Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, the authors compute the transverse momentum distributions of muons from kaon and pion decays at forward rapidity for various centrality classes. This is done using a fast Monte Carlo simulation combined with the PYTHIA6 event generator to simulate the decays.

The primary aim of the study is to gain an understanding of hadron decay kinematics and possible medium effects in heavy-ion collisions. The authors estimate muon yields from pion and kaon decays by assuming fixed pion and kaon spectra, which are not derived from any underlying dynamical model. Instead, the momentum distributions of the parent hadrons are sampled based on experimental data and its extrapolation to forward rapidity.

However, the manuscript does not provide a discussion of how the results contribute to our understanding of hadronic interactions or decay kinematics. As such, the study lacks new scientific insights and does not present significant results that would advance the field. I therefore do not recommend this manuscript for publication in its current form.

In addition to above issue,
there are several unclear statements that should be addressed if the authors choose to revise the manuscript:

* Line 51: The term "enhancement" is vague. Please clarify what is being enhanced — is it the muon yield, decay rate, or something else?

* Line 98 and Equation (1): Do the statistical and systematic uncertainties refer to the experimental uncertainties reported by the ALICE Collaboration? Please clarify the source of these uncertainties.

* Equation (5): The rapidity extrapolation factor is derived from pp collisions using PYTHIA6, yet it is applied to Pb + Pb collisions. How do the authors justify this extrapolation? Given the potential influence of medium effects, the reliability of such a procedure should be discussed.

* Line 200: The term "consistency" is ambiguous. Consistency with what — experimental data, previous simulations, or theoretical expectations?

* Line 201: What exactly is meant by "enhancement by approximately a factor of two"? Is this referring to the muon yield compared to some baseline?

Author Response

Comments1: However, the manuscript does not provide a discussion of how the results contribute to our understanding of hadronic interactions or decay kinematics. As such, the study lacks new scientific insights and does not present significant results that would advance the field. I therefore do not recommend this manuscript for publication in its current form.

 

Response1: Thank you for your questions and suggestions. We have developed a procedure to determine muon yields from measured charged kaon and pion yields. This is aimed at estimating the muon background for measuring open heavy-flavor production through the semi-leptonic decays of charm and beauty hadrons.

Our approach relies on published ALICE data regarding charged π± and K± yields in Pb-Pb collisions at √sNN = 2.76 TeV around mid-rapidity (|y| < 0.8). The measured spectra are compared with fast Monte Carlo simulation results. These simulations utilize the PYTHIA 6 event generator to produce uniform pion and kaon distributions in transverse momentum pT (3 – 20 GeV/c) and rapidity y.

To enhance statistical precision, the measured pion and kaon spectra are rebinned and then the simulated spectra are reweighted to fit them. Subsequently, the kinematics of decay muons from pions and kaons is simulated using the PYTHIA 6.4 code.

The simulation results provide a reasonable estimate of muon yields and distributions from charged pion and kaon decays. This will assist in separating muons originating from the semi-leptonic decays of charm and beauty hadrons in the same collision system. Additionally, studying decay muons from K and π can offer complementary insights into hadron production and propagation within the hot medium. The scaling behavior of muon yields from these decays can also yield valuable information concerning hadronic interactions and decay kinematics.

 

Comments2: * Line 51: The term "enhancement" is vague. Please clarify what is being enhanced — is it the muon yield, decay rate, or something else?

Response2: Thank you for your questions and suggestions. In the updated draft, we have included specific details：they enhancement the systematic uncertainty of the kaon  yields by approximately a factor of two in the pT region where it is later observed that the peaks of the kaon-to-pion ratios are locate [13].

 

Comments3: * Line 98 and Equation (1): Do the statistical and systematic uncertainties refer to the experimental uncertainties reported by the ALICE Collaboration? Please clarify the source of these uncertainties.

Response3: Thank you for your questions and suggestions. Yes , The statistical and systematic uncertainties refer to the experimental uncertainties reported by the ALICE Collaboration. In the updated draft, we have included specific details: The statistical and systematic uncertainties refer to the experimental uncertainties reported by the ALICE Collaboration. The total uncertainty for each pT-y bin is calculated by combining these statistical and systematic uncertainties in quadrature, as shown in Equation (1). This total uncertainty defines the upper and lower bounds of the input spectra, which are then propagated to the final muon yields through the simulation process. （please see attached file）

\left[\frac{\mathrm{d}^{2}N^{\pi^{\pm}(\kappa^{\pm})}}{\mathrm{d}y}\right]_{\mathrm{A}\mathrm{A}}=\langle N_{\mathrm{call}}\rangle\times\left[R_{\mathrm{A}\mathrm{A}}^{\pi^{\pm}(\kappa^{\pm})}\right]\times\left[F_{\mathrm{extrap}}^{\pi^{\pm}(\kappa^{\pm})}(y)\right]_{\mathrm{pp}}\times\left[\frac{\mathrm{d}^{2}N^{\pi^{\pm}(\kappa^{\pm})}}{\mathrm{d}y}\right]_{\mathrm{pp}}^{\mathrm{mbd-y}}

\left[\frac{\mathrm{d}^{2}N^{\mathrm{m}^{\pm}(\mathrm{k}^{\pm})}}{\mathrm{d}y}\right]_{\mathrm{A}A}=\left[F_{\mathrm{extrep}}^{\mathrm{m}^{\pm}(\mathrm{k}^{\pm})}(y)\right]_{\mathrm{PP}}\times\left[\frac{\mathrm{d}^{2}N^{\mathrm{m}^{\pm}(\mathrm{k}^{\pm})}}{\mathrm{d}y}\right]_{\mathrm{AA}}^{\mathrm{m}\mathrm{d}\mathrm{d}-\mathrm{y}}

 

Comments4: * Equation (5): The rapidity extrapolation factor is derived from pp collisions using PYTHIA6, yet it is applied to Pb + Pb collisions. How do the authors justify this extrapolation? Given the potential influence of medium effects, the reliability of such a procedure should be discussed.

Response4: Thank you for your questions and suggestions.  By using the following formula, we can obtain the result： The rapidity extrapolation factor is derived from pp collisions using model, yet it is applied to Pb + Pb collisions.

 

 

 

 

Comments5: * Line 200: The term "consistency" is ambiguous. Consistency with what — experimental data, previous simulations, or theoretical expectations?

Response5: Thank you for your questions and suggestions. In the updated draft, we have included specific details: The transverse momentum (pT) distributions of muons originating from charged pion and kaon decays exhibit a high degree of consistency, remaining within uncertainties across all centrality classes.

 

Comments6 * Line 201: What exactly is meant by "enhancement by approximately a factor of two"? Is this referring to the muon yield compared to some baseline?

Response6: Thank you for your questions and suggestions. In the updated draft, we have included specific details: The ratio of muons from kaon decay to those from pion decay, relative to the kaon-pion ratio [13] (approximately 0.5), shows an enhancement by about a factor of two.

 

 

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. The fast simulation method to study kaon and pion yelds for the heavy ion collision was developped for CMS: M Bedjidian and O Kodolova, “Quarkonia measurements in heavy-ion collisions in CMS”, 2007 J. Phys. G: Nucl. Part. Phys. 34 N 143. For ALICE it should have some difference because the fast simulation depends on the concrete detector and LHC is already running, thus, data driven approach is available..
   
2.  It is not clear why pions and kaons spectra are extrapolated using simulation to the forward region. One has to include the description of ALICE detector. For me it means that tracker cover one pseudorapidity range but muon detector covers another pseudorapidity range. This fast simulation method is developed for ALICE detector and it should be clear why it is done in that way.
3. Section 3.3. Upper Limit of pT for Charged Pion and Kaon Decay to Muons is unclear.
4. Line 188. Why an upper limit of muon pT = 10 GeV/c is applied to the generated muons?  It ia not described clearly in section 3.3 which is refered. Most probably it is connected with some peculiarity of ALICE muon arms. Thus, again I see the lack of explanation here.
5. Lines 201-202 " In particular, anenhancement by approximately a factor of two is observed in the pion and kaon yields within the pT range of 3-20 GeV/c, consistent with previous measurements [13]." Enhancement should be with respect of some other values. I do not see any comparions in Figure 4. Figure 4 needs more explanations.

Author Response

Comments1:The fast simulation method to study kaon and pion yelds for the heavy ion collision was developped for CMS: M Bedjidian and O Kodolova, “Quarkonia measurements in heavy-ion collisions in CMS”, 2007 J. Phys. G: Nucl. Part. Phys. 34 N 143. For ALICE it should have some difference because the fast simulation depends on the concrete detector and LHC is already running, thus, data driven approach is available..

 

Response1: yes, the fast simulation depends on the concrete detector and LHC is already running, thus, data driven approach is available.

 

 

Comments2: It is not clear why pions and kaons spectra are extrapolated using simulation to the forward region. One has to include the description of ALICE detector. For me it means that tracker cover one pseudorapidity range but muon detector covers another pseudorapidity range. This fast simulation method is developed for ALICE detector and it should be clear why it is done in that way.

 

Response2: Yes, In the updated article draft, we have added the reference to the ALICE muon detector's rapidity range of [-4, -2.5], as indicated in the "Technical Design Report for the Muon Forward Tracker" by the ALICE Collaboration (CERN-LHCC-2015-001, 2015)

 

Comments3:Section 3.3. Upper Limit of pT for Charged Pion and Kaon Decay to Muons is unclear.

Line 188. Why an upper limit of muon pT = 10 GeV/c is applied to the generated muons?  It ia not described clearly in section 3.3 which is refered. Most probably it is connected with some peculiarity of ALICE muon arms. Thus, again I see the lack of explanation here.

 

Response3: In the updated draft, we have included specific details: In Section 3.3, the upper limit of muon pT = 10 GeV/c is applied to the generated muons primarily because the measured pion and kaon spectra in the ALICE central barrel are limited to pT = 20 GeV/c. The control plots in Figure 3 show that the difference between the number of muons from pion and kaon decays with pT < 10 GeV/c and those from pion and kaon decays with pT < pmax T saturates at pmax T = 20 GeV/c. This implies that pions and kaons with pT > 20 GeV/c contribute negligibly to muons with pT < 10 GeV/c. Therefore, the upper limit of muon pT = 10 GeV/c is set to ignore the contribution of pions and kaons with pT > 20 GeV/c to muons in this pT range.

 

 

Comments4:Lines 201-202 " In particular, anenhancement by approximately a factor of two is observed in the pion and kaon yields within the pT range of 3-20 GeV/c, consistent with previous measurements [13]." Enhancement should be with respect of some other values. I do not see any comparions in Figure 4. Figure 4 needs more explanations.

 

Response4: Thank you for your questions and suggestions. In the updated draft, we have included specific details: the ratio of muons from kaon decay to those from pion decay, relative to the kaon-pion ratio [13] (approximately 0.5), shows an enhancement by about a factor of two.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript treats a very interesting study of muon decay challes for charged pions and kains. It is scientifically important for the HIC Community engaged in the study QGP and nuclear modification factors. The work is based only on simulations with a Montecarlo code, using a technique to increase the speeding the simulations. It is presented as a novel method, even if this definition goes too far. These techniques are indeed frequently used in Montecarlo simulations to try to take detector efficiency into account.

However, the manuscript is very well written and scientifically sound. I think that it can be published.

I would just recommend the authors to increase the size of the labels inside Fig. 4. The previous figures are much more readable. It should be an easy fix. 

 

 

Author Response

Comments1: I would just recommend the authors to increase the size of the labels inside Fig. 4. The previous figures are much more readable. It should be an easy fix.

 

 

Response1: Thank you very much for your positive comments and helpful suggestion.

We appreciate your feedback regarding Fig. 4. Following your suggestion, in the updated article draft, we have increased the size of the labels to improve readability, ensuring consistency with the previous figures.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

please clarify your statement, that muons probe the hot medium, although they are produced far ouside the reaction volume

Comments for author File: Comments.pdf

Author Response

Comments1: please clarify your statement, that muons probe the hot medium, although they are produced far ouside the reaction volume.

 

Response1: Thank you for your insightful comment. We agree that, the πand K decay muons themselves do not directly probe the hot medium.

To clarify our point, we revise the statement in the Summary of our manuscript as follows:

“While muons from charged pion and kaon decays are produced outside the hot medium, their yields and momentum distributions can indirectly reflect the parent hadrons’ production characteristics, which be influenced by the medium.”

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Before publication, I recommend that the authors revise the following points:

Regarding the Response4: I suggest that the author include the formula mentioned in the response in the manuscript before Eq.(5), as it is helpful to clarify  how the rapidity dependence
in AA collisions is predicted.

The function F_{fit} in Eq.(6) account only for account rapidity dependence. How do you
incorporate the pT dependence?

It seems that R_AA is assumed to be independent of rapidity. It is well known that R_AA strongly depends on the rapidity range, because kinematics is very different: collisions occur between high x-parton and very small-x parton. Thus, one expects strong shadowing effects. See, e.g. R_dA for d+Au collisions from  BRAHMS collaboration, (Phys. Rev. Lett. 93, 242303 (2004)).
The authors should discuss the systematic uncertainties associated with the rapidity
dependence of the R_AA.

p51 they enhancement -> they enhance

 

Author Response

Comments1: Regarding the Response4: I suggest that the author include the formula mentioned in the response in the manuscript before Eq.(5), as it is helpful to clarify  how the rapidity dependence in AA collisions is predicted.

Response1: Thank you for your questions and suggestions. in the revised manuscript, line145，We add: If we previously assumed that $R_{\mathrm{AA}}$ is independent of rapidity，the differential yield of these particles as a function of transverse momentum ($p_{\rm T}$) and rapidity ($y$) is expressed as follows (Eqs. (5) and (6))

\begin{equation} \label{eq:rapidity_extrap_1} \left[ \frac{\mathrm{d}^2 N^{\pi^\pm (\kappa^\pm)}}{\mathrm{d}p_T \mathrm{d}y} \right]_{\mathrm{AA}} = \langle N_{\mathrm{coll}} \rangle \cdot \left[ R_{\mathrm{AA}}^{\pi^\pm (\kappa^\pm)} \right] \cdot \left[ F_{\mathrm{extrap}}^{\pi^\pm (\kappa^\pm)}(p_T, y) \right]_{\mathrm{pp}} \cdot \left[ \frac{\mathrm{d}^2 N^{\pi^\pm (\kappa^\pm)}}{\mathrm{d}p_T \mathrm{d}y} \right]^{\mathrm{mid-}y}_{\mathrm{pp}}, \end{equation} \begin{equation} \label{eq:rapidity_extrap_2} \left[ \frac{\mathrm{d}^2 N^{\pi^\pm (\kappa^\pm)}}{\mathrm{d}p_T \mathrm{d}y} \right]_{\mathrm{AA}} = \left[ F_{\mathrm{extrap}}^{\pi^\pm (\kappa^\pm)}(p_T, y) \right]_{\mathrm{pp}} \cdot \left[ \frac{\mathrm{d}^2 N^{\pi^\pm (\kappa^\pm)}}{\mathrm{d}p_T \mathrm{d}y} \right]^{\mathrm{mid-}y}_{\mathrm{AA}}, \end{equation}

 

 

Comments2: The function F_{fit} in Eq.(6) account only for account rapidity dependence. How do you incorporate the pT dependence?

Response2: The pT- and y-dependence is incorporated through a reweighting method applied during the fast simulation procedure. Specifically, in Section 2.1, step 2 of the paper, the initially generated pions and kaons (which are sampled uniformly in pT and rapidity-y) are reweighted to match the experimentally measured pT- and y-dependent shape from MC simulation ( PYTHIA 6). So, the pT dependence is directly input via data-driven reweighting to real experimental pT spectra.

 

Comments3: It seems that R_AA is assumed to be independent of rapidity. It is well known that R_AA strongly depends on the rapidity range, because kinematics is very different: collisions occur between high x-parton and very small-x parton. Thus, one expects strong shadowing effects. See, e.g. R_dA for d+Au collisions from  BRAHMS collaboration, (Phys. Rev. Lett. 93, 242303 (2004)). The authors should discuss the systematic uncertainties associated with the rapidity dependence of the R_AA.

Response3: Thank you for your insightful questions and suggestions, which have been instrumental in enhancing the research presented in this paper. In Eqs. (5) and (6), we previously assumed that \( R_{\mathrm{AA}} \) is independent of rapidity. However, it is well recognized in the field that \( R_{\mathrm{AA}} \) exhibits a strong dependence on the rapidity range. To address this, in the revised manuscript, we have explicitly acknowledged this assumption and provided a detailed discussion on the potential impact of the rapidity dependence of \( R_{\mathrm{AA}} \).

In addition to considering the uncertainties in the mid-rapidity charged pion and kaon spectra, we have now incorporated the systematic uncertainties associated with the rapidity dependence of \( R_{\mathrm{AA}} \) for charged pions and kaons. Drawing on the findings from the BRAHMS Collaboration (Phys. Rev. Lett. 93, 242303 (2004)) and the ATLAS Collaboration (arXiv:1107.0460) (we add these reference in our revised manuscript ), we have estimated an additional systematic uncertainty of 30% for charged pion and kaon spectra to account this rapidity dependence of \( R_{\mathrm{AA}} \)  effect.

Based on these comprehensive considerations of both the mid-rapidity charged pion and kaon spectra uncertainties and the rapidity-dependent \( R_{\mathrm{AA}} \) uncertainties, we have recalculated the \( p_T \)-distributions of muons originating from charged pion (black) and kaon (blue) decays in the rapidity range \( 2.5 < y < 4.0 \). The revised results are presented in Fig. 4 of the updated manuscript, reflecting these enhanced analyses.

The revised manuscript now includes detailed discussions on these methodological improvements and their implications for our findings. (line 105 - line 112)

 

Comments4: p51 they enhancement -> they enhance

Response4: Thank you for your questions and suggestions. In the updated draft, we have taken action to improve the content.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

It starts to be better however it has to be checked by native english speaker.

I do not understand the sentence:

"Furthermore, ALICE has reported that in different centrality intervals, they enhancement the systematic uncertainty of the kaon yields by approximately a factor of two in the pT region where it is later observed that the peaks of the kaon-to-pion ratios are locate [13]."

The sentence is not understandable. ALICE do see the increase of K/pi ratio from 0.2 to 0.6 with increase of particle momentum up to 3 GeV/c and then the ratio goes to plateau.

 

Comments on the Quality of English Language

It starts to be better however it has to be checked by native english speaker.

Some sentences are not understandable.

Author Response

Comments1: "Furthermore, ALICE has reported that in different centrality intervals, they enhancement the systematic uncertainty of the kaon yields by approximately a factor of two in the pT region where it is later observed that the peaks of the kaon-to-pion ratios are locate [13]."

 

The sentence is not understandable. ALICE do see the increase of K/pi ratio from 0.2 to 0.6 with increase of particle momentum up to 3 GeV/c and then the ratio goes to plateau.

 

Response1: Thank you for your insightful questions and valuable suggestions. Our study on decay muons from K/pi mainly focuses on the momentum range above 3 GeV/c. In the revised manuscript, we have incorporated the following statement to provide a more comprehensive context: "ALICE has reported that the K/pi ratio exhibits an increasing trend from approximately 0.2 to 0.6 as the particle momentum rises to 3 GeV/c, beyond which the ratio approaches a plateau." Line53-Line56.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all of my comments.
I recommend the publication of this manuscript in the Journal of Particles.