Hoi,
we have a phone conference reservation for tomorrow for 1.5 hours:
A MeetingPlace conference has been scheduled.
Call: 510-665-5437
When: September 25, 2003, 09:00 AM America/Los_Angeles
Meeting ID: 2146
I have moving people coming into my appartment at 10:00am (nominally,
maybe earlier, maybe later).
I append a draft of what we might use as a basis for discussion.
Cheers,
--U.
Hi Ed,
thank you for your mail. We appreciate your interest in our analysis
and take your concerns very seriously. Please find our answers below.
> Also, you do not include an estimate of error for the assumption
> that the two sets of parameters are IDENTICAL, rather than related
> somehow in a way that is not understood. I understand that not all
> theorists feel as strongly as Neubert that your assumption that they
> are identical is unreasonable, but don't they all feel that SOME
> error must be assigned to this assumption?
We do include an error for the assumption that the parameters are
identical. We made a decision (based on discussions with theorists)
not to use 90MeV as error on mb or LambdaBar (the agreement/outcome of
the CKM workshop 2002), but rather use the full error including the
dominating theoretical uncertainties (mostly from higher orders) to
account for this. It is obviously a point of discussion whether this
is an appropriate or good estimate of the error and whether or not
this also covers the central value and error on lone or "a".
It is difficult to assign meaningful errors to unknown effects. For
example, "everybody" agrees that "weak annihilation" has potentially
large effects in certain restricted regions of phase space, but so far
nobody has determined an error for this (e.g., in endpoint analyses).
Quark-hadron duality is in the same category. We are therefore not
setting a precedence by not assigning an arbitrary error to something
unknown.
> In our phone meeting of 3 July, the question was raised as to whether the
> range of exponential shape function parameters (/\bar, lambda_1) gave
> <E_gamma> values and errors consistent with CLEO's published values. In Email
> on July 4 I gave you the numbers showing that it did. A correlary of this is
> that if one calculates <E_gamma> using the values of (/\bar, lambda_1) that YOU
> have been using, one will get an <E_gamma> value, with error, not in good
> agreement with CLEO's measurement and error. We have carried out this
> exercise, and find:
>
> Measured 2.346 +/- 0.032 GeV
> calculated, using correct /\bar, lambda_1 2.353 +/- 0.031 GeV
> calculated, using your /\bar, lambda_1 2.377 +/- 0.043 GeV
>
> Note the differnce in the central value, 31 MeV. Your values of /\bar and
> lambda_1 come from our <E_gamma>, with its error, 2.346 +/- 0.032. Your
> procedure should, MUST get that back, to an accuracy small compared to the
> statistical error on the measurement (32 MeV), if using the HQET /\bar and
> lambda_1 in the shape function is reasonable. You don't, and the only possible
> interpretation is that HQET /\bar, lambda_1 don't mean the same thing as
> Light Cone /\bar, lambda_1. This conclusion is TOTALLY INDEPENDENT of what any
> theorist tells you, or us. It's an empirical fact, the output must match the
> input, if what you're doing is right, and it doesn't.
The parameters (LambdaBar, lone) that we use are derived from CLEO's
publications of both photon spectrum AND hadronic mass moments (else
there would be no lone). Your argument is therefore not valid. The
fact that <E_g> in the first and third row agree even within the
*statistical* error is actually supporting our position that there is
no evidence that the HQET and SF parameters are different (within the
precision currently achieved).
To avoid a misunderstanding: Your calculation is based only on the
two-parameter shape function, is that right? Assuming that is the
case, the agreement between the first and second row seems a (lucky)
coincidence, as subleading corrections will have an effect. Is there
any reason to assume that the photon spectrum is controlled only by a
two-parameter shape function? Furthermore, the HQET parameters
(LambdaBar, lone) are certainly prone to higher order corrections,
which are not expected to be covered by the statistical error alone.
From all this we would conclude that the results should be consistent
only within the statistical + systematic + theoretical error (whereas
they are already consistent within the statistical error alone).
> If you choose not to use CLEO's determination of the shape function, but
> instead use CLEO's determination of HQET parameters /\bar and lambda_1, as you
> have done, then shouldn't you include SOME error for this approximation? I
> think the answer is a clear "Yes". How big? Hard to say. Would it matter?
> YES! This is your dominant error. You're clearly better off having it
> determined by an objective procedure than by a guess. And you're clearly
> better off having it determined by a guess than by setting it equal to zero!
We disagree here. The relationship between the HQET and SF parameters
is about as unknown as weak annihilation and QHD, both of which are
commonly not assigned errors.
> I recall, and Dave Cassel recalls, that you mentioned that the range of
> uncertainty in /\bar, lambda_1 that we obtain from our b -> s gamma measurement
> gives a varaiation in M_X distribution that you find in poor agreement with your
> measured M_X distribution. If this is true, if you indeed can reduce the errors
> on the shape function parameters, that is great! It certainly deserves mention
> in your paper, since we're talking about the dominant error.
This measurement will be the topic of a future paper. We feel we
allude to this in the concluding section.
> Finally there is your third error, for which you quote +/-0.40, but
> I say you should quote +/-0.60, 13.0%. ("I say you should" means
> that's what you would get if you used the light cone /\bar, lambda_1
> from our b -> s gamma determination.) That is to be compared with
> our second (+/-0.44) and fourth (+/-0.24) error, => +/-0.50, 12.3%.
> These errors, yours and ours, in addition to being comparable (13%
> vs. 12.3%), are HIGHLY CORRELATED. So, collecting errors, 8.4%
> vs. 8.3% (uncorrelated), 5.6% (completely correlated), 13.0%
> vs. 12.3% (highly correlated). The correlated errors dominate.
> Conclusions from this part.
> 1. Your statement of smaller systematic errors is incorrect,if you
> include theory errors in the systematic errors.
You use "theory errors" to varying degrees. Why do you not include
errors for quark-hadron duality or weak annihilation? Both of them
are expected to be significantly larger in the endpoint due to the
much smaller phase space. Should the error due to subleading
contributions to the shape function be included?
> 2. Putting all the errors together, your analysis and our analysis have
> very nearly equal errors, if theory errors are treated in a
> consistent way.
> 3. There is very substantial correlation between your errors and ours.
Much more than just the error for BF->|Vub| is correlated. The
b->clnu modeling is also correlated, for instance.
Cheers,
BABAR
