Hi all,
since I am following this HQET stuff now for some time (that includes also
the bsg part) I would be very much interested to understand Ed's
argumentation concerning the compatibility (or better incompatibility) of
the used set of Lambda and l1 with the mean of the photon energy spectrum
from CLEO. Unfortunately, I somewhat fail to understand his definition of
the individual values:
> 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
I can only assume that he uses a shape function Ansatz in order to
translate Lambda and l1 into <Eg>  right? The only other alternative
is that Ed utilizes the OPE for <Eg> but here I totally fail to reproduce
his values! Hence in the following I assume that the shape function is
used to obtain the prediction of <Eg>.
Ed argues (see below), that the OPE(HQET) values for Lambda and l1 have to
reproduce the mean of the photon energy spectrum better than just within
their experimental precision because they contain conceptually the same
information  Of course, only if OPE and shape function parameter have
the same physical meaning. Since in his exercise he obtains a 31 MeV shift
and the experimental precession is also around 30 MeV he concludes that
OPE and shape function parameters are not the same.
> 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.
>From my point of view, this is a rather premature conclusion based on a
very weak argument. First of all one has to keep in mined that the used
OPE parameter set of Lambda and l1 is NOT only based on <Eg> BUT also on
the CLEO lepton moments (otherwise we would not have a l1). Therefore,
there is no reason to believe that this set of parameters will exactly
reproduce <Eg> because also the information of the lepton moments is
folded into this result. Only with a proper correlation estimate between
<Eg> and lepton moments one would be able to claim that 31 MeV is
significant  knowing that the lepton moments carry the largest
information on Lambda and l1 I personally doubt it!
Another important issue Ed completely ignores , is the fact, that the OPE
parameters Lambda and l1 have rather large uncertainties due to the
unknown 1/mb3 corrections. For example, Lambda ~ 350 MeV form CLEO <Eg>
has a ~70 MeV experimental error and a ~100 MeV theory error where the
theory error is dominated by the unknown 1/mb3 corrections! Therefore,
the errors are dominated by our poor knowledge of the 1/mb3 corrections.
Given this fact, a meaningful compatibility comparison between OPE and
shape function has to include also the uncertainties due to higher order
corrections. Since this unknown corrections are currently our dominant
uncertainties Ed should have included them into his argumentation  then
he would have immediately realized that the OPE parameters of Lambda and
l1 only have to reproduce <Eg> within their theoretical errors AND NOT
EXCACTLY. Since the observed shift of 30 MeV in <Eg> is covered by the
~100 MeV theory error on Lambda nobody can claim that he has observed a
significant difference between OPE parameters and shape function  at
least not from my point of view!
Given this argumentation, I would NOT quote an additional error due to the
assumption that OPE and Shape function parameter are identical. We
don't have experimental evidence that contradict this rather basic
assumption. However, as I have stated several times in the past, I do
believe that is important that theory establishes this link between OPE
and shape function a.s.a.p..
Hope this helps!
Oliver
On Fri, 19 Sep 2003, Urs Langenegger wrote:
>
> Hoi,
>
> today we got the following. Keep reading, especially to the last
> paragraph.
>
> We should discuss this next week. For various reasons, it looks
> difficult before Thursday. Thursday 8:30 am PDT?
>
> Cheers,
> U.
>
>
> > From: Ed Thorndike <[log in to unmask]>
> > To: [log in to unmask], [log in to unmask]
> > Subject: Concerns with Vub PRL
> > Date: Fri, 19 Sep 2003 18:02:54 0400 (EDT)
> >
> > Hi Vera, Hi Urs,
> > As Dave Cassel conveyed to Vera by phone in late July, I was in shock that
> > you continued to use HQET OPE values of /\bar, lambda_1 in the shape function.
> > I apologize for being so slow in getting my concerns to you. My lateness in
> > writing in no way is due to a lack of concern. Let me try to be very explicit
> > about my concerns.
> >
> > You do explicitly say what you do, which is good. However, you bury it in a
> > Reference, Ref. 18, which is not so good. In Ref. 18 you say: "We assume
> > that the shape function parameters in Ref. [9] can be related to the HQET
> > parameters /\bar and lambda_1." We can all agree that this is true, but the
> > essential point is that nobody knows exactly what this relationship is!
> > Hence, the statement is misleading to the casual reader who is not aware that
> > the relationship between the two sets of parameters is not known. 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?
> >
> > 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.
> > (As an aside, our /\bar, lambda_1 Shape Function are obtained from a fit to the
> > spectrum down to 1.5 GeV, and so what we obtain (line 2) needn't perfectly match
> > line 1, as line 3 should. Nonetheless, it differs by only 7 Mev, and matches
> > the error perfectly. The latter is probably fortuitous.)
> >
> > 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!
> >
> > 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.
> >
> >
> > On a somewhat separate matter, I disagree with the first sentence in your
> > conclusions paragraph "This result is consistent with previous measurements [4],
> > but has a smaller systematic error, ..." Ref. [4] is to the four LEP
> > experiments, and to CLEO's endpoint result. Far be it for me to defend the LEP
> > experiments. However, let's compare your result with CLEO's endpoint result.
> > For statistical plus experimental systematic errors, you quote +/0.28,
> > +/0.27 => +/0.39, 8.4%. We quote +/0.34, 8.3%. Pretty comparable. Your
> > fourth error, +/0.26, corresponds to our third, for which we quote +/0.16, but
> > would quote +/0.23 for a treatment consistent with yours. Those errors, going
> > from branching fraction to Vub, are 100% correlated. 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.
> > 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.
> > I think Point (3.) is worth your mentioning.
> >
> >
> >
> > If you are not able to show that the issues that I raise here are incorrect,
> > I very much hope that you will revise your paper before it appears in
> > PRL. If it is too late for that, then I think that you should submit an
> > Erratum. Failing that, we would feel forced to submit a Comment, calling
> > attention to the unresolved scientific contraversy concerning the key
> > theoretical assumption in your paper. Clearly this would be good for
> > none of us.
> >
> > Regards,
> > Ed
>
>
