n Etapi- Comments 3/1/97

E852 experiment

Analysis of Eta Pi0 system with the decay Eta -> Pi+ Pi- Pi0

TRC (txt-file)

Draft 1 (ps-file) (pdf-file)

Draft 2 (ps-file) (pdf-file)

Draft 3 (ps-file) (pdf-file)

Draft 4 (ps-file) (pdf-file)

Draft 5 (ps-file) (pdf-file)

Draft 5_1 (ps-file) (pdf-file)

Draft 5_2 (ps-file) (pdf-file)

Draft 5_3s (ps-file) (pdf-file)

Draft 6 (ps-file) (pdf-file)

Draft 6_1 (ps-file) (pdf-file)

Draft 6_2 (ps-file) (pdf-file)

Draft 6_3 (ps-file) (pdf-file)

Draft 6_3a (ps-file) (pdf-file)

Draft 6_4 (ps-file) (pdf-file)

Draft 6_4a (ps-file) (pdf-file)

Draft 6_4b (ps-file) (pdf-file)

Draft 7 (ps-file) (pdf-file)

Draft 8 (ps-file) (pdf-file)

Draft 8 (ps-file) (pdf-file)


Draft 9 (ps-file) (pdf-file) Accepted in Phys. Lett. B at July 2007


Outline. (ps-file) (pdf-file)

Note 1. (ps-file) (pdf-file) Analysis of Eta Pi0 system

Note 2. (ps-file) (pdf-file) Mass dependent fit of PWA

Note 3. (ps-file) (pdf-file) Mass dependent partial wave analysis

Note 4. (ppt-file) (pdf-file) Report for Conferece at 10 Nov 2005

Note 5. (ps-file) (pdf-file) MDPWA. All parameters are free.

Note 6. (ps-file) (pdf-file) Comparison the relative phases.

Note 7. (ps-file) (pdf-file) PWA with modufied Decay Amplitudes.

Note 8. (ps-file) (pdf-file) Mass dependent fit of PWA results for $\eta \pi^0 $ system.

Note 9. (ps-file) (pdf-file) Outline, excerpts and critique of Dzierba et al.

Note 10. (ps-file) (pdf-file) Resonant phenomene in E852 experimental data.

xvf-files: Standart PWA results


Comments of TRC members on Notes

Gary Adams (comments)

Suh-Urk Chung (comments)

Denis Weygand (comments)

Neal Cason (comments)


TRC on draft3 and responses (comments)

Minghui Lu (comments)


Comments on draft4 and responses

Suh-Urk Chung, 14 Mar, 4 Apr (comments)

Neal Cason, 16 Mar, 24 Mar (comments)

John Daud, 29 Mar (comments)

Gary Adams, 3 Apr (comments)


Comments on draft5 and responses

Neal and Bob edited draft5, see draft5_3s

Neal Cason, Gary Adams, Suh-Urk Chung 17 Apr (comments)

Gary Adams, 24 May (comments)

Suh-Urk Chung, Gary Adams, Neal Cason, 25 May (comments)

Rob Hackenburg, 1 June (comments)


Summer comments on draft5_3 and responses

See Draft6 (minimal changes)

Gary Adams, 7 Jul

Please remove M. Chasse and J. Krenkel from the author list of the eta pi0 paper. Also, remove the footnote on J. Kuhn's affiliation. RPI is already listed in the author list.


Neal Cason, 10 Jul

Hi all: I have another suggestion regarding how one should determine the answer in the MDF. As it is now, the masses and widths are taken using the fit with the average solutions and the average error matrix. I never really did care for this method, but couldn't come up with a better one. Having looked more carefully at the procedures, it seems to me that the best number to quote might be the most probable values when you plot the results of a large number of fits such as was done for the systematic error study. If you look at figure 6 in Note 2 you would get values of M = 1290 MeV and Gamma = 280 MeV using this procedure. What do you think???

See Note 8

Ludmila Malinina, 10 July

1) If you'll take the average from the large number of fits (fig.6 Note 2) you'll consider all the combinations of solutions as equal. There are the combinations with large errors of parameters.

We produce the ambiguous solutions from one solution using MakeAmbig.cc (Sadovsky's procedure). The errors of ambiguous solutions are different. If we have a combination with solutions with large errors this combination isn't good and should be suppressed. But in random procedure for determination the systematic errors all such combinations enter with the equal probabilities. The usual E852 averaging procedure takes into account the error matrix of each combination. So it seems to me that the usual procedure is more adequate.

2) If we fix a2 parameters correctly , we make a choice of correct solutions between different combinations.

3) So it seems to me that we already obtained the correct result by this way. The large systematic error interval which was in the paper before reflected the other procedure to calculate the systematic errors, nothing more.

Gary Adams, 24 Aug

I think you and Neal have identified the remaining big question. We need to understand why chisq/ndf looks so big in the plots. I was a bit surprised to see that the resonance parameters are not correlated with chisq but the figures are clear. Item 5 is encouraging. It suggests that table 1 values can be explained easily in your paper.

Neal Cason, 23 Aug

Hi all: In response to the TRC question about the chisq/ndf, Ludmila notes that the chisq values for fits to individual random selection of solutions is distributed around a value of 3 wheras the chisq/ndf for the "average" solution is of the order of 1. I don't understand why this is so. It doesn't seem right to me. Ludmila: how is the error matrix for the "average" solution method obtained? I thought it was the average of the values for the individual solutions, but if this is the case I would expect a similar chisq for the two methods. I think we need to get to the bottom of this in order to understand whether our fits are "good" and what procedure should be used to give the "final" numbers. Neal

Ludmila Malinina, 4 Sep

Dear colleagues,

After discussion with Alexander Ostrovidov we can conclude: The better chi2 in the case of average solutions is logically understandable. Any procedure of averaging smooth over the statistical dispersal of the points of individual solutions. The smooth behavior of the points should be better reproduced by the smooth function used in the fit procedure.

Roughly speaking: if for an individual solution the average dispersion of the points from the fit line is equal to "Delta", then for the points of the solution averaged over 8 solutions it'll be "Delta/sqrt(8)". It is in good coincidence with our results (Note 8, Table 1): (chi^2)/ndf of average solution (Widht=120 MeV)~1.14 mean chi^2/ndf of the individual solutions ~3.2 (from fig.3) (chi^2)Average/mean(chi^2)Individual=1.14/3.2=0.356 ~1/sqrt(8)=0.353.

Is this the last "remaining big question" ? Can we start preparation of the new version of Draft ? My vacations is over so, being completely involved in the other projects, I'm very interesting in the speedy completion of this project. With my best regards, Malinina Ludmila

Neal Cason, 23 Aug

Hi all:

I guess I'm a bit confused. The error on the average solutions goes down by a factor of sqrt(8), so the chisq should go up, not down, right? I thought the answer was going to be that Sasha increased the error bars so that they would encompass the extremes of the solutions. That's what was done for the original etapi- PRL if I remember correctly. Neal

Vladimir, 14 Sep

Hi Neal,

there is some misunderstanding in Ludmila's message.

>Roughly speaking: if for an individual solution the average dispersion of >the points from the fit line is equal to "Delta", >then for the points of the solution averaged over 8 solutions it'll be >"Delta/sqrt(8)".

She means Delta as the spread of solutions (not average error). So the average point will be more close to fit line then in case in seperate individual solutions. Your remark on Sasha's code is rigth and it is a reason that chisq in average case is less then in the fit of individual solution. Regards, Vladimir

Vladimir, 15 Sep

Gary Adams for TRC and response, 7 July (comments)

Response and Comments on Draft6:

1. See Draft 6

2. No correlation mass(Pi1) and width(Pi1) with chisq/ndf.

It seems to me the very interesting result is approximately absent of the correlations between mass (width) and chisq/ndf in Fig.4 of Note 8. Malinina suggest to use it and to calculate sys errors with cut chisq/ndf <2. (Table 1 in Note 8, string chisq/ndf <2).

3. Sorting of individual selected combination

The sorting of individual selected combinations of solution is not the select of the physical solution. In our opinion it is a way of systematic error estimation. We have no an argument to decide that the mean value or any other in Fig.6 for mass or width correspond to physical solution. As far as I understand Neal suggested to estimate sys errors as RMS of mass (width) distributions in Fig.6 (Note 8) which are extrapolated by Gaussian. So we take the Pi1 parameters in Draft6 from Table 1 (Note 8), string chisq/ndf <2, which correspond to mean mass and RMS of Gaussian in Fig.6 (Note 8).


We left one paragraph instead of large section of MDPWA in Draft6. In MDPWA it is necessary to parameterize the mass dependence of every UNP wave and all relative phases, which are not known. So we insert the MDPWA results with simple polinomial mass dependence of UNP waves. These results are consistent with our MDF results.

5. t' - dependence

We insert a piece of t' analysis before PWA as it was in Draft4 and new part in conclusion about it. If we refused to show the analysis of UNPW we have to demonstrate, that our result UNPW/NPW coinsistent to famous model.

6. Leakage

We insert our investigation of leakage in MDF, which show that the leakage contribution to the $P_+$ wave from the $D_+$ wave shows that it is very small.

7. Interpretation

In conclusion we insert one more interpretation of the difference of mass Pi1 in Etapi0 and Etapi-. There are two or more the resonant 1^{-+} states in Etapi0 decay channel in interval mass of 1200-1400 MeV.

8. Fig.2

A main figure 2 and its caption is changed. Dotted line of a2 resonant phase is added to demonstrate a difference with fitted relative phase.


Vladimir comment on Neal's Note9, 13 July

Critique of Dzierba by Neal..

Neal's note is in time. We need to have the well_wounded comment on IU paper (PRD 67) in our EtaPi0 paper. Future referee and physical community have not to doubt that we are right in our conclusions.

We agree with all Neal's comment. Hear we underline his milestones.

* IU method of selecting the "correct" solution is rather subjective.

* There are no any systematic errors in IU results.

* Fit to the moments is a fit of the averaged D-functions mass dependence, but not the direct fit of angular distributions. Besides the results of P+ mass dependence are fully not satisfactory (see Fig.22 -24, Neal's note) with the parameters of this fit.

* Leakage from D+ to P+ wave can't do any phase mass dependence. So the relative phase must be only D+ wave phase. It is not in Fig.27. And it is not in our Etapi0 paper. Lets draw attention that the relative phase (D+ - P+) is more insensitive measurable value to ambiguous solutions in the region mass 1.1 - 1.74 GeV.


See Draft6_1

Comments on Draft6_1

Neal Cason, 26 September

Hi Gary, Suh Urk, and Dennis: Gary is in the process of moving to Cornell for his sabbatical and asked me to take over with the etapizero paper until he gets back into commission. As you know, Vladimir sent us draft 6.0 last week. I've since gone through the draft and made wording changes and I attach version 6.1 for you. There are several things which I think we need to decide before I can firm up the final draft. Perhaps you could think about the following and let us know what you think.

1. The mass and width now quoted use the technique we suggested on the last go around. They took the fits which randomly chose among the ambiguous solution (~1000 fits), plotted up the masses and widths obtained, did a Gaussian fit to them, and obtained the mass and width from that Gaussian fit. The Sigma of the fit was chosen to be the systematic error.

2. The statistical error is taken to be that obtained from the fit to the "average" PWA solution using average errors.

It seems to me that both of these are reasonable things to do. Does anyone have a problem with these issues ( or have other suggestions)?

Here are my questions then:

** Is #1 above OK? (Perhaps the systematic error is understated.)

** Is #2 above OK?

** Since we are using the distributions from the multiple fits, should these distributions go into the paper? (I've attached the appropriate figure from the memo on the website.)

** How should we end the paper? Note that the "Conclusions" section contains 4 paragraphs (not counting the acknowledgments). I haven't touched the last two of these. I think that we need to carefully consider what to say here. Please look these over. Neal

Gary Adams, 27 September

eta pi0 folks:

I am extremely pleased with draft 6.1! I think we now have a result that integrates our different methods into one coherent conclusion. Regarding Neal's questions, obviously I think 1 and 2 are "OK". It would be nice to include the distribution plots but they will not fit in a letter, and they could prompt more questions than usual from the reviewers. I think we should leave them out.

Regarding the conclusions, I think the second, third and fourth paras (Evidence....) should be moved to the results section, shortened, and referenced. In their place I would add a sentence to the conclusion, "This result, together with the previous results from Crystal Barrel and E852 provide strong indications for one or more spin-exotic mesons near 1400 MeV/c2."


See Draft6_2


Doen, see Neal's corrections in Draft6_2

Draft 6_2 becomes significantly better after Neal's corrections and Gary's suggestions.

I also have a remnant question. Should we point out that one of the IU results (moments fit, low t, table I) is in good agreement with our result, even though their conclusion disagrees? It's pretty clear that they were able to see the pi1 only at low t.


Doen, see Neal's corrections in Draft6_2

Here are a few detailed suggestions on the draft:

1) The title is a bit nondescript. I suggest, "Confirmation of the Exotic Meson pi1(1400)".


Title of Draft6_2 in new edition tells a reader that there is one Pi0 meson. It may be not so. We suppose in text "one or more spin-exotic meson near 1400 MeV". So, we suggest a title

"Meson Exotics JPC=1-+ in the EtaPi0 System"

2) page 3, column 2, line5, add number of DOF.


A sentence (p.3, coulomn 1, bottom in Draft6_2) have to change

In the MDF we fit the |D+|^2 distribution with free parameters: its intencity and two parameters of the smooth background, as we done in [12]. Then we fit the |P+|^2 distribution and the relative phase Delta Phi(D+ - P+) with three BW parameters and one for the production phase (assumed constant).

page 3, column 2, line6

a Chisq/DoF=1.14, DoF=28

line 7

gives Chisq/DoF=3.87,

3) page 4, column 1, para 2, line 1, Change to "In [12] it was shown ....."


Doen, see Neal's corrections in Draft6_2

4) page1, column 2, line 4 from bottom, change "...fitting all the data." to ""...fitting all the data using the method in ref [12]."


Doen, see Neal's corrections in Draft6_2

5) Vladimir, color figs require special handling and extra cost in PRL. You may want to remove color from your figs.

Regards, Gary


The figures look better if we keep its as colour but allow PRL to print as white/black mode. For example the yellow points (average) in fig.4 look as grey points and we do not miss them on white background. I try to remove color but figures become worse.So I change the caption in fig.2 for white/black mode.


Comments of E852 members on Draft6_2

Gary, Bob (comments)


See Draft6_3a

Suh-Urk suggest to include a paragrath on discussion about two EtaPi0 states at 1280-1380 MeV.



See Draft6_4a


1. In Figure 1a the peak is at 500 events per bin and the average of the background looks to be about 100 events/bin. This is a signal to background of (500-100)/100 =4 to 1. But in text a ratio of 6:1 is claimed.


2. In Figure 2 the caption and the text do not make it clear what the solid lines and the dots (grey or yellow) refer to. It is clear from the caption that the dots refer to the average pwa solution (method 1), but is the line the MDF results from method 1 or method 2? The text says it is method 2 but it would be clearer for the reader if the caption also specified which method the line referred to.



See Draft6_4b


See Draft7 for PRL (4 pages)



PRL comments on Draft7

PRL First (A) and second (B) referee (comments)

PRL Third (C) referee (comments)

PRL Third (C) referee (addendum) (comments)


See Draft8 for PL