Measurement of $\as$ with Radiative Hadronic Events

Here we collect the comments for the OPAL editorial board EB 721 for the paper " Measurement of $\as$ with Radiative Hadronic Events" received after draft 1 of the paper was dispatched http://opalinfo.cern.ch/opal/doc/dispatch/dp1926.info .

The author of the paper is Daisuke Toya. You find his Ph.D. thesis from Tokyo University (2003) containing many details of the analysis here: toya-Dron.pdf .

The physics coordinator for this paper is Thorsten Wengler.

The members of the EB 721 are: Matthew Ford, Tatsuo Kawamoto, Stefan Kluth, Steve Lloyd.

Since the author has left physics the EB and the author and the editorial board agreed that a member of the EB, S.~Kluth, makes the neccessary changes to the draft in response to comments by the collaboration in consultation with the author and the EB.

The public reading took place on Monday, 18 June, 15:00 CERN time. The following significant changes were made in order to satisfy requests from the public reading. The latest draft 1.2 is astoya-draft-1.2.ps and includes the OPAL author/institute list and acknowledgements.

• Abstract: mention consistency with running and QCD at lower sqrt(s'), result in-line
• Section 1: mention ISR supressed on Z peak, drop paper overview, move description of analysis method and MC test to new section
• Section 2: new, describes event shapes and analysis method with MC tests
• Section 3: a new table with MC sample statistics could not be made, because not all numbers are availble in the paper draft or Daisukes thesis; the last para is therefore left unchanged.
• Section 4.1: consistent tense.
• Section 4.2.2: change cluster shape fit variable name to S, mention that fit quality depends on assumed resolution.
• Section 4.3: new, summarise data sample.
• Section 4.4: mention general backgrounds first, then discuss MC problem and background estimation from data, Figure 4 is removed (see below).
• Section 5: move event shape description to section 2, mention that data available in Daisukes thesis and in HEPDATA.
• Section 6.1.1: motivate systematic checks, mention that ECAL scale and resolution not important.
• Section 6.1.2: add reference for MC default values.
• Section 6.2: better description of figures of results, more consistent comparison with other results, discussion of consistency with running alpha_S.
• Section 7: mention main results only, repeat result inline only.
• References: new references to OPAL and JADE 4-jet analyses, these also study alpha_S running
• Tables: small text fixes.
• Figure 1: It is not easy to make all modifactions suggested at the public reading. Improved caption, high and low energy is separated vertically and by black/grey points and lines.
• Figure 2: fixed axis label symbol \theta and redundant legend on figure e).
• old Figure 4: removed. After comparing with the corresponding figure 5.8 from Daisukes thesis I am convinced that our figure 4 has problems. I also think that the old figure 4 is not essential for the paper. Figure 3 already shows that with backgrounds from data the distribution is described by MC.
• Figure 6: fixed postscript bugs showing misplaced error bars.
• Figure 9: show legend alpha_S= 0.1182 +/- 0.0102 for shaded band and line.
• Figure 10: show only OPAL LEP 1 event shape result and L3 rad. Z decays result.

Version 1.1 of the paper draft is here: astoya-draft-1.1.ps . Draft 1.1 covers Otmars comments and contains the following changes:

• Figure 1: caption improved
• Section 2: use past tense
• Section 3.1: remove last sentence (tau+tau- and 2-photon backgound), because it creates confusion here. The tau+tau- and 2-photon backgrounds are given in section 3.2.1 after the isolated photon selection. There is more detail in Daisukes thesis, which is referenced here.
• Section 4: footnote added to explain reuse of symbol C for C-parameter
• Section 3.2.2: 1st paragrapgh, improved explanation of likelihood variables
• Section 3.3: last paragraph remove statement that in fig. 4 a) the distribution is well reproduced by MC.
• Section 6, last sentence: reformulated
• Figure 3: better placement (?)
• Figure 4: caption changed to explain scaling of MC

Comments by Otmar Biebel (5 June 2007) and Stefan Kluths answers (11 June 2007)

> =========== begin of comments/annotations =======================
> Here are my comments and annotations. I hope, it's a little useful
> at least.
>
> o) p.1, end of 4th para
> "In this picture ... produced at an early stage..."
> As we should consider radiation of photons and gluons as
> quantum mechanical processes the term 'early stage' is
> probably misleading. From a q.m. point of view I would
> argue that the wavelength of the photon must be less
> than the wavelength of the gluon such that the photon
> can already resolve between quark and antiquark while
> the gluon cannot. Such a photon can be radiated >before<
> the gluon and, hence, the effective energy scale of the
> gluon radiation would be reduced.
> If my argument is correct then one should consider cuts
> such that the photon's energy is larger than the energy
> of the gluon. Or, otherwise, one should exclude the regions
> of event shapes where this condition is not (safely) fulfilled.
> So, in general, I would expect some systematic bias for the
> least photon energy bin, i.e. the highest sqrt(s') bin (which,
> in fact, can be seen from fig.1)

This discussion is at the heart of this paper of course. The text of para 4 refers to the parton shower model of jet evolution, where ordering of emmissions is an essential part. The "ordering argument" in the parton showers of PYHTIA or HERWIG is known to correctly reproduce QCD in approximation ("leading log") and thus the statement of para 4 should be correct as qualified at the beginning of the last sentence "In this picture ... ".

I remember that I contributed this paragraph ... I am happy for any improvements to go in here.

> o) p.2, 1st para, and Fig.1
> Could you add some quantitative statement about the agreement
> between the low sqrt(s) distributions and the FSR distributions,
> e.g. the result of a Kolmogorov test?
> In Fig. 1, I cannot see, whether JETSET, HERWIG, ARIADNE, or the
> sum of all are shown. Please state this in more detail.

Hm, I'll have to dig into the archive which Daisuke sent to me. I'll improve the caption of figure 1 to explain that each figure shows the MC as indicated in the title below.

> o) Sect.2
> I feel that this section has a mixture of tense (".. the x axis
> IS horizontal..', ... 'Generated events WERE processed...'). It
> would be helpful if a native speaker could check this

I'll go through this section again and check.

> o) p.3, Sect.3.1, last sentence
> Could you add a reference to the tau tau and two-photon contamination.

Daisuke did these checks himself using the MCs explained in section 2, so there is no need for a reference.

> o) p.3, Sect.3.2.1, last line
> Why did the two-photon background decrease after selection cuts
> while the tau tau background increased sixfold?

I can't give a detailed explanation, but these are the effects which Daisuke found in his analysis. Somehow in tau+tau- events there is large chance to observe an isolated ECAL cluster, perhaps due to the low multiplicity in these events.

> o) p.4, Eq.(1) vs. Eq.(7)
> The variable 'C' is used in two different ways: Once as a cluster
> shape parameter, once as an event shape parameter

Yes, but the event shape observable C is quite different from the cluster shape fit variable such that there is no chance for mistaking one for the other. I'll put a little comment in the definition of the event shape observable: "The symbol C is used here since it is the conventional choice for this observable and in the following it cannot be confused with the cluster shape fit variable."

> o) p.4, Sect.3.2.2, last paragraph
> It is unclear to me which variables were used for the likelihood
> and whether the MC simulation for these variables agrees with the
> measured data!

I try to improve the text for your first comment. The second comment is discussed in this (3.2.2) and the next section (3.3).

> o) p.5, Sect.3.3, last para
> I don't think that 'The cluster energy in Figure 4a) is well
> reproduced by the Monte Carlo..'. Every test of this hypothetical
> agreement must fail when looking at Figure 4a!

I'll change the text in section 3.3, last para, first sentence: " ... Figure 4 a) is compared with the Monte Carlo ... "

> o) Sect.5.1.1
> I miss a systematic error due to the lorentz boost to the rest
> frame of the event. At least the error on the FSR photon energy
> measurement must be considered for the determination of sqrt(s').
> Since the photon energy spectrum is rather steeply falling, the
> error on sqrt(s') should be asymmetric, shouldn't it?

The OPAL ECAL resolution was in practice something like 15%/sqrt(E). Using that the uncertainty on a 10 GeV cluster is 0.5 GeV and on a 45 GeV cluster it is 1 GeV. The variations in alpha_S due to these uncertainties are well below 1 % and thus we can ignore them. Do you want us to explain this in the text?

> o) Sect.5.1.1, 4th bullet
> You mention something very important just when passing by. What is
> up with the chi^2 in the cluster shape fits? Why doesn't it match
> between data and simulation? Doesn't this bias your subtraction
> of background photons from decays?

There could be a bias and its possible effect should be covered by the corresponding systematic study mentioned in this bullet.

> o) Sect.6, p.10, last sentence
> This last sentence is only true if the photon's energy is larger
> than the gluon's energy, which is roughly sqrt(y_cut * s).

I think we should rephrase this sentence somewhat, how about:

"Our result supports within its uncertainties our assumption that the effects of high energy and large angle FSR on hadronic Z decays can be effectively described by QCD with a lowered cms energy sqrt(s')."

> o) References
> I feel there are more references listed than referred to in the
> main text. Maybe it is good to remove the unused ones?

Yes indeed. I found and connected a few orphaned references.

> o) Fig.2
> b) and e) show very large discrepancies between data and MC in
> the selected regions. This should affect your results shouldn't
> it?

Yes, as discussed in section 3.

> o) Fig.3
> Title is cut.

not on my printout ... but I'll arrange to have figure 3 on its own page which should solve the problem.

> o) Fig.4
> Caption says "as explained in the text' but it isn't explained.
> I cannot distinguish the dotted from the solid histogram

I'll change the caption: "The neutral hadron background fractions in the Monte Carlo are scaled using the values shown in table 1."

> o) Fig.7
> The fitrange for y_23^D extends into a range of large R_i^had
> corrections. Shouldn't one keep away from such ranges to avoid
> potential biases due to the chosen hadronization model?

With hindsight, probably yes. Now we have to live with slightly above average hadronisation uncertainties for y_23.

> =========== end of comments/annotations =======================

-- StefanKluth - 11 Jun 2007