Introduction

The answers to each comments are shown bellow. The color code is the following:

  • To be discussed
  • Comment
  • Implemented

Formatting comments based on draft v16 (in CADI)

From Bill Gary

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 -> lead-tungstate
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

Follow-up comments

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 HIN-19-014-paper-v16-prl.

Diff file between v15 and v16 can be found in HIN-19-014-v15-v16-diff.

Diff file between v13 (1st FR) and v16 can be found in HIN-19-014-v13-v16-diff.

The pre v16 draft can be found in HIN-19-014-paper-prev16.

From Austin Baty

Comments Appendix: For the measured neutron multiplicity class with asymmetric neutron numbers, the dimuon rapidity is divided into two hemispheres, the same- and the opposite-rapidity 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

From George Stephans

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 same-sign muons. --> using events containing same-sign muons.
Answer Implemented

Comments LL125-126: 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 dot-dot-dashed ... Eq. 1. --> The dot-dot-dashed 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 LL219-221: 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

Comments during final reading meeting on October 30th

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 HIN-19-014-paper-v15-prl.

Diff file between v13 (1st FR) and v15 can be found in HIN-19-014-v13-v15-diff.

Diff file between v14 (2nd FR) and v15 can be found in HIN-19-014-v14-v15-diff.

Reading introduction and summary

Comments L5: Two-photon collisions --> Photon-photon 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 LL32-32: These neutrons --> These forward neutrons
Answer Implemented

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

Comments LL43-44: 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 LL48-49: presented to probe --> presented as a probe of
Answer Implemented

Comments L54: remove "pseudorapidity"
Answer Implemented

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

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

Comments LL212-213: 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

Comments during final reading meeting on October 23rd

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 HIN-19-014-paper-v14.

Diff file can be found in HIN-19-014-diff-v13-prev14.

Reading abstract

Abstract
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 lead-lead 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 quark-gluon plasma in hadronic heavy ion collisions --> lepton pairs caused by traversing a quark-gluon plasma produced in hadronic heavy ion collisions
Answer Implemented

From David d'Enterria

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 1.35e-3
Answer Implemented

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

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

From George Stephans

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

From Sevil Salur

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 187-189, explicitly spell-out 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%"

From Michael Murray

Comments

Line 19 Current text
Therefore, final-state EM modifications of lepton pairs in the presence of a QGP ... broadening effect [25,26, 29]. However, a QED calculation [30] indicates that the observed broadening effect can be largely explained by a higher average pT for initial-state photons toward central hadronic collisions. However, theoretical models of the initial photon flux pT integrated over a restricted b range have large uncertainties [8, 30, 31].

Proposed text
Therefore, final-state EM modifications of lepton past in the presence of a QGP ... broadening effect [25,26, 29]. However the initial pt of the di-lepton pairs depends upon the overlap integral of the virtual photon fluxes produced by the left and right going nuclei which in any given event are separated by a particular impact parameter b. This results in a larger di-lepton Pt and greater broadening for small b. It should also be noted that models of the flux of photons integrated over a given b range have large uncertainties [8,30,31].

Answer

According to the message exchange among Michale, George, David, and Wei, the related text is changed to,

Therefore, final-state 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.

Comments before final reading meeting on October 23rd

Following comments are based on paper draft v12. Paper v13 is the updated one with implementing comments. Diff file can be found by HIN-19-014-diff-v12-v13.

From George Stephans

Title
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

Abstract
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 ... lead-lead collisions" to define "forward" and mention angular correlations.
Answer We would like to discuss it during FR

Comments L6-7: I suggest changing "strong" to "narrow", and then you need to say "expected from calculations using leading-order photon-photon 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 L9-11: 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

Text
Comments 8: The photon-induced -> Photon-induced
Answer We removed this sentence

Comments 11: What does "quasi-real" 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 25-26: 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: photon-induced -> photon-photon
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 40-41: 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 71-74: 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 -> opposite-sign
Answer Implemented

Comments 93: same sign -> same-sign
Answer Implemented

Comments 93: "in the same event"?? What does this mean? All events have exactly 2 muons so you cannot have same-side muon pairs in the "same event" as opposite-sign muon pairs.
Answer We could see the same-sign pair if you have background tracks (+ signal) but miss one/two tracks due to detector inefficiency

Comments 93-94 opposite or -> opposite- or same sign -> same-sign
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 120-121: 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 HIN-19-014 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 189-196/197-204: 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 209-211: 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 ultra-peripheral heavy
Answer Not just in UPC but also in hadronic, we prefer to keep as it is

Comments 213-214: 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

From Sevil Salur

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 leading-order QED calculation incorporating b dependent of photon pt, has the straight-line approximation for the incoming projectile and target nuclei, charge distribution, and has no final-state 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 non-identical 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 photo-produced also in couple other places in the paper.
Answer "photoproduced" is a widely used UPC term, and it means photon-nuclear 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 zero-bias event is dropped if it has a valid vertex or has any reconstructed high purity track, to reject the hadronic, photon-photon, and photon-nuclear events. The probability of missing all high purity tracks of hadronic or photon-induced 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 self-normalization (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 leading-order and high-order photon-photon 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 correct-sign pairs but only 2 same-sign 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 photon-photon 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

From Michael Murray

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 non-linear 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.

From David d'Enterria

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 same-sign pairs compared to 87066 opposite-sign 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.
Follow-up 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 normalized-to-unity 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 cross-section results.

Comments The main numerical result of the paper <alpha_core> = (1227 ± 7 (stat.) ± 8 (syst.))*10e-3 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 rounded-off everywhere)
Follow-up clarification I understand that the uncertainties of the neutron-dependence 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 1.3-5.1% 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 round-off 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 clear-cut 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 "b-dependent 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 leading-order 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

Everywhere
Comments ultra-peripheral --> 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 spell-checker before re-releasing a draft.
Answer Implemented

Abstract
Comments have an impact parameter dependence.
Answer Implemented

Comments L2: can be treated as a flux of linearly polarized quasi-real 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 so-called ultra-peripheral collisions (UPCs). --> , the so-called ultraperipheral collisions (UPCs) [3--8].
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 photon-induced processes have been extensively studied in UPCs at the BNL RHIC and the CERN LHC [9--18]. --> [The selection of Refs. [9--18] is unclear. This is not a complete list of photon-induced or UPC results, e.g. key photon-photon studies (in particular those related to gamma-gamma->l+l- and light-by-light scattering) are missing. Better just keep the photon-nucleus citations, dropping the single gamma-gamma 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 [9,11-18].
Answer We added more literatures in ultraperipheral pA and AA collisions here, and put them at the end of the sentences related to photon-photon, photon-nuclear processes, respectively. We also removed "The photon-induced processes have been extensively studied in UPCs at the BNL RHIC and the CERN LHC"

Comments L39: center-of-mass energy (\sqrtsNN) of 5.02 TeV --> center-of-mass 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 leading-order gamma-gamma scatterings corresponds to fewer back-to-back azimuthal correlations, and thus larger initial pT of colliding photons. --> [This statement neglects any final-state effects affecting the pT (phi) of the photons (pairs)] A large alpha value corresponds to increased back-to-back azimuthal decorrelation of the lepton pairs that, in the absence of final-state effects on the muons, is due to larger initial pT of the colliding photons.
Answer We prefer the orignal sentence, because we classify the final-state effects on leptons to higher-order photon-photon 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: ∼95--99% at --> ∼95--99% 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] --> zero-bias 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: soft-photon 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: multiple-photon interactions, --> [I am not sure how multiple photon exchanges impact the single gamma-gamma->mu+mu- acoplanarity... I would drop this, if unsure.]
Answer We refer to mutiple-photon scattering produces only one mu+mu- pair, as shown in Fig. 40 in HIN-19-014 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 goodness-of-fit 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 --> zero-bias 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 gamma-gamma scattering in the Υ mass region. --> to interpolate the contribution of gamma-gamma 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 "b-dependent \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 dashed-dot (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 1.348x10-3 , also shown in Fig. 2 (top). --> at variance with the constant <alpha_core> = 1.350x10-3 prediction of STARLIGHT (dashed-dotted line in Fig. 2, top).
Answer

Added the dashed-dotted 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 CMS-FSQ-16-012

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: higher-order 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 gamma-gamma scattering in ultra-peripheral 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 photon-induced interactions tends to be larger --> the energy of the photons involved in UPCs is on average larger
Answer Implemented

Comments L208: correlations from the leading-order \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 leading-order QED calculation. --> The neutron-multiplicity dependence of the dimuon acoplanarity is reproduced by leading-order QED calculations that include an impact-parameter dependent photon \pT flux.
Answer Implemented

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

Comments L214: modeling the photon-induced interactions. --> modeling photon-induced interactions
Answer Implemented

Comments L215: QGP-induced final-state 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 one-dimensional Minus ZDC energy distribution together with multi-Gaussian 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 multi-Gaussian 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

Refs.
Comments Drop Refs. [2], [10] as suggested above.
Answer See our response to your L8 comment

From Sijin Qian

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 sub-item (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 leading-order photon-photon scattering (gammagamma -> l+l-) ..." "from leading-order (LO) photon-photon scattering ..." or "from leading-order (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 [6-8, 26, 27]. The GDRs typically decay by" --> "dipole resonances or higher excited states [6-8, 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 p-value 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 leading-order QED calculation." --> "a leading-order quantum electrodynamics calculation."
L215: "searches for QGP-induced final-state ..." --> "searches for quark-gluon plasma induced final-state ..."
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(non-italic) 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
Topic attachments
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PDFpdf HIN-19-014-diff-v13-v15.pdf r1 manage 907.5 K 2020-11-02 - 05:15 ShuaiYang  
PDFpdf HIN-19-014-diff-v13-v16.pdf r1 manage 910.2 K 2020-11-06 - 16:55 ShuaiYang  
PDFpdf HIN-19-014-diff-v15-v16.pdf r1 manage 902.3 K 2020-11-06 - 17:18 ShuaiYang  
PDFpdf HIN-19-014-paper-prev16.pdf r1 manage 897.7 K 2020-11-06 - 00:51 ShuaiYang  
PDFpdf HIN-19-014-paper-v14.pdf r1 manage 897.0 K 2020-10-29 - 17:09 ShuaiYang  
PDFpdf HIN-19-014-paper-v15-prl.pdf r1 manage 684.3 K 2020-11-02 - 01:35 ShuaiYang  
PDFpdf HIN-19-014-paper-v15.pdf r1 manage 897.2 K 2020-10-31 - 17:10 ShuaiYang  
PDFpdf HIN-19-014-paper-v16-prl.pdf r1 manage 684.3 K 2020-11-06 - 17:00 ShuaiYang  
PDFpdf HIN-19-014-v12_vs_v13.pdf r1 manage 865.3 K 2020-10-23 - 05:43 ShuaiYang  
PDFpdf HIN-19-014-v13-v14.pdf r1 manage 905.3 K 2020-10-29 - 17:09 ShuaiYang  
PDFpdf HIN-19-014-v14-v15-diff.pdf r1 manage 901.4 K 2020-10-31 - 00:37 ShuaiYang  
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