2%. If one then assumes that this full 2% is in
the region accepted by our cuts, then the effect on the BF is 2%/fu and on
Vub is 1%/fu. It would be nice if someone checked my math....
> > 9) We should compare the semileptonic partial rates of D0 and Ds. Any
> > chances to do these measurements in BaBar?
> >
> >10) There are no measurements we can make regarding subleading SFs; we
> > can only limit their form by only using functions compatible with
> > fits to the b->sg spectrum. In the new calculations from Neubert et
> > al. three SSF are included and we should try out any functional form
> > with the only constraint that the mean value is 0 and the first
> > moment is related to the OPE parameters by the relationships in the
> > talk of Paz.
> >
> >11) The results of the unfolding technique on b-->u l nu spectra is
> > quite surprising because it apparently shows that we are capable of
> > measuring moments on the whole phase space (i.e. predictable by OPE
> > only) and this of course appeals theorists a lot. (When Neubert say
> > the unfolded spectrum he said "If you can do this then I guess we can
> > all go home!") Can we really do this? In particular is the impact of
> First of all, we have never claimed that we can extract the full rate
> (that is the zeroth moment) with high precision. This would be of course
> the final aim (-> Urs's long-standing dream becomes reality???).
>
> Actually, I can not imagine that it can be done better than we can extract
> right now the BF in the traditional mX recoil analysis: when pushing up
> the cut up to e.g. 1.8 GeV than the error blows up.
> The only way to have a useful BF measurement with such a cut is to work
> hard and bring the systematic errors down.
> > the models used in the detector response so small? Can we really
> > control the spectrum even where we have an enormous background, i.e.
> > for mx>1.8 GeV, or is this an artefact of regularization? We need to
> I agree that we should convince ourselves that we understand the
> uncertainties on the unfolded spectrum.
> But I think it is already clear from Kerstin's studies that the systematic
> errors start to hurt us for the first and second moment when using the full
> RUN1-RUN4 measurement.
>
> > make a detailed plan on how to address these concerns, to make sure
> > we are not neglecting anything. I (Ric) would suggest adding up all
> > bins of the spectrum and showing that the error on BF due to b-->ulnu
> > models is consistent with the one we quote in the BF measurement. The
> > technical problems encountered doing this on Run 1+2 may be overcome
> Yes, that is certainly a good test to perform.
>
> > on run1-4 statistics. Suggestions of other tests are welcome.
> Maybe we could check 'Coverage' when extracting OPE and/or SF parameters,
> respectively V_ub?
>
> >12) Measure also third moments of the b-->s gamma moments.
>
> Cheers,
> Heiko
>
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