The answers to each comments are shown bellow. The color code is the following:
Comments  Use standard macros p_\mathrm{T} > \pt 

Answer  Implemented 
Comments  Please keeo in mind >for the next time< that the CMS convention is to use a lower case "m" for a mass \newcommand {\MeanMass} {\ensuremath{\langle M_{\mu\mu} \rangle}\xspace} M_{\mu\mu} 

Answer  We changed the capital "M" to lower case "m" in both text and figure legends this time. 
Comments  6 m > 6\unit{m} 

Answer  Implemented 
Comments  3.8 T > 3.8\unit{T} 

Answer  Implemented 
Comments  sub detectors > subdetectors 

Answer  Implemented 
Comments  lead tungstate > leadtungstate 

Answer  Implemented 
Comments  20 cm > 20\unit{cm} 

Answer  Implemented 
Comments  Use \rd for the derivative "d" symbol, see step 30 of https://twiki.cern.ch/twiki/bin/view/CMS/Internal/PaperSubmissionFormat dN_{\mathrm{s}}/d\alpha 

Answer  Implemented (also in appendix) 
Comments  22 fm > 22\unit{fm} 

Answer  Implemented 
Comments  _{11.2}\syst$~b > _{11.2}\syst\unit{b}$ 

Answer  Implemented 
Comments  Ref. [16]: eliminate "no. 6" 

Answer  Implemented 
Comments  Ref. [20] eliminate "no. 23" 

Answer  Implemented 
Following comments are based on paper draft v15 (in CADI).
The v16 (CADI version for requesting submission) draft with PRL format can be found in HIN19014paperv16prl.
Diff file between v15 and v16 can be found in HIN19014v15v16diff.
Diff file between v13 (1st FR) and v16 can be found in HIN19014v13v16diff.
The pre v16 draft can be found in HIN19014paperprev16.
Comments  Appendix: For the measured neutron multiplicity class with asymmetric neutron numbers, the dimuon rapidity is divided into two hemispheres, the same and the oppositerapidity hemisphere with larger neutron multiplicities > For the measured neutron multiplicity class with asymmetric neutron numbers, the dimuon rapidity is divided into two hemispheres using the plane defined by $y = 0$. The region containing the larger (smaller) forward neutron multiplicity is denoted as the same (opposite) side hemisphere. 

Answer  Implemented 
Comments  Appendix Figure A. 2 Caption: drop "within the central muon acceptance" 

Answer  Implemented 
Comments  Appendix Figure A. 2 Caption: The solid red (open blue) symbols correspond to events where the dimuon rapidity is in the same (opposite) hemisphere with larger neutron multiplicity > The solid red (open blue) symbols correspond to events where the dimuon rapidity is in the same (opposite) side hemisphere. 

Answer  Implemented 
Comments  Abstract: demonstration that the transverse momenta of colliding photons emitted from relativistic heavy ions have an impact parameter dependence > demonstration that the average transverse momentum of photons emitted from relativistic heavy ions has an impact parameter dependence 

Answer  Implemented 
Comments  L93: using the events containing the samesign muons. > using events containing samesign muons. 

Answer  Implemented 
Comments  LL125126: central muon acceptance > kinematic range 

Answer  Implemented 
Comments  Fig. 1 caption: within the CMS central muon acceptance for 8 < M_mumu < 60 GeV > for [repeat list from line 134] and 8 < M_mumu < 60 GeV 

Answer  Implemented 
Comments  Fig. 1 caption: The dotdotdashed ... Eq. 1. > The dotdotdashed and dotted lines indicate the core and tail contributions, respectively, found using a fit to Eq. 1. 

Answer  Implemented 
Comments  L162: as estimated by > estimated by 

Answer  Implemented 
Comments  L173: Drop "within the CMS central muon acceptance" since by now you've repeated this kinematic range several times. 

Answer  Implemented 
Comments  LL219221: should establish a baseline where these initial broadening effects are properly taken into account based on the new data constraints presented in this Letter. > should incorporate a baseline where the initial broadening effects presented in this Letter are properly taken into account. 

Answer  Implemented 
Following comments are based on paper draft v14. Paper draft v15 (in CADI) is the updated one with implementing all the comments received during the second FR meeting.
The v15 draft with PRL format can be found in HIN19014paperv15prl.
Diff file between v13 (1st FR) and v15 can be found in HIN19014v13v15diff.
Diff file between v14 (2nd FR) and v15 can be found in HIN19014v14v15diff.
Comments  L5: Twophoton collisions > Photonphoton interactions 

Answer  Implemented 
Comments  L10: is on the scale of > is small, on the scale of 

Answer  Implemented 
Comments  L11: The lepton pairs > Therefore, the lepton pairs 

Answer  Implemented 
Comments  L14: drop "also" 

Answer  Implemented 
Comments  L16: Add "in hadronic collisions" after "is observed" 

Answer  Implemented 
Comments  L16: Add ref[25, 26] after UPCs 

Answer  Implemented 
Comments  L19: Remove "," after "Coulomb rescattering" 

Answer  Implemented 
Comments  LL3232: These neutrons > These forward neutrons 

Answer  Implemented 
Comments  L42: Azimuthal correlations of muon pairs measured by the acoplanarity > 

Answer  Implemented 
Comments  LL4344: in the very forward region > in the forward pseudorapidity range $\abs{\eta} > 8.3$ 

Answer  Implemented 
Comments  L44: represents > represent 

Answer  Implemented 
Comments  L46: colliding > interacting 

Answer  Implemented 
Comments  LL4849: presented to probe > presented as a probe of 

Answer  Implemented 
Comments  L54: remove "pseudorapidity" 

Answer  Implemented 
Comments  L93: estimated by combining the samesign muons in the same event. > estimated using the events containing the samesign muons. 

Answer  Implemented 
Comments  L185: add Ref. [31] after "the initial photon \pt" 

Answer  Implemented 
Comments  LL212213: quantum electrodynamics calculation that includes an impact parameter dependent photon \pt flux > quantum electrodynamics calculation, demonstrating the importance of an impact parameter dependent photon \pt 

Answer  Implemented 
Comments  L216: remove "," after "collisions" 

Answer  Implemented 
Comments  L219: remove "model" after "baseline" 

Answer  Implemented 
Following comments are based on paper draft v13. Paper draft v14 (in CADI) is the updated one with implementing comments received during the first FR meeting.
The v14 draft can be found in HIN19014paperv14.
Diff file can be found in HIN19014diffv13prev14.
Comments  Repherase the first sentence to, The first measurement of the dependence of $\gamma\gamma \to \mu^{+}\mu^{}$ production on the multiplicity of neutrons emitted very close to the beam direction in ultraperipheral heavy ion collisions is reported. Data for leadlead interactions at $\sqrtsNN = 5.02\TeV$, with an integrated luminosity of approximately 1.5\nbinv, were collected using the CMS detector at the LHC. The azimuthal correlations between the two muons in the invariant mass region $8 < M_{\mu\mu} < 60\GeV$ are extracted for events including zero, one, or at least two neutrons detected in the forward pseudorapidity range $\abs{\eta} > 8.3$. 

Answer  Implemented 
Comments  a larger number of neutrons from each nucleus > a larger number of emitted neutrons from each nucleus 

Answer  Implemented 
Comments  the transverse momentum of photons emitted from relativistic ions > the transverse momenta of colliding photons emitted from relativistic heavy ions 

Answer  Implemented 
Comments  lepton pairs resulting from the production of a quarkgluon plasma in hadronic heavy ion collisions > lepton pairs caused by traversing a quarkgluon plasma produced in hadronic heavy ion collisions 

Answer  Implemented 
Comments  L3: ions accelerated at colliders interact > ions accelerated at colliders can interact 

Answer  Implemented 
Comments  L8: allow a direct measurement of the gluon distribution > probe the gluon distribution 

Answer  Implemented 
Comments  L10: L10: quasireal [no dash] 

Answer  Implemented 
Comments  L124: (and other places) CMS acceptance > central muon acceptance 

Answer  Implemented 
Comments  Fig. 1 uses log(x)log(y) style 

Answer  Implemented 
Comments  L163: less than 5.1% > at most 5.1% 

Answer  Implemented 
Comments  L173: at a value of 1.348e−3 > at a value of about 1.35e3 

Answer  Implemented 
Comments  Fig. 2: Legend LO QED > bdep. $\gamma$ $p_{T}$ flux 

Answer  Implemented 
Comments  L175: about 9% lower than > about 10% lower than 

Answer  Implemented 
Comments  L71 73: a）add Vz range; b) a PbPb collisions at that vertex location 

Answer  Now, I break this sentence into two sentences: a) Events are required to have a primary interaction vertex consisting of at least two reconstructed tracks, and the cluster shapes in the pixel detector must be compatible with those expected from particles produced by a PbPb collision > Events are required to have a primary interaction vertex, formed by two or more tracks, within 20 cm from the CMS detector center along the beam axis. The cluster shapes in the pixel detector must be compatible with those expected from particles produced by a PbPb collision [36]. b) We checked the source code, the vertex is not used for the cluster compatibility filter, therefore, we keep as it is.

Comments  Fig. 1: make dotted line more prominent 

Answer  Solved this issue by using log(x)log(y) style for this figure 
Comments  L160: estimated from data. > estimated by fitting the invariant mass distribution. 

Answer  Implemented 
Comments  Fig. 1.: Add "given by Eq. (1)" after the tail contribution. 

Answer  Implemented 
Comments  176: A constant dependence of ⟨alpha^core⟩ on the neutron multiplicity > A fit to the dependence of $\MeanAlphaCore$ on the neutron multiplicity with a constant value 

Answer  Implemented 
Comments  187189, explicitly spellout the model has no uncertainty estimation 

Answer  higher than the model calculation by about 5% > "higher than the model calculation (plotted without uncertainties) by about 5%" 
Comments  Line 19 Current text Proposed text 

Answer  According to the message exchange among Michale, George, David, and Wei, the related text is changed to, Therefore, finalstate EM modifications of lepton pairs inside a QGP medium (e.g., Coulomb rescattering or deflection by magnetic fields trapped in the QGP) have been proposed as possible interpretations of the broadening effect [25, 26, 29]. The initial \pt of the lepton pairs depends on the overlap integral of the photon fluxes produced by the two nuclei, and as a result the average pair \pt ($\MeanPt$) could depend on the $b$ between the two colliding ions. Although models of the flux of photons integrated over a given $b$ range have large uncertainties [8, 30, 31], a QED calculation [31] predicts larger $\MeanPt$ for smaller $b$ values. Such a larger $\MeanPt$ in the initial state would broaden the pair angular correlation, which could explain the effects observed in more central hadronic collisions. 
Following comments are based on paper draft v12. Paper v13 is the updated one with implementing comments. Diff file can be found by HIN19014diffv12v13.
Comments  A bit long but the only idea I have to shorten it is to drop "Observation of" and (maybe) the cm energy at the end. It's also loaded with jargon but I couldn't think of any easy solution to that problem. 

Answer  We prefer to keep current title but open to hear your suggestions during FR 
Comments  General: "forward" is jargon that needs to be defined. 

Answer  It is not straightforward to define it use rapidity number here, because the emitted neutrons almost retain the beam rapidity 
Comments  First sentence is too long. I suggest putting CMS, the luminosity, and the cm energy in a separate sentence and expand "The first ... leadlead collisions" to define "forward" and mention angular correlations. 

Answer  We would like to discuss it during FR 
Comments  L67: I suggest changing "strong" to "narrow", and then you need to say "expected from calculations using leadingorder photonphoton scattering" or something similar. 

Answer  We dropped the "strong" but prefer not to add the model related thing. Need to discuss during FR 
Comments  L9: I assume that the two nuclei never touch in these collisions, so the connections of more neutrons and smaller impact parameter is not so obvious. Is it just that larger energy transfers (leading to more neutrons emitted) are more likely if the two nuclei pass closer to each other? 

Answer  Bascially yes. The number of exchanged soft photons between two nuclei and the photon energy are on average larger when the two nulcei are closer. The the nucleus (nuclei) is (are) likely to be exicited into higher excited states to emit more neutrons. We briefly talked about this stuff in paragraph 3 and added some references there. 
Comments  L911: I don't really understand this sentence and it would take a lot more words to make it clearer. I suggest dropping it entirely since the next sentence makes the point equally well and more concisely. 

Answer  Photon transverse momentum is related to the lepton pair acoplanarity, and photon energy is related to the lepton pair mass. We would like to keep it but open to hear the suggestion during FR 
Comments  L12: constraints to > constraints on 

Answer  Implemented 
Comments  8: The photoninduced > Photoninduced 

Answer  We removed this sentence 
Comments  11: What does "quasireal" mean? 

Answer  The equivalent photon is virtual photon but the virtuality is tiny Q2 < (1/R)^2 
Comments  15: azimuth > azimuthal 

Answer  Implemented 
Comments  18: I think you need to say something like "more central" so as not to imply that every hadronic collisions produces a QGP. Alternatively, you could change "is formed" to "can be formed". 

Answer  Implemented 
Comments  24: "pT hardening" is jargon. Why not just say "... explained by a higher average pT for initial ..."? 

Answer  Implemented 
Comments  24: photons, as the b decreases toward central hadronic collisions. > photons in the more central hadronic collisions. 

Answer  Implemented 
Comments  2526: Theoretical modelings of ... range still have large uncertainties [8, 24, 25]. > However, theoretical models of ... range have large uncertainties [8, 24, 25]. 

Answer  Implemented 
Comments  29: photoninduced > photonphoton 

Answer  Implemented 
Comments  35: Define "forward". 

Answer  Please see our reply to your previous comment 
Comments  38: "production" or "angular correlations"? 

Answer  "production" is better becasue we also have mass measurement 
Comments  39 (sqrt{s_NN}) of 5.02 > sqrt{s_NN}=5.02 

Answer  Implemented 
Comments  4041: sample, when ... (ZDC), corresponds > sample that includes information about forward neutrons corresponds [ZDC is described later] 

Answer  Implemented 
Comments  45: larger \alpha of > larger average \alpha for 

Answer  Implemented 
Comments  46: of colliding > of the colliding 

Answer  Implemented 
Comments  61: Having removed the definition of ZDC earlier, it needs to be added here. 

Answer  Implemented 
Comments  66: selected by > selected online using 

Answer  Implemented 
Comments  7174: Is there no restriction on the primary vertex location? 

Answer  No, but the Vz is within 20 cm 
Comments  72: vertex, consisting > vertex consisting 

Answer  Implemented 
Comments  74: PbPb collision [30]. > PbPb collision at that vertex location [30]. 

Answer  We prefer to keep as it is 
Comments  79: Drop "with different thresholds". 

Answer  Implemented 
Comments  80 and 190: Are we allowed to refer to supplementary material in this way? I don't remember ever seeing something like this that didn't refer to an appendix. 

Answer  Change "supplementary material" to "appendix". We will submit those materials as an appendix 
Comments  91: opposite sign > oppositesign 

Answer  Implemented 
Comments  93: same sign > samesign 

Answer  Implemented 
Comments  93: "in the same event"?? What does this mean? All events have exactly 2 muons so you cannot have sameside muon pairs in the "same event" as oppositesign muon pairs. 

Answer  We could see the samesign pair if you have background tracks (+ signal) but miss one/two tracks due to detector inefficiency 
Comments  9394 opposite or > opposite or same sign > samesign 

Answer  Implemented 
Comments  98: Is the mixing of upper case text sizes in STARLIGHT intentional? 

Answer  Yeah, generated by \textsc{STARlight} 
Comments  111: [35]: it > [35]. It 

Answer  Implemented 
Comments  114: EMD events. > EMD events, i.e. two EMD events occurring in the same crossing of two beam bunches. 

Answer  Implemented 
Comments  120121: being classified into an incorrect neutron multiplicity class because > being assigned an incorrect neutron multiplicity because 

Answer  Implemented 
Comments  121: of the pileup > of pileup 

Answer  Implemented 
Comments  123: by the EMD > by EMD 

Answer  Implemented 
Comments  Figure 1: The "dotted" line looks solid to me. 

Answer  The dotted line is overlap with one solid line 
Comments  137: c{_i}s and t{_i}s > c_i and t_i 

Answer  Implemented 
Comments  159: "as estimated from data" needs a reference or references. 

Answer  Estimated in this analysis, see Fig. 57 in HIN19014 AN v7 
Comments  Figure 2: Caption should mention the theory lines for <alpha> and give references. 

Answer  Implemented 
Comments  169: of mu+mu > for mu+mu 

Answer  Implemented 
Comments  172: is a constant > is constant at a value of 

Answer  Implemented 
Comments  189196/197204: Switch the order of these two paragraphs to finish the discussion of Fig. 2 before going onto something else. 

Answer  The logic here is to discuss all the physics results related to acoplanarity. We perfer to keep as it is 
Comments  195: fits by > fits using 

Answer  Implemented 
Comments  199: Again, strong > As for <aplha>, a strong 

Answer  We rephrased this sentence 
Comments  201: events, with > events with 

Answer  Implemented 
Comments  209211: Switch the order of these two sentences and change "The observed trend" in 210 to "This observed trend". 

Answer  Implemented 
Comments  213: of heavy > of ultraperipheral heavy 

Answer  Not just in UPC but also in hadronic, we prefer to keep as it is 
Comments  213214: Awkwardly worded sentence. I don't even know what needs to be "more precise" about the models. Please clarify. 

Answer  For instance, full QED calculation. We would like to discuss this during FR 
Comments  217: from data > from the data 

Answer  Implemented 
Comments  Is the plan to have the appendix figures attached to the paper or these are purely meant to be supplementary figures? Why is the supplementary figures are in the appendix rather than in the paper? 

Answer  We will have the appendix figures attached to the paper 
Comments  Abstract: Not sure why we need “strong” in the sentence starting with “The strong… “ In the same sentence I would also consider dropping “significantly” as the data in Fig 2 is not compared bin by bin with each other statistically. 

Answer  We dropped "strong" but would like to keep "significantly" because we observed an overall trend with >5σ significance 
Comments  Line 8: Reference after "in the nucleon or nucleus. “ 

Answer  Implemented 
Comments  Line 25: we talk about uncertainties in the theory but don’t show any in Fig 2. See comments below. 

Answer  The refered EPA model (e.g. STARlight) only considers the uncertainty of photon flux intensity which does not affect the photon pt shape, thus predict a constant mean pt as a function of b. The refered leadingorder QED calculation incorporating b dependent of photon pt, has the straightline approximation for the incoming projectile and target nuclei, charge distribution, and has no finalstate correction to the produced leptons. Unfortunate, all of these missing ingridents are not reflected in the quoted theoretical results. 
Comments  Line 75: Mention why there is asymmetry in the negative and positive rapidity, It states that it is the noise but what is the reason of that noise that result in an symmetric energy? 

Answer  These two numbers are purely from the empty BX data. The asymmetric numbers might be caused by the nonidentical calorimenter calibrations between both sides 
Comments  Line 83: Not sure which purity is being discussed here. So far the discussion was about selecting events. 

Answer  The selected neutron samples. Changed "The corresponding purities" > "The corresponding purities of selected neutron multiplicity classes" 
Comments  Line 94: "should match" or "is required to match “ 

Answer  Implemented 
Comments  Line 96: photoproduced or photoproduced also in couple other places in the paper. 

Answer  "photoproduced" is a widely used UPC term, and it means photonnuclear interaction produced 
Comments  Line 102: It needs a connection of the MC events and the detector simulation. How about something like: ..response is simulated further using GEANT4 with these (or by propagating) STARLight generated events [32]. 

Answer  Implemented 
Comments  Line 117: How do you ensure that we didn’t miss a valid collision vertex due to detector inefficiency? Similarly for the efficient and acceptance of detecting neutrons of 0, 1, 2. Maybe add a sentence here to clarify that. 

Answer  First question: The zerobias event is dropped if it has a valid vertex or has any reconstructed high purity track, to reject the hadronic, photonphoton, and photonnuclear events. The probability of missing all high purity tracks of hadronic or photoninduced interactions is negligiable considering the super high track reconstruction efficiency of CMS tracker. Second question: As the ZDC group suggested, the efficiency is essentially 100% considering the neutron energy is ~ 2.51 TeV when the neutron falls into the large ZDC acceptance. Oliver Suranyi did a simulation of GDR neutrons, showing >99% neutrons fall into ZDC accpetance (p8 and p9 in https://indico.cern.ch/event/838998/contributions/3519520/attachments/1889336/3115429/ZDC_sim_acc_lbl.pdf ) 
Comments  Line 118: Not sure why we need “However” as the starting of the sentence. 

Answer  Changed "However, the" to "The" 
Comments  Fig 1: Is the normalization of the integral to 1 chosen to avoid normalization of the event count? Legend of core, some, tail could be improved by writing the full empirical function. Or somehow state that they are empirical fits. Otherwise fig is not self consistent without the text in the paper. Similarly in the caption, state that these are empirical fit functions. 

Answer  1) Yes, because we do not have offical TnP scaling factors, we do selfnormalization (not senstive to TnP scaling) to aovid to report the absolute cross sections. 2) For the emperial function related comment, we prefer to keep as it is. The emperical functions are just employed to decoupe the leadingorder and highorder photonphoton contributions. It might distract the reader if we keep emphasizing the technique itself. 
Comments  Line 152: Why 5 Gev is chosen but not some other number? 

Answer  This is a little bit arbitrary and pretty conservative choice. There are 87066 correctsign pairs but only 2 samesign pairs for the default HF veto thresholds, which already tells us the hadronic contribution is negligible. Thus, the physical results should not be sensitive to the further tightened HF veto thresholds. To conservatively estimate the impact of HF veto thresholds, we tighten the HF veto thresholds to remove 20% more events resulting in a 5 GeV value. Meanwhile, we also tried to completely remove the HF veto, giving us similar systematic uncertainty values. 
Comments  Line 164: What is “Y mass region”? It is unclear why this region is excluded before <Minv> is calculated. Maybe missing text? 

Answer  Here, the mass region is 9<M<11 GeV (1S, 2S, and 3S). What we did here is not excluding all the data in this Y mass region but only equivalently removing the contribution of photoproduced Y 
Comments  Line 172: Why is there no uncertainty (even statistical) in the STARLight? 

Answer  The STARlight only considers the photon flux intensity uncertainty which does not affect the pt shape (<alpha> or <pt>) of lepton pairs. Regarding to the statistical uncertainty, we produced 30M STARlight events, resulting in a completely negligible value. 
Comments  Line 173: Is the inclusive one means averaging out all the data points? Is this statistically weighted average or just pure average of the data points presented in the Fig 2? 

Answer  We did an independent analysis for the inclusive acoplanarity distribution of muon pairs from photonphoton scattering (combined all neutron multiplicity classes) 
Comments  Did we do the calculation by ourselves or asked the authors of [36] to provide us these values? Is performed is kind of misleading if it is the other. Again is there no model uncertainty? 

Answer  We asked the authors to provide us these values 
Comments  Line 200: Drop Again, strong and rephrase with the 5 sigma difference only. 

Answer  Implemented 
Comments  Line 212: drop “new” 

Answer  Implemented 
Comments  I really like this paper and think that the text and figures are in good shape. My main concern is with the explaination of the Pt broadening by "leading order QED calculations." I am not saying that anything is incorrect but rather that I may be misunderstanding something. On line 12 there is a comment that the Pt of the quasi real photons is of order omega/gamma. This reflects that the shock front of the electric field has an angle of 1/gamma away from the transverse direction. I understand that as we decrease the impact parameter omega and so the photon energy, and the photon Pt increases. Then of course the mass of the mu mu pair increases. But everything is scaling linearly with omega. So if the mass is 5 GeV and the Pt 50 MeV at one impact parameter then at a smaller b the mass may be 10 GeV and the Pt 100 MeV. Thus I don't see who the ANGLE between the two muons should change to first order. I can well believe that at higher order extra excitations come into play but the text says at leading order. I am probably completely misunderstanding what is happening here but it we could add a little more explanation as to why increasing w and the mass causes a change of opening angle I think it would be helpful. 

Answer  Michael, thank you for this very nice comment. It is not easy to use a simple picture to explain everything. I would like to start with the Eq. (2) in https://arxiv.org/pdf/1812.02820.pdf to address your concern. There is a term named exp(ib*qt) in Eq. (2) and the integration of the Eq. (2) over b leads to the famous EPA expression, which means the kinematics of the photons coming from the two nuclei are independent . In this case, the single photon pt and pair mass is linearly scaled with b in a narrow midrapidity region (otherwise, the mass is not an energy sum of two photons). However, the lepton pair pt is a vector sum of two photon pt, and the correlation distribution of two photon vectors may be different in different b regions, thus the photon pair (lepton pair) pt may not scale linerly with pair mass. Another thing I would like to point out is that the average photon pt = omega/gamma is also an approximation. The most important thing is that the exp(ib*qt) in Eq. (2) cannot be integrated out over b according to the refered literature. That term play a role in the the amplitude space for the photons from two nuclei, reasulting in a correlation of the photon kinematics. Therefore, the single photon pt and pair mass is not linearly scaled as a function of b anymore, thus the pair pt and pair mass are definitly nonlinear when we change b range. We can think in this way, for a very narrow mass region where the single lepton <pt> is approximately a constant, the lepton pair pt still changes when b changes, resulting in a change of angle between two leptons. 
Comments  How come we don't use the endcap (or CASTOR) region to select UPC events? We only require exclusivity at the tracker (eta<2.4) and HF (3 < eta< 5) levels, but nothing is said about the endcap (2.5<eta <3) or CASTOR (6.6<eta<5.2) ranges. Why not? 

Answer  With current tracker and HF selections, we only have 2 samesign pairs compared to 87066 oppositesign pairs in this analysis, which tells us the selected UPC events are pretty pure. Therefore, we decide not to use endcap or CASTOR to avoid further complications. 
Comments  Figure 1 should be plotted in log(x)log(y) scale to show more clearly the interesting core region. We claim in the text (L174) that "Total cross sections of the core component in data and STARlight have a reasonable agreement within about 10%", but nowhere this is shown in the paper. Why don't we plot the STARlight predictions as curves on Fig. 1? At a minimum, this statement should be moved from L174 to the paragraph where we first discuss Fig. 1. 

Followup clarification  We cannot claim agreement at the cross section level, as we don't provide any cross section results (why not? we could scale the integrated luminosity...), but only normalizedtounity yields. We should change this sentence too to: "The total yields of the core component..." 
Answer  1) In log(x)log(y) plot, as shown in https://twiki.cern.ch/twiki/pub/Main/HIN19UPCDiMuNNeutron/asyPhiSpec_Logx_Logy.pdf, we do not gain more information except the small depletion in the extremely small α. Meanwhile, the strong contrast between narrow core and long tail is lost. If possible, authors would like to keep the current style. 2) Now, we deleted the sentence related to cross section comparision between data and STARlight. The main reason of not reporting the cross section is that we do not have official TnP efficiency scale factors now. To avoid futher delay of this paper, we decide not to report the crosssection results. 
Comments  The main numerical result of the paper <alpha_core> = (1227 ± 7 (stat.) ± 8 (syst.))*10e3 has a 0.65% systematic uncertainty, whereas the paper claims 5.1% total systematics. Am I missing something? (If there is a real mistake, apart from changing the uncertainties, the numbers should be appropriately roundedoff everywhere) 

Followup clarification  I understand that the uncertainties of the neutrondependence of the <alpha_core> do not play a role, but I don't see how the rest of uncertainties (hadronic contamination, exclusivity thresholds, Y contributions,...) disappear from this value. can you please clarify? 
Answer  1) All the reported systematic values are the uplimits for the considered uncertainty sources. The total systematic uncertainties are evalated to be 1.35.1% for the reproted differential neutron multiplicity classes, in which, the 5.1% is for the 1n1n class with the worst statistics. The dominate contirbution to 1n1n's systematic uncertainty, comes from "bin width" source (4%), which is highly correlated with statistics. 2) The numbers you refered is for the inclusive result. The uncertainty caused by "bin width" variation for inclusived class is reduced to be 0.1%, meanwhile, there is no EM pileup correction for inclusive class. This is why the total uncertainty is much smaller than that for differential classes. Moreover, the systematic uncertainties are comparable with the statistical uncertainties for all differetial neutron multiplicity classes, which is also the case for the inclusive result. 3) Related to the roundoff of numbers, we would like to keep consistency between data and STARlight prediction

Comments  "CMS acceptance" is repeated several times in the text. I guess you mean "central muon CMS acceptance", but even this is not clearcut as different pT,eta ranges can be defined depending on how efficient one wants to be. I've changed this below in a few instances to be more precise. 

Answer  We agree what you suggested is accurate but is a little bit verbose if we spell out the kinematics everywhere. We would like to keep the current way that we spell out the kinematics when we firstly use the "CMS accpetance" term. For the figure caption, there should be no confusion, because the quoted kimatics are printed in the plots. 
Comments  You keep simplistically calling "LO QED" a calculation that is basically a "bdependent photon \pT flux" LO QED model. STARLIGHT is also LO QED... I've changed this in various places (see below). 

Answer  We implemented this suggestion everywhere except the legend in the plot. It is true that STARlight only considers the leadingorder QED interactions, however, STARlight uses EPA method to simplify the numerical calculaiton instead of performing LO QED calculation. It is common in the field to used "STARlight"("EPA") vs. "QED" to distinguish these two scenarios, e.g., https://inspirehep.net/literature/647869; https://inspirehep.net/literature/1707594 
Comments  ultraperipheral > ultraperipheral 

Answer  Implemented 
Comments  Use the official \stat and \syst symbols to label statistical and systematics uncertainties. 

Answer  Implemented 
Comments  We shouldn't have any typo at the FR stage. I caught at least 3 of them (see below). Please make sure to run a spellchecker before rereleasing a draft. 

Answer  Implemented 
Comments  have an impact parameter dependence. 

Answer  Implemented 
Comments  L2: can be treated as a flux of linearly polarized quasireal photons [1, 2] > [Whether the photons are polarized (linearly or transversely) is not relevant for this measurement, and a (unpublished) experimental result is not the appropriate reference here. The historical photon flux EPA papers that are commonly cited are those of Weizsacker & Williams] can be treated as a flux of quasireal photons [1, https://inspirehep.net/literature/3184 ] 

Answer  Implemented 
Comments  L3: Therefore, two ions can still interact when their impact parameter > Therefore, ions accelerated at colliders interact 

Answer  Change "Therefore, two ions can still interact" > "Therefore, ions accelerated at colliders interact"? 
Comments  L5: [3–8], the socalled ultraperipheral collisions (UPCs). > , the socalled ultraperipheral collisions (UPCs) [38]. 

Answer  Implemented 
Comments  L7: and to search for physics beyond the standard model. > and to search for physics beyond the standard model [https://inspirehep.net/literature/1697838, https://inspirehep.net/literature/1709994 ]. 

Answer  Implemented 
Comments  L8:The photoninduced processes have been extensively studied in UPCs at the BNL RHIC and the CERN LHC [918]. > [The selection of Refs. [918] is unclear. This is not a complete list of photoninduced or UPC results, e.g. key photonphoton studies (in particular those related to gammagamma>l+l and lightbylight scattering) are missing. Better just keep the photonnucleus citations, dropping the single gammagamma paper quoted here [10], and merge this sentence with the former as follows] Photonuclear processes have been extensively studied in UPCs at the BNL RHIC and CERN LHC [9,1118]. 

Answer  We added more literatures in ultraperipheral pA and AA collisions here, and put them at the end of the sentences related to photonphoton, photonnuclear processes, respectively. We also removed "The photoninduced processes have been extensively studied in UPCs at the BNL RHIC and the CERN LHC" 
Comments  L39: centerofmass energy (\sqrtsNN) of 5.02 TeV > centerofmass energy of \sqrtsNN = 5.02 TeV 

Answer  Implemented 
Comments  L41: zero degree calorimeters (ZDC), > zero degree calorimeters (ZDC) [https://inspirehep.net/literature/725038 ], 

Answer  The CMS detector paper covers the ZDC subsystem, so we decide not to add this proceedings in the reference 
Comments  L45: A larger alpha of lepton pairs from leadingorder gammagamma scatterings corresponds to fewer backtoback azimuthal correlations, and thus larger initial pT of colliding photons. > [This statement neglects any finalstate effects affecting the pT (phi) of the photons (pairs)] A large alpha value corresponds to increased backtoback azimuthal decorrelation of the lepton pairs that, in the absence of finalstate effects on the muons, is due to larger initial pT of the colliding photons. 

Answer  We prefer the orignal sentence, because we classify the finalstate effects on leptons to higherorder photonphoton interactions in this paper 
Comments  L47: superior experimental resolution. 

Answer  Implemented 
Comments  L97: The detector performance > [We don't study the detector, we study the detection efficiencies] > The detector reconstruction efficiency 

Answer  Implemented 
Comments  L99: of each nucleus > of either nucleus 

Answer  Implemented 
Comments  L104: each muon pair is weighted by > [we don't weight pairs] > each muon pair event is scaled by 

Answer  Implemented 
Comments  L106: ∼9599% at > ∼9599% above 

Answer  Implemented 
Comments  L113: may contain concurrent EMD events > may contain concurrent EMD PbPb events in the same bunch crossing. 

Answer  Implemented 
Comments  L118: event. However, the > event, but the 

Answer  Implemented 
Comments  L119: zero bias events > [two first nouns act as joint adjective] > zerobias events 

Answer  Implemented 
Comments  L125: within the CMS acceptance (pT^\mu ... > (with pT^\mu .. 

Answer  We would like to keep as it is 
Comments  L129: while in the tail component, > while in the tail component (as already observed in our previous \gamma\gamma \to e+e measurement [https://inspirehep.net/literature/1697838]), 

Answer  Not sure we need this additional explaination because of the PRL length requirement 
Comments  L130: softphoton radiation from the produced lepton > [the tail indicates also hard bremsstrahlung photons, as observed in our https://inspirehep.net/literature/1697838 paper] extra photon radiation from the produced lepton(s) 

Answer  Implemented. Howerever, the bremsstrahlung effect of muon should be much smaller than that of electron. 
Comments  L130: multiplephoton interactions, > [I am not sure how multiple photon exchanges impact the single gammagamma>mu+mu acoplanarity... I would drop this, if unsure.] 

Answer  We refer to mutiplephoton scattering produces only one mu+mu pair, as shown in Fig. 40 in HIN19014 AN v7. 
Comments  L131: and scattering of two photons from a proton and a nucleus > or scattering of (one or both) photons emitted from one of the protons of the nucleus 

Answer  Implemented 
Comments  L137: where c_is and t_is > where c_i and t_i 

Answer  Implemented 
Comments  L143: A binned chi^2 minimization > A binned chi^2 goodnessoffit minimization 

Answer  Implemented 
Comments  Caption Fig. 1: from gamma gamma \to mu+mu within the CMS acceptance for 8 < M_mumu < 60 GeV in > from gamma gamma \to mu+mu events with 8 < M_mumu < 60 GeV (within the quoted \pT^\mu, \eta^\mu, y^\mumu acceptance). 

Answer  As we explained in your general comment, we explicitly defined the CMS acceptance in this analysis, thus we would like to keep as it is 
Comments  Fig. 1: There are also horizontal black lines indicating the bin width. Please remove those, or update the caption accordingly. 

Answer  Implemented 
Comments  L145: (<alpha^core>) of mu+mu pairs from the core component > of mu+mu pairs from the core component (<alpha^core>) 

Answer  Implemented 
Comments  L147: the dissociative pileup correction > the EMD pileup correction 

Answer  Implemented 
Comments  L152: zero bias triggered events > zerobias triggered events 

Answer  Implemented 
Comments  L154: impure 1n class selection > ['impure' undefined] > events wrongly misidentified in the 1n class 

Answer  We defined the purity of 1n class in L83, we would like to keep as it is. Another reason of not adopting this comment is that the EMD pileup also causes the neutron misclassfication. But the impurity we are taking here is casued by the ZDC resolution. 
Comments  L164: to interpolate the contribution of gammagamma scattering in the Υ mass region. > to interpolate the contribution of gammagamma scattering to dimuon pair production over the Υ mass range. 

Answer  Implemented 
Comments  L166: to the one obtained 

Answer  Implemented 
Comments  L170: within the CMS acceptance is shown in Fig. 2 (top), in the mass region 8 < M_mumu < 60 GeV. > is shown in Fig. 2 (top), in the mass region 8 < M_mumu < 60 GeV (with the quoted \pT^\mu, \eta^\mu, y^\mumu criteria). 

Answer  See our previous response to your comment(s) related to CMS acceptance 
Comments  Fig. 2: The label "LO QED" doesn't mean anything here, STARlight is also "LO QED". Change it to "bdependent \gamma \pT flux [36]" (or similar) 

Answer  If possible, we would like to keep the current legend. See our response to the last general comment 
Comments  Caption Fig. 2: of mu+mu pairs. > measured in muon pair events in ultraperipheral PbPb collisions at sqrtsNN = 5.02\TeV. 

Answer  Implemented 
Comments  Caption Fig. 2. Add: In the top plot, the dasheddot (red) line shows the \STARlight prediction, and the dotted (black) line corresponds to the calculations of Ref. [36]. 

Answer  Implemented 
Comments  L172: while the <alpha_core> predicted by STARLIGHT is a constant 1.348x103 , also shown in Fig. 2 (top). > at variance with the constant <alpha_core> = 1.350x103 prediction of STARLIGHT (dasheddotted line in Fig. 2, top). 

Answer  Added the dasheddotted line

Comments  L175: STARlight > [use command with small caps] > \STARlight 

Answer  Both formats are widely used. The current one is suggested by other colleagues to keep consistency with CMSFSQ16012 
Comments  L177: corresponding to 5.7sigma. > corresponding to 5.7 standard deviations. 

Answer  Implemented 
Comments  L183: is performed for > has provided results for 

Answer  Implemented 
Comments  L184: range over about 112 to 22 fm from the 0n0n to XnXn neutron multiplicity class. > range from about 112 to 22 fm for the 0n0n to XnXn neutron multiplicity classes, respectively. 

Answer  Implemented 
Comments  L186: neutron multiplicity, as shown in Fig. 2 (top). > neutron multiplicity (dotted line in Fig. 2, top). 

Answer  Implemented 
Comments  L187: to soft photon radiation from muons [23]. > to the presence in data of soft photon radiation from the muons [23]. 

Answer  Implemented

Comments  L194: higherorder processes that correlate with the dimuon pair production. 

Answer  Implemented 
Comments  L195: from fits by Eq. 1. > from the fits to Eq. (1). 

Answer  Implemented 
Comments  L197: of all muon pairs from gammagamma scattering in ultraperipheral PbPb collisions at sNN = 5.02 TeV within the CMS acceptance is shown as a function of the neutron multiplicity, in the mass range 8 < M_mumu < 60 GeV. > [unneeded verbosity] of all muon pairs events passing our event selection, is shown as a function of the neutron multiplicity. 

Answer  Implemented 
Comments  L199: Again, strong neutron multiplicity dependence of < M_mumu> is observed and the < M_mumu> in XnXn events is larger than that in 0n0n events, with a significance exceeding 5sigma. > A clear neutron multiplicity dependence of the average dimuon pair mass is observed, with the <M_mumu> value measured in XnXn events being larger than that in 0n0n events with a significance exceeding 5 standard deviations. 

Answer  Implemented 
Comments  L203: the average energy of photons involved in photoninduced interactions tends to be larger > the energy of the photons involved in UPCs is on average larger 

Answer  Implemented 
Comments  L208: correlations from the leadingorder \gamma\gamma \to \mu+\mu process is seen as the neutron multiplicity in the forward region increases. > correlations is seen, with respect to the leading order \gamma\gamma \to \mu+\mu process, for increasing multiplicities of emitted forward neutrons. 

Answer  Implemented 
Comments  L210: The observed trend is qualitatively reproduced by a leadingorder QED calculation. > The neutronmultiplicity dependence of the dimuon acoplanarity is reproduced by leadingorder QED calculations that include an impactparameter dependent photon \pT flux. 

Answer  Implemented 
Comments  L212: that initial photon energy and transverse momentum photoninduced interactions of heavy ion collisions have impact parameter dependence. > that the initial energy and transverse momentum of photons exchanged in ultraperipheral heavyion collisions, depend on the impact parameter of the interaction. 

Answer  Implemented 
Comments  L214: modeling the photoninduced interactions. > modeling photoninduced interactions 

Answer  Implemented 
Comments  L215: QGPinduced finalstate electromagnetic interactions in hadronic heavy ion collisions > electromagnetic interactions of leptons inside the QGP created in heavy ion collisions 

Answer  Implemented 
Comments  L217: considered with new constraints from data > taken into account based on the new data constraints 

Answer  Implemented 
Comments  L340: rapdity > rapidity 

Answer  Implemented 
Comments  L342: Figure A.1 shows the correlation between energy distributions of the Minus and Plus ZDC detectors for events selected for the analysis (left) and a projection onto the onedimensional Minus ZDC energy distribution together with multiGaussian function fit (right). > ['Minus' and 'Plus' should be defined. Sentence split and clarified to make it understandable] Figure A.1 (left) shows the correlation between energy distributions of the ZDC detectors, located on the positive (Plus) and negative (Minus) directions with respect to the CMS interaction point, for events selected in the analysis. Figure A.1 (right) shows the measured Minus ZDC energy distribution together with a multiGaussian function fit. 

Answer  Implemented 
Comments  Caption Fig. A.1: (left), and [comma] 

Answer  Implemented 
Comments  L347: larger > largest 

Answer  We think "larger" is better 
Comments  L348: yeilds > yields 

Answer  Implemented 
Comments  Fig. A.2: Typo label "oppsite". 

Answer  Implemented 
Comments  Caption Fig. A.2: Rapidity dependence of acoplanarity distributions from gamma gamma \to mu+mu within the CMS acceptance in the mass region 8 < M_mumu < 60 GeV for neutron multiplicity classes with asymmetric neutron numbers. > [There is no "rapidity dependence" shown here] Acoplanarity distributions of gamma gamma \to mu+mu events (within the phase space quoted) for 3 different neutron multiplicity classes with asymmetric neutron numbers. The solid red (open blue) symbols correspond to events where the dimuon rapidity is in the same (opposite) hemisphere as that of the ZDC detector with the largest neutron multiplicity. 

Answer  Implemented 
Comments  Caption Fig. A.2: See also comment to Fig. 1 above 

Answer  "Figure. A.1" is automatically generated by TDR 
Comments  Fig. A.2: Typo label "oppsite". 

Answer  Implemented 
Comments  Drop Refs. [2], [10] as suggested above. 

Answer  See our response to your L8 comment 
Comments  In v12, thank you for the explanation; but, in case that you would like to have a shorter Abstract (now it is 15 lines long), the "gamma(greek)" can help. 

Answer  We prefer to keep as it is 
Comments  In v12, this item has not been answered and touched yet. In the light that the "LO" has been used in the legend of Fig.2, it should be explained at least in the caption of Fig.2, or it would be even better if being explained on L14 as suggested in the subitem (a) above, i.e. (in addition, since the lepton "l" has not been used afterward in whole paper, it can be simply removed from L14) "from leadingorder photonphoton scattering (gammagamma > l+l) ..." "from leadingorder (LO) photonphoton scattering ..." or "from leadingorder (LO) gammagamma scattering ..." Afterward, L45, L99, L128, L142, L182 and L196 can be shortened from (at six places) "leading order" > "LO" On the other hand, if the "l+l" would be kept on L14, then it can be used to shorten L17, L20, L29 and L45 from (four places) "lepton pair" > "l+l" 

Answer  For the LO QED legend in Fig. 2, we added one sentence in the caption. We prefer not to use abbreviation everywhere, should be fine to keep as it is. 
Comments  L31, as the "GDRs" has been used for only one time in whole paper at the 2nd half of L31, it seems not necessary to be introduced, then its sole usage on L31 can be simply spelled out, i.e. "dipole resonances (GDRs) or higher excited states [68, 26, 27]. The GDRs typically decay by" > "dipole resonances or higher excited states [68, 26, 27]. This dipole resonances typically decay by" 

Answer  Implemented 
Comments  L110, as the "EM" has been introduced on L1, here it may be used to shorten from "The cross section of single electromagnetic dissociation (EMD) ..." > "The cross section of single EM dissociation (EMD) ..." 

Answer  We prefer to keep as it is 
Comments  Eq.(1) in v12, to be consistent in this paper, an extra space should be removed before the colon on each of two lines of Equation, i.e. "core : c1 x ... tail : t1 x (1 ..." > "core: c1 x ... tail: t1 x (1 ..." 

Answer  We already removed all the space between "core/tail" and ":" 
Comments  Fig.2's caption, L170, L172, L186 and L197. To be distinguishable from the "top" and "bottom" quarks, and to follow the good examples of many other CMS papers, the position indicators may be better to be changed from (a) Fig.2's caption: (the 1st line) "(top) and <Mmumu> (bottom) of mu+mu pairs." > "(upper) and <Mmumu> (lower) of mu+mu pairs." (b) L170, L172 and L186: (three places) "shown in Fig. 2 (top)" > "shown in Fig. 2 (upper)" (c) L197: "shown in Fig. 2 (bottom)" > "shown in Fig. 2 (lower)" 

Answer  Implemented 
Comments  In v12, thank you for having changed the font of "p" as suggested; however, a Reference seems have not been given yet. Please cross check. 

Answer  pvalue is a statistical term, we think it is fine not to add the reference 
Comments  L195, to be consistent with all other CMS papers, the Equation index should be put into a pair of brackets, i.e. "extracted from fits by Eq. 1." > "extracted from fits by Eq.(1)." 

Answer  Implemented 
Comments  L211 and L215, in the Summary paragraph, the "QED" and "QGP" should be explained (or be spelled out if it would not be used again in this paragraph) at their 1st appearances in the paragraph, since some readers may only read the Abstract and Summary paragraph instead of whole paper, i.e. L211: "a leadingorder QED calculation." > "a leadingorder quantum electrodynamics calculation." L215: "searches for QGPinduced finalstate ..." > "searches for quarkgluon plasma induced finalstate ..." 

Answer  Implemented 
Comments  L317, in [28], to be consistent in this Section and this paper, the font of "pp" in the article title should be changed from "of CMS muon reconstruction in pp(italic) collision events at" > "of CMS muon reconstruction in pp(nonitalic) collision events at" 

Answer  Implemented 
Comments  L340, a letter "i" is missing yet and should be added, i.e. "A ZDC energy distributions and rapdity ..." > "A ZDC energy distributions and rapidity ..." 

Answer  Implemented 
I  Attachment  History  Action  Size  Date  Who  Comment 

HIN19014diffv13v15.pdf  r1  manage  907.5 K  20201102  05:15  ShuaiYang  
HIN19014diffv13v16.pdf  r1  manage  910.2 K  20201106  16:55  ShuaiYang  
HIN19014diffv15v16.pdf  r1  manage  902.3 K  20201106  17:18  ShuaiYang  
HIN19014paperprev16.pdf  r1  manage  897.7 K  20201106  00:51  ShuaiYang  
HIN19014paperv14.pdf  r1  manage  897.0 K  20201029  17:09  ShuaiYang  
HIN19014paperv15prl.pdf  r1  manage  684.3 K  20201102  01:35  ShuaiYang  
HIN19014paperv15.pdf  r1  manage  897.2 K  20201031  17:10  ShuaiYang  
HIN19014paperv16prl.pdf  r1  manage  684.3 K  20201106  17:00  ShuaiYang  
HIN19014v12_vs_v13.pdf  r1  manage  865.3 K  20201023  05:43  ShuaiYang  
HIN19014v13v14.pdf  r1  manage  905.3 K  20201029  17:09  ShuaiYang  
HIN19014v14v15diff.pdf  r1  manage  901.4 K  20201031  00:37  ShuaiYang 
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