STAR Correlations and Fluctuations PWG

[Xin Dong <xdong AT lbl.gov>]

Hi Jin,

Thank you for addressing my comments and answering my questions. I only have a couple of more suggestions to the newly added beta_q vs. q figure.

1) It will be better to make the plot in a linear scale and not apply many folds of scaling factors. You want to reveal the power law dependence, but currently it is hard to see any dependence. You may just add a shift to different energies or make the plot in multiple panels. 

2) If you prefer to leave the figure on Slide 5, the last statement on Slide 4 should be attached here.

3) Slide 5, It will be better to enlarge these figures a bit more so they are more readable, while you may move down the texts a bit and make them more concise, for example

     " Scaling exponent vs. collision energy:   non-monotonic behavior in central collisions / flat distribution for 30-40% centrality collisions.

       Scaling exponent vs. centrality:    decrease from mid-central to central collisions.

       Model studies / theory input to understand the baseline and the observed energy/centrality dependence."

Thank you and Best Regards

/xin

On Tue, Mar 29, 2022 at 8:29 PM JinWu <wj2016113394 AT mails.ccnu.edu.cn> wrote:

Dear Xin and Conveners,

Thank you very much for your nice suggestions and comments. I have implemented comments  in the updated version at link:https://drupal.star.bnl.gov/STAR/node/58816

 

And, kindly please find my answers to your comments/suggestions as below:

 

1) General comments:

     a) Slide 2-5, in the title, you have some numbers in the front which I assume you try to indicate the ordering. I see this is redundant since you have page numbers at the bottom and as it has no separation from the rest text, this may cause some confusion. e.g. Slide 3, it may read like 2*F_q etc.

    Answer: Done. I have modified the titles.

     b) you may save the foot region on each slide to give your space on each slide. The left and middle texts are not necessary, you may just leave the page numbers on the bottom right corner.

     Answer: Done.

     c) In all the figures on Slide 3,4,5, please label (pT, eta) region of this analysis.

      Answer: Done.

2) Slide 1

     a) Third sentence, "The scaling exponent is related to the critical component ..". I am not sure what you mean by "critical component" here? I find this part is not needed, since in the next sentence you mention the potential relation to the CP search. I would suggest dropping "is related to the critical component and".

     Answer: Done.

     b) Third line from bottom, my understanding is the analysis is for charged particle at |eta|<0.5. This should be also mentioned here.

      Answer: Done.

     c) The abstract ends with the observations, but doesn't contain any physics message (see my comment to the last slide).

     Answer: I add "The physics of observed non-monotonic behavior needs to be understood with more theoretical and model inputs".

3) Slide 2

     a) Right figure, need a title on what distribution this is (presumably particle density distribution within one single event (what event, real/model)). Need units for (X,Y)-axis titles.

    Answer: This figure is taken from Ref (PLB 801, 135186 (2020)) which shows the critical local density fluctuations from Critical Monte Carlo Model, not the case of data.  I add a caption and Ref at the bottom of figure.

     b) Second bullet, for completeness, need to define n_i.  And for M_D, is the current analysis done in 2D (px,py)? If so, you can simplify by removing the superscript D and explain how the 2D space is partitioned.

    Answer: n_{i} is defined. Yes, the current analysis is done in 2D (px,py)  and i  short illustrate this as the second bullet in the Analysis Techniques. To my understand, the superscript D is necessary for correct definition of scaled factorial moment.

     c) One technical question on the calculation for my own understanding, what if (n_i-q+1)<=0, so the contribution from this cell will be zero or do you truncate? In the case of M sufficiently large, all cells will have only 1 or 0 tracks, for q>=2, will F_q turn to zero? In the case of M=1, for mixed-event, shall I expect F_q to be 1?

     Answer: In the i-th cell, the calculation of n_{i}*(n_{i}-1)...(n_{i}-q+1), for example, when q=3, the term is  n_{i}*(n_{i}-1)*(n_{i}-2) and it is equal zero if n_{i}<3. So, yes, the contribution from this cell will be zero.  Also, that is right , F_q(M) turn to zero when M is infinite, and F_q(M) close to 1 when M=1.

     d) Analysis techniques:

            i) Hadrons? Did you do particle identification? Or is the analysis done with all charged particles? Then we need to be precise here.

            Answer: Yes, i do particle identification. In this analysis, protons, kaons, pions are analysed as identified charged particles. I completely revised this bullet.

            ii) Centrality:  presumably, these are "uncorrected" charged particle multiplicity.

             Answer: Yes, it's the charged particle multiplicity.

            iii) Can you elaborate how the mixed event is constructed? Shall we call "to remove backgrounds" or "to estimate statistical contribution" (one is interested in the dynamic contribution)?

             Answer: Yes, the word "estimate" is better.  Follow the intermittency analysis from the NA49 experiment (Eur. Phys. J. C 75, 587 (2015)), mixed events are constructed by randomly selecting particles from original events while reproducing the same multiplicity distributions. The correlations between pairs of particles which exist in the original event, are eliminated in the mixed event samples since each particle now is chosen from different events. By assuming that multiplicity for measured particles in each cell can be simply divided into background and critical contributions, the correlator of \Delta Fq (M) is supposed to contain only critical contributions. I don't elaborate the rules of mixed events due to limitation of 5 page slides. 

            iv) For interested particles, what is the pT region and how the space is partitioned, in (px,py) or (pT, phi)?

              Answer: In px and py space, 0.4 < pT < 2.0 (GeV/c) for protons, 0.2<pT< 1.6 (GeV/c) for kaons and pions. I illustrate this as the first bullet.

             v) The analysis is done within each centrality bin or each multiplicity bin and then averaged within the centrality? In either case, how the finite centrality bin width effect is considered in this analysis?

             Answer: The analysis is done within each Refmult2 centrality bin. We can not apply the CNWC to the intermittency analysis, because we need to calculate the Fq(M) to higher order and at large M which require enough statistic events, also the rule of mixed events method also require enough events. In the intermittency analysis, it's suggest the mixed events method to subtract the finite centrality bin width effect, kindly see the chapter 4.3 in the analysis note at link: https://drupal.star.bnl.gov/STAR/system/files/Analysis_note__Intermittency.pdf.

           

            vi) Efficiency correction, the observable is looking at the fluctuation with the local momentum bin. However, if two or more tracks have very close momenta, I am worried that they may be reconstructed as one merged track (clusters in TPC merge). I don't know how our efficiency correction takes this into account.

           Answer: We apply the cell-by-cell method to the efficiency correction on F_{q}(M),  based on the pt-dependent efficiency for protons, kaons and pions which is obtained from the TPC embedding efficiency and TOF macthing efficiency.  That's right, the track merging will weak the signal of intermittency. However,  how to recover the lose of signal based on the calculation of Fq_(M) is really challenge, we and intermittency group from NA61 experiment do not have a good solution yet.  We will trying to do this in the future. 

4) Slide 3

      a) Please also label the (pT, eta) region.

       Answer: Done.

      b) What is the reason for the X-axis starting from ~100? Why not start from 1?

       Answer:  At range of M^{2} from 1 to 100, the Fq(M) of data are almost overlapped with those of associated mixed events, which means the \Delta Fq(M) is about zero. Therefore, these point for small M is trivial. Moreover,  we only fit the \Delta Fq(M) at large M to extract the exponent \betaq, since the effect of power-law is associated with small momentum scales (PRC 81, 064907 (2010)).  In our analysis, only Fq(M) for M>30  are used.

      c) It seems all distributions seem to jump up a bit at 2nd, 5th, 8th data points for all energies? Is there any reason for this?

       Answer: This is because the influence of background effects and acceptance cuts. In the analysis from NA49 experiment (PRC 81, 064907 (2010)) and model (PLB 818, 136393(2021) , some points also jump and decrease a bit.

5) Slide 4

      a) in both top and bottom figures, Y-axises are missing the labels for scales.

        Answer: Done.

      b) bottom figure, data points in the first panel have uncertainties along the X-axis, but not in other panels? Any reason?

      Answer: Well, the first panel shows the result  of collision energy at 7.7 GeV which only have 3 Million events , uncertainties along the X-axis is the error of \Delta F_2(M) due to smaller statistic than other higher energies.   

      c) I would strongly recommend adding a figure showing beta_q vs. q which you use to extract the exponential quantity which is the key quantity nv.

       Answer: Done. I add the plot of \betaq Vs q in slide 5.

      d) top right formula, you introduced DeltaF_q ~ (M^2)^phi_q, but didn't discuss phi_q?

       Answer: This is because that \DeltaF_q  (q=2-6) do not obey a good power-law behavior with M^{2} for large M,  you can see that the relationship between \Delta F_q and M^{2} is not a straight line and the fitting by DeltaF_q ~ (M^2)^phi_q is bad. Therefore, we can not extract the phi_{q} and discuss it accordingly . However, higher order \Delta F_q(M)  (q=3-6) do obey a very good power-law behavior with \DeltaF_2(M), and can be fit well by \Delta F_q(M)~\Delta F_q(M)^{beta q}, and hence we can extract the \betaq.

      d) The two statements in the bottom.

              i) first bullet, first, not sure what you mean by "DeltaF_q(M)/M scaling function". Second "DeltaF_q(M)/M scaling behavior is observed but not strong." I don't quite follow what scaling behavior you mean here. The top figure shows dF_q vs. M^2, it increases slower than a linear, but not clear about the exact relation.

              Answer:  The power-law behavior of \Delta F_q ~ (M^2)^phi_q is referred as \Delta F_q(M)/M scaling,  and power-law behavior of \Delta F_q(M)~\Delta F_q(M)^{beta q} is referred as \Delta F_q(M)/ Delta F_2(M)  scaling.  I add the these equations in bullet.  In the top figures, \Delta F_q  rises with increasing M^2, but the relationship is not linear, and can not be fitted well by \Delta F_q ~ (M^2)^phi_q.

              ii) second bullet, as commented in (c), we need beta_q vs. q to illustrate this point.

               Answer: Ok, done, the plot is show in slide 5 (left figure).

6) Slide 5

       a) As I mentioned in the General Comment, please label (pT,eta) regions on each figure.

        Answer: Done.

       b) Right figure, I understand you want to scale up some energy data points so they can be separated, but the choice of these scaling factors seems too random. The point here is you want to illustrate the centrality dependence. I think you can make a six-panel figure for energies from 19.6 - 200 GeV (low energies don't matter here), and you don't need to apply a scaling factor for each panel.

       Answer: I remove the data point from low energies (7.7-14.5).  Well, these scaling factors are not chosen randomly,  and if chosen randomly, it can not separate data points. Also, I  think there not enough space for six-panel figures and there well be too much figures in this slides.  To my understand,  the most important result in this slides is the energy dependence of \nu, so, i need to left enough space for this plot. Therefore, i still scale up data points in the plot.     

       c) On the physics discussion, are there any model calculations one can compare to? Hijing, AMPT or UrQMD? If not available, I would still need to add a bullet point to comment on the to-do studies, something like "Model studies to understand the baseline for the extracted quantity nv etc.". On the analysis side, I think we need to perform the Model + GEANT studies to understand the impact of the detector effect on multiplicities in the local momentum bin as I commented in 3-d-v.

       Answer: Thank you for the nice suggestions. I add "Model studies to understand the baseline for the extracted quantity ν. The physics of observed non-monotonic behavior needs to be understood with more theoretical inputs." We have studied the intermittency from the UrQMD model. And it is shown the F_q(M) of data are overlap with those of mixed events,  the \Delta F_q(M) is around zero, therefore, we can not extract the \nu from the UrQMD model (see chapter 5 in the analysis note at https://drupal.star.bnl.gov/STAR/system/files/Analysis_note__Intermittency.pdf).  I do not  show the results from the UrQMD in this poster due to the limitation of slides.

                Now, we are trying to describe the non-monotonic energy dependence of \nu by the UrQMD+CMC(signal) model.  Also, the track merging effect for this analysis,  will be consider by the  Model + GEANT studies. 

Now

Tha Thanks,

No   Best regards,

Jin

------------------ Original ------------------

From:  "star-cf-l"<star-cf-l AT lists.bnl.gov>;

Date:  Mon, Mar 28, 2022 02:50 AM

To:  "webmaster AT star.bnl.gov"<webmaster AT star.bnl.gov>; "star-cf-l"<star-cf-l AT lists.bnl.gov>;

Subject:  Re: [Star-cf-l] STAR presentation by Jin Wu for Quark Matter 2022 submitted for review

 

Hi Jin,

I was asked by Rongrong and Tafafumi to review your nicely prepared QM poster draft. Please find my comments/suggestions below.

1) General comments:

     a) Slide 2-5, in the title, you have some numbers in the front which I assume you try to indicate the ordering. I see this is redundant since you have page numbers at the bottom and as it has no separation from the rest text, this may cause some confusion. e.g. Slide 3, it may read like 2*F_q etc.

     b) you may save the foot region on each slide to give your space on each slide. The left and middle texts are not necessary, you may just leave the page numbers on the bottom right corner.

     c) In all the figures on Slide 3,4,5, please label (pT, eta) region of this analysis.

2) Slide 1

     a) Third sentence, "The scaling exponent is related to the critical component ..". I am not sure what you mean by "critical component" here? I find this part is not needed, since in the next sentence you mention the potential relation to the CP search. I would suggest dropping "is related to the critical component and".

     b) Third line from bottom, my understanding is the analysis is for charged particle at |eta|<0.5. This should be also mentioned here.

     c) The abstract ends with the observations, but doesn't contain any physics message (see my comment to the last slide)

3) Slide 2

     a) Right figure, need a title on what distribution this is (presumably particle density distribution within one single event (what event, real/model)). Need units for (X,Y)-axis titles.

     b) Second bullet, for completeness, need to define n_i.  And for M_D, is the current analysis done in 2D (px,py)? If so, you can simplify by removing the superscript D and explain how the 2D space is partitioned.

     c) One technical question on the calculation for my own understanding, what if (n_i-q+1)<=0, so the contribution from this cell will be zero or do you truncate? In the case of M sufficiently large, all cells will have only 1 or 0 tracks, for q>=2, will F_q turn to zero? In the case of M=1, for mixed-event, shall I expect F_q to be 1?

     d) Analysis techniques:

            i) Hadrons? Did you do particle identification? Or is the analysis done with all charged particles? Then we need to be precise here.

            ii) Centrality:  presumably, these are "uncorrected" charged particle multiplicity.

            iii) Can you elaborate how the mixed event is constructed? Shall we call "to remove backgrounds" or "to estimate statistical contribution" (one is interested in the dynamic contribution)?

            iv) For interested particles, what is the pT region and how the space is partitioned, in (px,py) or (pT, phi)?

             v) The analysis is done within each centrality bin or each multiplicity bin and then averaged within the centrality? In either case, how the finite centrality bin width effect is considered in this analysis?

            vi) Efficiency correction, the observable is looking at the fluctuation with the local momentum bin. However, if two or more tracks have very close momenta, I am worried that they may be reconstructed as one merged track (clusters in TPC merge). I don't know how our efficiency correction takes this into account.

4) Slide 3

      a) Please also label the (pT, eta) region.

      b) What is the reason for the X-axis starting from ~100? Why not start from 1?

      c) It seems all distributions seem to jump up a bit at 2nd, 5th, 8th data points for all energies? Is there any reason for this?

5) Slide 4

      a) in both top and bottom figures, Y-axises are missing the labels for scales.

      b) bottom figure, data points in the first panel have uncertainties along the X-axis, but not in other panels? Any reason?

      c) I would strongly recommend adding a figure showing beta_q vs. q which you use to extract the exponential quantity which is the key quantity nv.

      d) top right formula, you introduced DeltaF_q ~ (M^2)^phi_q, but didn't discuss phi_q?

      d) The two statements in the bottom.

              i) first bullet, first, not sure what you mean by "DeltaF_q(M)/M scaling function". Second "DeltaF_q(M)/M scaling behavior is observed but not strong." I don't quite follow what scaling behavior you mean here. The top figure shows dF_q vs. M^2, it increases slower than a linear, but not clear about the exact relation.

              ii) second bullet, as commented in (c), we need beta_q vs. q to illustrate this point.

6) Slide 5

       a) As I mentioned in the General Comment, please label (pT,eta) regions on each figure.

       b) Right figure, I understand you want to scale up some energy data points so they can be separated, but the choice of these scaling factors seems too random. The point here is you want to illustrate the centrality dependence. I think you can make a six-panel figure for energies from 19.6 - 200 GeV (low energies don't matter here), and you don't need to apply a scaling factor for each panel.

       c) On the physics discussion, are there any model calculations one can compare to? Hijing, AMPT or UrQMD? If not available, I would still need to add a bullet point to comment on the to-do studies, something like "Model studies to understand the baseline for the extracted quantity nv etc.". On the analysis side, I think we need to perform the Model + GEANT studies to understand the impact of the detector effect on multiplicities in the local momentum bin as I commented in 3-d-v.

Thanks and Best Regards

/xin

On Wed, Mar 9, 2022 at 5:25 PM webmaster--- via Star-cf-l <star-cf-l AT lists.bnl.gov> wrote:

Dear star-cf-l AT lists.bnl.gov members,

Jin Wu (wj2016113394 AT mails.ccnu.edu.cn) has submitted a material for a 
review, please have a look:
https://drupal.star.bnl.gov/STAR/node/58816

---
If you have any problems with the review process, please contact 
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--

==================================================
Xin Dong
Nuclear Science Division, Lawrence Berkeley National Laboratory
MS70R0319, One Cyclotron Road
Berkeley, CA 94720, USA
Tel: +1-510-486-4121
Email: XDong AT lbl.gov
==================================================

--

==================================================
Xin Dong
Nuclear Science Division, Lawrence Berkeley National Laboratory
MS70R0319, One Cyclotron Road
Berkeley, CA 94720, USA
Tel: +1-510-486-4121
Email: XDong AT lbl.gov
==================================================