Beam Energy Dependence of the Linear and Mode-Coupled Flow Harmonics Using the a Multi-Phase Transport Model
Round 1
Reviewer 1 Report
This manuscript investigates the energy dependence of the linear and mode-coupled flow harmonics from the AMPT model in AuAu collisions using the multi-particle azimuthal cumulant method. The results shown in this work indicate that the linear and mode-coupled contributions to v4 may have different energy dependence compared to the correlations between different order flow symmetry planes and the mode-coupled response coefficient. This information emphasizes that the systematic experimental measurements of higher order flow harmonics can be useful to constrain different theoretical models. I have some minor comments on the current version of the paper draft.
I suggest the author include the version number of the AMPT model used for this study in the method part.
In Fig.3, the author observes an energy dependence of the three-particle correlators and claims that they can constrain the interplay between the final and initial state interactions in the AMPT model. The author may need to further expand this part by discussing the underlying mechanism in AMPT which leads to this energy dependence and connecting this feature to the initial and final state effects in the AMPT model.
In the description of Fig.4, the centrality dependences of the linear v4 and the mode-coupled v4 are found to be different. It might be better to provide some discussions on why they have different centrality dependence.
Based on the results shown in Fig.5, the author concludes that initial-state effects dominate the correlations of event plane and the non-linear response coefficients. It might be helpful to clarify what kind of initial-state effects implemented in AMPT dictates the behavior. Also, it could be interesting to discuss a bit whether this feature is also observed in other model calculations like the hydrodynamic models.
Line 52, a space is needed between “crosssection“.
Line 55, sigma_pp is not unitless, it should be “1.5 mb”.
Line 63, “two-subevents” should be “two sub-events”, “\Delta\eta>0.7” should be “|\Delta\eta|>0.7”.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
General Comment:
This study presents the beam energy dependence of Non-linear flow modes (or Mode-coupled component) for 4 different energies.
The the non-linear flow component is being / had been investigated by several Experimental collaborations e.g. STAR collaboration in USA (ALICE Collaboration in CERN, Europe). The results presented is estimated using a phenomenological model and compared with experimental measurements at STAR Collaboration. Hence such a measurement provide an insight in the origin of the observed phenomena. The study is also helpful in the sense that it motivates theoreticians to tune their models to include more features which would make them more useful for further prediction of experimental observables.
However, I have some major suggestion regarding the method applied for the simulation study. The main comment is on the estimation of centrality in AMPT. The author has used impact parameter distribution to estimate the centrality class. However, in real experimental data, one used the charge particle multiplicity either in midrapidity (e.g. STAR) or in forward region (e.g. V0 in ALICE). Therefore, to make this comparison apple-to-apple, I would strongly suggest the author to redo the analysis of all observables with redefined centrality, where it has been estimated from the charge multiplicity distribution of AMPT in the mid-rapidity (suitable for STAR). The centrality should be estimated separately for each energy.
Another important suggestion I have is to include the STAR collaboration measurements that have been recently submitted to arxiv:2211.11637. For example Fig.1 from this STAR paper shows the c4,22 and c5,32 cumulants which have been also shown in this article (in Fig.3). Other simulation results (v4, rho4,22, Chi4,22) can also be directly compared to experimental results from arxiv:2211.11637. Although the author cites this STAR measurements in [82], there is no comparison figures for the observables I mentioned. Such comparison figures would give extreme importance to this phenomenological study, as we can see both qualitative and quantitative comparison with model and experimental data.
With these two major comments included, I would request one more round of review just to make sure the physics conclusions are proper (with new definition of centrality). After that this article should be ready for publication.
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Minor line-by-line comments. (The rest of the comments on results, I would provide once I see the revised version. ):
l21: are the value and angel => are the magnitude and the angle
l30: author mentions both \epsilon_2 and \epsilon_3 but the equation of v4,22 only contains \epsilon_2 .
l36: will design additional constraints => will provide additional constraints
equation 7: I would suggest the author to mention the actual values used for \alpha_s, and \mu in the text. Also please include the ampt version that has been used. This helps for anyone to reproduce the results presented here, for a cross check.
Line 63-65 Author mentions how he used two sub-event for particle selection. The two particle correlation need two particle from two different eta subs. However, how the 3rd and 4th particles are chosen for 3- and 4-particle correlators are not mentioned. if 3 particles are chosen from same eta for 4-particle correlation, then obviously the result will be biased by non-flow. One can use 4different eta ranges (with eta-gap = 0) to choose 4 particles, thereby reducing the non-flow effect. I would like the author to clarify the how 3 and 4 particles are used and from which eta range.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
This version looks good to me. Thanks for the great work.
Reviewer 2 Report
The updated manuscript is much improved. There are some editorial / grammatical mistakes which I leave it to the editors of the Journals to Fix. I have only few comments regarding the conclusions from the results. After including these, the draft should be published. ---------------------------------------------------------------------- Comments: with line-number corresponding to updated draft: L90 - 91: "The AMPT calculations overestimate the STAR experiment measurements at 200 GeV " ==> The AMPT calculations qualitatively reproduce the trend observed in data. However, AMPT overestimate C4,22 for centrality > 30% and C5,32 for mid central (10-50%) region. L98-99 : "These results are in agreement with the STAR experiment measurements at 200 GeV" ==> The AMPT results are in qualitative agreement with the experimental measurements from STAR in Au+Au collisions at \sqrt{s_NN} = 200 GeV". ( Also every where in the texts, "200 GeV" => "in Au+Au collisions at \sqrt{s_NN} = 200 GeV" ) L120-121: "My AMPT model calculations suggest that initial-state effects dominate the correlations of event plane angles and the non-linear response coefficients " ==> This is strong conclusion based on only qualitative reproduction of data from AMPT (Fig.3 and Fig.4). I would suggest to tone down a bit: "The AMPT model calculations suggest that initial-state effects might be the dominant factors behind the correlations of event plane angles and the non-linear response coefficients". ---------------------------------------------------------------------- With all these suggestions included. I sign off for the publication.Author Response
The updated manuscript is much improved. There are some editorial/grammatical mistakes which I leave it to the editors of the Journals to Fix. I have only few comments regarding the conclusions from the results. After including these, the draft should be published.
>>I thank the Referee for her/his detailed review of my manuscript. This critique has improved both the readability and substance of the manuscript. Below, I give responses to each of his/her concerns and point to modifications to the manuscript as appropriate.
Comments: with line-number corresponding to updated draft:
L90 - 91: "The AMPT calculations overestimate the STAR experiment measurements at 200 GeV ” ==> The AMPT calculations qualitatively reproduce the trend observed in data. However, AMPT overestimate C4,22 for centrality > 30% and C5,32 for mid central (10-50%) region.
>>I followed the Referee's advice and updated the text accordingly.
L98-99: "These results are in agreement with the STAR experiment measurements at 200 GeV" ==> The AMPT results are in qualitative agreement with the experimental measurements from STAR in Au+Au collisions at \sqrt{s_NN} = 200 GeV". (Also every where in the texts, "200 GeV" => "in Au+Au collisions at \sqrt{s_NN} = 200 GeV" )
>>I followed the Referee's advice and updated the text accordingly.
L120-121: "My AMPT model calculations suggest that initial-state effects dominate the correlations of event plane angles and the non-linear response coefficients " ==> This is strong conclusion based on only qualitative reproduction of data from AMPT (Fig.3 and Fig.4). I would suggest to tone down a bit: "The AMPT model calculations suggest that initial-state effects might be the dominant factors behind the correlations of event plane angles and the non-linear response coefficients."
>>I followed the Referee's advice and updated the text accordingly.
