STAR Correlations and Fluctuations PWG

[Hanna Paulina Zbroszczyk <hanna.zbroszczyk AT pw.edu.pl>]

Dear Ke,

Thank you for addressing my comments. Here I copy here your responses and add my comments.

Most of my comments come after reading the Analysis Note.

1. Theory correlation function section does not include QS effects.
And how do you treat it in your calculation?
The QS effects are considered in the spin symmetric/antisymmetric. For the indistinguishable particle pair (e.g p-p, d-d) with even/odd total spin, the two quantum mechanical amplitudes is added/subtracted to yield the amplitude which is symmetric/antisymmetric. More details are added into analysis note page 4.

Thank you for clarifying this.

It would help if, for a good understanding of all sources of correlations, you separate all contributions in the p-d and d-d cases as well.
Prepare such a figure and add to the theory part regarding descriptions of all correlations.

Figures added into analysis note, page 6.

Thank you for adding these figures. However, for the d-d case, it should be clarified in more detail how you obtained this result. As LL formalism assumes only s-wave, later direct comparison to CRAB and the results of your experiment do not match. I will comment more on this comparison later.

2. Figures 19, 20. Surprisingly, splitting is so minor in your results.
Did you apply with an anti-merging additional cut on \delta \phi* and \delta \eta?
For these two figures, no anti-merging cuts is applied, only check how the CF changes when splitting level (SL) change. Figures 19 (now it’s 20) is proton- deuteron pair, for identical pair, the splitting effect is small, as expected. For deuteron-deuteron, figure 20 (now it’s 21), splitting effect is large, please see the first 4 points at low k*.

Ok, thank you.

3. Page 23, missing reference to the figure ??

Correct the figure reference.

Thank you.

4. Momentum smearing. How do you calculate C(q_smear) correlation function? If you calculate q_smear, did you put the weight for smeared or not smeared momentum difference?
The q_smear is calculated with smeared momentum, eta and phi. The resolution of pT, eta, phi are calculated from embedding data. Please see figure 32 (proton) and 33 (deuteron).

The question is different. q_smear should be calculated from smeared momenta (considering \eta and \phi angles). For q_smear, the value of the correlation function should be calculated for real, not smeared momenta.

5. In Figure 33, all panels have a typo: protonn instead of a proton.
There is almost no effect for smeared function, which is surprising compared to other measurements (e.g., pion-kaon at BES, see Pawel paper proposal). Typo corrected. And yes, the momentum smearing correction is small in this analysis. According to non-identical pion CF at 3GeV, the momentum.

Please clarify if you include weights for your correlation function for non-smeared momenta.

smearing effect is also negligible (please see slide 22: https:// drupal.star.bnl.gov/STAR/system/files/Meeting_1_June.pdf).

6. Systematic uncertainties. What is the contribution to systematics for taking into account different fitting ranges? It should be mentioned in the paper proposal, all together with other variables.
Add two tables discussing the systematic uncertainties of extracted R_G, f_0 and d_0, please see Table 11 (p-d) and 12 (d-d).

Systematic uncertainties are calculated for the separate data points of the correlation functions, and then, there is another set of systematic uncertainties for the extracted parameters. Having a separate set of tables for data points (both systems, separate centrality classes, and a separate set of tables for extracted parameters would be clearer. Each table should contain the list of systematic uncertainties in case data points and extracted parameters. Keep in mind that the range of fitting and normalization affect only extracted parameters, not data points. Please carefully list all contributions for separate data points and extracted parameters.

7. I see you applied the Barlow test. Which variables did not pass and were excluded from systematics due to limited statistics?
I checked this in the region of 0< k* < 200 MeV/c. For both p-d and d-d case, all variables have passed Barlow test.

Ok, so which criteria (if any?) do you reject due to low statistics?

8. Prepare a table with % for which element included in your systematic studies, separately for p-p and p-d (separate centrality bins).
Added Table 40, 41 discussing the systematics.

Thank you, see by above comment.

9. Data and model comparison. Since you use the LL model for data and CRAB for the model, can you please prove the consistency of these two approaches for considered small sources (between 1.5 and 2 fm for d-d and 2.5 and 3.5 fm for p-d?)? Please plot the correlation functions and compare them point by point.

It is unusual that you use CRAB to calculate the model function and then extract the parameters of the interaction from the LL model. It would be better if you use LL model with fixed parameters f0 and d0 that you got from the experiment to calculate theoretical correlation function from SMASH, and then, to extract the source size.
If you use both parametrizations based on different assumptions, one should prove their consistency for few source sizes (especially for these relatively low, of the order of 2 fm or even smaller).
Yes, in this analysis we use two different approaches to compare with data. These two approaches have some difference regarding on how to build the wave function.
In LL model, the scattering parameters are used to construct the wave function. While in CRAB, the Wood-Saxon potential is used, and wave function is obtained by solving Schrödinger equation. One should not expect exactly same results coming from these two approaches (there’s a detailed study: https://link.springer.com/article/10.1140/epjc/s10052-018-5859-0).
A comparison can be found in figure 54. For d-d pair, things are much more complicated. In L-L approach, only s-wave is considered, S=1 channel is irrelevant to s-wave, so we adjust the spin weights accordingly (suggested by Prof.Lednicky). While in CRAB, full spin are considered. This will make the comparison more difficult.

The reason of showing SMASH+CRAB is to emphasise the production mechanism of light nuclei. Under the same potential, the CF show different behaviour with two types of deuteron.

Yes, that was indeed my point. Thank you for preparing these figures. For p-d (Fig. 54), if you show the ratio of LL/CRAB, you will automatically account for the consistency. 

However, for the d-d case, the consistency between LL and CRAB is much more challenging to prove, as you mention. If you use the LL model to fit your data, you should also use LL formalism to calculate the correlation function in SMASH. Setting extracted from data parameters of the interaction, you can directly compare radius with and without coalescence included. Then, comparing the radius directly, you can conclude if you are closer to coalesce and thermal production of deuterons. If you would use the potential formalism to describe your data, then you can use the same for SMASH (again, with and without the coalescence assumed).

More details are added in the note (chapter 5.2).

10. Correct the description of Fig. 51, 52 and 54.

Corrected.

11. Fig. 52 should have experimental data and the SMASH model with and without the coalescence (to prove that the coalescence scenario better describes data).
This figure should also be updated in the manuscript draft.

Previously in the PWGC preview, we have two different types of SMASH radius to compare with data (with Coal. and without Coal.). During the preview, we found it will be confusing if all of them are shown in the same plot, together with experimental data. We decided to keep SMASH+Coal in this plot, since from correlation function comparison, the SMASH+Coal give a better description to data. Without the Coalescence, the correlation function show large deviation to data, it’s already excluded.

I update the Fig 52 (now it’s fig 55) in the analysis note, to keep consistent with plot in paper draft.

Indeed, it should be solved how to demonstrate visibly in the figure that the coalescence scenario describes data better for p-d and d-d cases. I remember this discussion from the past. I think one should not remove model prediction without the assumed coalescence scenario but rather think about how to show them more clearly. 

 The judgment is made based on the source size. However, as I mentioned, we need to ensure that the strong interaction description is consistent between the data and the model.

Thanks,

Hanna

Hanna Paulina Zbroszczyk

PhD DSc Eng, Professor WUT

E-mail: hanna.zbroszczyk AT pw.edu.pl

Tel: +48 22 234 5851 (office)

Address:

Warsaw University of Technology

Faculty of Physics

Nuclear Physics Division

Koszykowa 75

Office: 117b (via 115)

00-662 Warsaw, Poland

Wiadomość napisana przez K.Mi <mike1996 AT mails.ccnu.edu.cn> w dniu 20.07.2023, o godz. 11:10:

Dear Hanna,

Thank you very much for the comments. We have considered all your suggestion and update the analysis note accordingly. 

Please see the reply and updated analysis note in the following links:

Reply:

star.bnl.gov

Update analysis note: 

star.bnl.gov

And also the related links:

Webpage: 

star.bnl.gov

Paper draft:

star.bnl.gov

Please kindly let us know if you have any comments or suggestion. We look forward to hearing from you soon. 

Thank you.

Best regards,

Ke for the PAs

On 17. Jul 2023, at 17:37, Hanna Paulina Zbroszczyk via Star-cf-l <star-cf-l AT lists.bnl.gov> wrote:

Dear Ke,

Thanks for posting materials regarding the paper proposal.

Most of my comments come after reading the Analysis Note.

1. Theory correlation function section does not include QS effects. 

And how do you treat it in your calculation?

It would help if, for a good understanding of all sources of correlations, you separate all contributions in the p-d and d-d cases as well. 

Prepare such a figure and add to the theory part regarding descriptions of all correlations. 

2. Figures 19, 20. Surprisingly, splitting is so minor in your results.

Did you apply with an anti-merging additional cut on \delta \phi* and \delta \eta?

3. Page 23, missing reference to the figure ??

4. Momentum smearing. How do you calculate C(q_smear) correlation function? If you calculate q_smear, did you put the weight for smeared or not smeared momentum difference?

5. In Figure 33, all panels have a typo: protonn instead of a proton.

There is almost no effect for smeared function, which is surprising compared to other measurements (e.g., pion-kaon at BES, see Pawel paper proposal).

6. Systematic uncertainties. What is the contribution to systematics for taking into account different fitting ranges? It should be mentioned in the paper proposal, all together with other variables.

7. I see you applied the Barlow test. Which variables did not pass and were excluded from systematics due to limited statistics?

8. Prepare a table with % for which element included in your systematic studies, separately for p-p and p-d (separate centrality bins).

9. Data and model comparison. Since you use the LL model for data and CRAB for the model, can you please prove the consistency of these two approaches for considered small sources (between 1.5 and 2 fm for d-d and 2.5 and 3.5 fm for p-d?)? Please plot the correlation functions and compare them point by point. 

It is unusual that you use CRAB to calculate the model function and then extract the parameters of the interaction from the LL model. It would be better if you use LL model with fixed parameters f0 and d0 that you got from the experiment to calculate theoretical correlation function from SMASH, and then, to extract the source size. 

If you use both parametrizations based on different assumptions, one should prove their consistency for few source sizes (especially for these relatively low, of the order of 2 fm or even smaller). 

10. Correct the description of Fig. 51, 52 and 54.

11. Fig. 52 should have experimental data and the SMASH model with and without the coalescence (to prove that the coalescence scenario better describes data).

This figure should also be updated in the manuscript draft. 

Having those clarified, I will comment on the manuscript. 

Thanks,

Hanna

Hanna Paulina Zbroszczyk

PhD DSc Eng, Professor WUT

E-mail: hanna.zbroszczyk AT pw.edu.pl

Tel: +48 22 234 5851 (office)

Address:

Warsaw University of Technology

Faculty of Physics

Nuclear Physics Division

Koszykowa 75

Office: 117b (via 115)

00-662 Warsaw, Poland

Wiadomość napisana przez K.Mi via Star-cf-l <star-cf-l AT lists.bnl.gov> w dniu 10.07.2023, o godz. 16:12:

Dear Conveners, 

The 'Light Nuclei Femtoscopy and Baryon Interactions in 3 GeV Au+Au Collisions at RHIC’ paper is ready for PWG review. 

Please find the related materials below including webpage, paper draft, analysis note and reply to PWGC preview.  

Paper Webpage:

star.bnl.gov

Paper draft:

star.bnl.gov

Analysis note:

star.bnl.gov

Reply to PWGC preview comments:

star.bnl.gov

We would appreciate it if you could review the documents and provide us with your valuable comments and suggestions. 

Thank you.

Best regards,

Ke for the PAs

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