Congratulations on making an important measurement of the 4j cross section, which is a precursor to the first use of these events for the DPS studies. The analysis itself seems to be carefully conducted and therefore I don't have many physics comments, apart from a major general comment below. The text of the paper, however, would require some work, as there are many internal inconsistencies, as well as non-compliance with the CMS style. All the plain English subscripts (soft, hard, jet, etc.) should be typeset in Roman, not in math mode; you should not use a mixture of small and capital p's to denote momenta, etc. Please, find below detailed comments split in the general, physics, and style sections.

GENERAL COMMENTS:

1) I find it a real pity that the paper stops short of trying to analyze the DPS contribution, as it is evident from Fig. 4 that a MC without MPI grossly fails to reproduce data. It would be very logical to at least make an attempt to extract effective DPS cross section using the fit to the three DPS-sensitive variables ΔS and two ΔrelpT's - for the hard and soft jet pair. With three variables with rather distinct shape even assigning large systematics for missing higher-order calculations, it should be possible to extract the DPS fraction to a decent precision. If I am not mistaken, this would be the first experimental use of a 4j process to extract the DPS effective cross section. I am aware that there is another analysis ongoing with 2j2b in the final state, but it shouldn't preclude us from at least trying to extract the DPS information from the present -- very nice -- analysis. I therefore strongly encourage you to attempt an extraction of σeff already in this paper, even if it comes with large systematics.

> The procedure to extract a sigma effective value is ongoing but it needs a further work that we think we can address to the next paper about 2b2j jets that is well ongoing. But indeed there is intention to use this measurement for a sigma effective cross section. The way which is used in the W+2jet paper is very model dependent and very time consuming, and does not make much sense for the 4 jets (where we do see already a relevant model dependence). We are working on another way using the MC but think it would delay this paper too much, if we would include it, as further studies are needed. In addition, we think the measurement of 4jets is important on its own, just as a standard model measurement and has already a good informative meaning with the various predictions we compare the data with.

2) The paper is designated for PRD, but it uses British English and the style often doesn't comply with the PRD one. Please, pay attention to the journal requirements (e.g., no vertical divider lines are allowed in the PRD tables) and adhere to their style, including American English ("center", "counterclockwise", "behavior", etc.).

> Spell check done.

PHYSICS COMMENTS:

1) Eqs. (1)-(3) and further in the text: subscripts "soft" should be typeset in Roman, e.g., Δϕsoft; ditto about the superscript "rel"; variable ΔS should have S in Roman [use pen names!] and its definition in Eq. (3) should have small p to denote momenta, not the capital ones; also j in the definition should all be typeset in Roman, e.g., p⃗ T(jhard1,jhard2).

> Done.

2) LL54-55: the sentence as is makes little sense, as you haven't introduced the barrel and endcap detectors. Replace with: "In addition, CMS has extensive forward calorimetry."

> Done.

3) L80: delete "The analysis uses full 2010 data sample" as irrelevant - you already provided the integrated luminosity; also this is not really a "full" sample, as it removes portions of data where calorimeter was not working properly; we have published on up to 40/pb from this dataset.

> Done.

4) LL86-87: Avoid starting a sentence with a proper name and add the reference to Lund mode: "In {\sc PYTHIA}, PS ordered in pT are generated and the Lund strong model [xx] is used for hadronization, while ..."

> Done.

5) L109: give a reference to {\sc MadGraph} here.

> Done.

6) An average reader is not interested in our PU reweighting procedure. Just say: "The MC samples include simulated pileup interactions with the distribution matching that in data." Further, on LL186-187, say: "{\bf Pileup:} an uncertainty due to pileup modeling in simulation is evaluated and ..."

> Done.

7) LL127-132: this paragraph logically belongs to the detector section; suggest moving it right after L60. Also, L127: The CMS experiment uses; of level-1 and high-level triggers (HLT) [29]. L129: with pT>140 GeV; L131: a pT and η dependent ...

> Changed and done.

8) LL136-137: delete the sentence "The jets are ... sub-detectors" as repetitious - this has been already explained in LL68-69.

> Done.

9) Figure 1: delete "2010" from the top legends; use a cross with a marker rather than a line with a marker to denote the data key in the legends. Either put the units in the x-axis labels in square brackets (e.g., [GeV]) or the ones on the y-axis labels in the round ones (e.g., (pb)). The last sentence in the caption is very cryptic: since you give the units as pb/GeV, naturally the bin width must be included in the scale on the y axis. What do you mean by "not normalized to the bin width" - please explain either in the text or in the caption.

> Done.

10) Tables 1 and 2: remove vertical dividers, as they are not allowed by the Phys, Rev. journals. Also, suggest starting and ending both tables with a double-line. In Table 2 body, the entries in the first column should read: "{\sc PYTHIA} 8, tune 4C" [note that PYTHIA should not be capitalized]; "{\sc POWHEG} + (\sc PYTHIA} 6, tune Z2' "; {\sc MadGraph} + {\sc PYTHIA} 6, tune Z2∗", "{\sc SHERPA}" [no need for LO as both PYTHIA and MadGraph are LO as well!]. Finally, the cross sections in the second column are given to a ridiculous precision; round them up to three significant digits, i.e. 423, 378, 234, and 293. In the final entry, add periods after "stat" and "syst".

> Done.

11) LL203-204: The text sounds odd: you first claim that the distribution in pseudorapidity is "quite flat", but then say that the difference between the central and forward regions is a factor of 10-15. I wouldn't call this "quite flat"; on the contrary, it is more than an order of magnitude in size! Do I understand correctly what you mean by "the difference" in the last sentence? If so, the text needs to be changed to avoid an obvious clash of the two contradictory statements.

> With "quite flat", we were thinking of a comparison with the hard jets. Now it's clearly stated that the distributions are more flat than the ones of the hard jets.

12) L209: give a reference to the Z2' tune.

> The Z2' tune has been used for the first time in this analysis because we realized that in a 4-jet scenario the amount of hard radiation (ruled by the parameters we changed) is crucial and needs to be reduced. So, basically we don't have any reference to quote for that.

9) Figure 2: delete "2010" from the top legends; use crosses with markers rather than lines with markers to denote the data keys in the legends (at least for the 3rd and 4th jets, where the statistical error bars can be seen). Either put the units in the x-axis labels in square brackets (e.g., [GeV]) or the ones on the y-axis labels in the round ones (e.g., (pb)).

> Done.

10) Figure 3: delete "2010" from the top legends. Put the units in the y-axis labels in round, instead of the square, brackets if this is the style you used for the first two figures. The axis labels are too small, particularly for the central pane.

> Done.

11) Figure 4: delete "2010" from the top legends. The axis labels are too small, particularly for the central pane.

> Done.

12) L263: σ4j=327±5 (stat.) ±45 (syst.) nb.

> Done.

13) LL273-274: the last sentence seems to contradict the one on LL222-224 - please clarify what you mean in the conclusion.

> We dropped the sentence. We were referring to the specific case of POWHEG, where we observed the dependence on the parameters related to the parton shower in the PYTHIA interface.

STYLE COMMENTS:

0) Title: suggest "Study of ..." - there are not so many studies done in this paper. Abstract, L4: center-of-mass; L6: jet algorithm with a distance parameter of 0.5, in a range; L8: with next-to-leading-order calculations;

> Changed in "measuments". Other corrections done.

1) Introduction, L2: with large transverse momenta (pT) in high-energy p collisions; L4: quantum chromodynamics (QCD). L5: high-pT jets; L6: measured by the ATLAS [2] and Compact Muon Solenoid (CMS) [1] Collaborations, and is in [swap the order of ATLAS and CMS appearance and Refs. [1] and [2] to match the chronological order]; LL6-7: with QCD predictions obtained at next-to-leading order (NLO). L10: add a comma before "as it"; strong-coupling constant; LL11-12: are needed to study the features of QCD. LL14-15: at lower transverse momenta. LL16-17: higher-order QCD calculations, as well as for the description of high-pT jets within the parton shower (PS) formalism. At high center-of-mass energies, the parton densities; L20: The SPS and DPS [can't start a sentence with an acronym]; L21: in Ref. [4]. L22: and pT balance; LL21-22: while a DPS event generally has an uncorrelated topology. LL24-25: Four-jet production at high pT is measured in pp collisions at a center-of-mass energy s√=7 TeV using the data sample collected with the CMS detector at the Large Hadron Collider (LHC) in 2010 and corresponding to an integrated luminosity of 36 pb−1. L26: distance parameter of 0.5; L27: |ηjet|<4.7 [all subscripts should be typeset in Roman, not in math mode]; L28: to the counterclockwise-beam direction. L29: must have pT>50 GeV, while the other; L32: no need for a comma at the end of the line; L34: are the momentum vectors for the; L35: stand for the leading (subleading) soft and hard jet pairs, respectively. L39: Monte Carlo (MC) event; L40: with PS and DPS; L41: in four-jet events; LL42-44: dijet production at NLO [the acronym is now introduced on L7] matched to PS, as well as to predictions of higher-order tree level diagrams matched with PS. L45: as follows. In Section 2, the detector and MC simulation; L46: In Section 3; add a comma before "and"; L47: in Section 5.

> Done.

2) Detector description ..., L48: Detector description and MC simulation; L49: of the CMS apparatus [the acronym is no introduced on L6]; L56: The CMS experiment uses [can't start a sentence with an acronym]; L58: counterclockwise-beam direction. L60: description of the CMS apparatus can be found; L67: add a comma before "while"; L69: by clustering PF candidates. LL71-72: The bulk ... is derived from simulation [12], with residual; L76: well-measured photon [10]; L78: multiple pp collisions in the same beam crossing [13], which ranged; L81: add a comma before "as a"; L84: that from data [10,11]. LL85-86: Simulated event samples for the four-jet production are produced using different MC [now introduced on L39] event generators; add commas after "[14]" and "[15]"; L88: in an angular-ordered region; L90: multiparton interactions (MPI) are simulated in both {\sc PYTHIA} and {\sc HERWIG++}. L91: The {\sc PYTHIA} 8 generator; L93: color; The {\sc PYTHIA} 6 generator with tune Z2∗ [18] applies; L95: CTEQ5L parton distribution functions (PDF), whereas; LL97-99: using CTEQ6L1 PDF set. The {\sc HERWIG++} generator tuned to the LHC data (tune UE-EE-3C [21]) with the MRST2001 PDF set [xx] is also used for comparison. L101: matched with {\sc PYTHIA} 6 PS, including the MPI simulation. L102: jet cross sections [1] and underlying event measurements [24,25] has; L103: with the {\sc POWHEG} matrix element (ME) calculations; L105: delete "[18]" [now given on L93]; LL107-108: initial- and final-state radiation; LL110-111: up to four partons in the final state on the basis of ME [now introduced on L103] calculations. The PS description for {\sc MadGraph} is provided by {\sc PYTHIA} 6, tune Z2∗; L113: inclusive jet cross section [1] and; L114: add a space before "[26]"; LL115-116: 2→2+n ME matched to PS (n =1 is used in this paper). The MPI effects are implemented; L117: but with different default parameter values. L118: delete this blank line; L119: {\sc GEANT4} package [28].

> Done.

3) Event selection, L123: low-pileup conditions. L138: non-physical jets; L141: add a comma before "and"; L143: and MC simulation at the; L145: add a comma before "and"; LL146-147: with the MC predictions ... and {\sc HERWIG++}. L148: the hard and soft pairs; L149: behavior; LL152-153: a rather significant dependence on the ME used in event generation is observed for |η|>4.0. L154: detector level for pT>50 GeV; L156: the different PS models used in two generators. L159: stable-particle (cτ>10 cm) level; L160: {\sc RooUnfold} [33]. L166: uncertainty in the; L167: stable-particle level; Fig. 1 caption, L2: pseudorapidity; the third; L173: MC generators; LL182-183: and simulation by 6--19\%; add a comma before "which"; L189: uncertainty in the; L190: add a space before "[34]"; in the cross section. L191: in Table 1. Table 1 caption, L3: summing the individual uncertainties in quadrature. In parentheses [plural!];

> Done.

4) Results, LL193-194: for four-jet production within |η|<4.7 and pT>50 (20) GeV; L197: The cross sections as a; L202: up to |η|∼4; L203: up to the edges of the acceptance. L204: the whole range of pseudorapidity. The difference; LL206-207: The {\sc PYTHIA} 8 predictions overshoot the data mainly in the low-pT region; L208: replace the period with a semicolon on this line to avoid starting a new sentence with a proper name. L210: low-pT region. L212: high-pT region. LL216-217: add spaces before the opening parentheses in the expression for the cross section and add periods after "stat" and "syst". LL217-218: in Table 2. While {\sc PYTHIA} 8, tune 4C; LL218-219: with the {\sc PYTHIA}6, tune Z2', including MPI; LL219-220: The {\sc MadGraph} generator, interfaced with {\sc PYTHIA} 6, tune Z2∗; LL223-224: while the difference in the number of partons included in the ME calculations is not very relevant. Table 2 caption, L1: for MC predictions; L227: Section 1. Fig. 2 caption, L2: add a comma before "and"; LL3-4: The {\sc POWHEG} and {\sc MadGraph} generators are interfaced with the PS model provided by {\sc PYTHIA} 6 with tunes Z2' and Z2∗, respectively. The lower panels show the ratios; L6: leading, subleading, and third jet. The yellow band represents the total uncertainty, including the statistical and systematic components. L234: of the initial- or final-state of the hard pair of jets. L238: over the entire phase space. Fig. 3 caption, L1: add a comma before "and"; L2: add a comma before "and"; finish line with a semicolon instead of a period. L4: the tunes Z2' and Z2∗, respectively. The lower panels show the ratios of theory predictions to; LL5-6: the statistical and systematic components. L239: add a comma before "and"; L242: is only LO in αs; L245: The {\sc MadGraph}; L246: by 20--30\%. L247: add a comma before "and"; shown in Fig. 4 [add a space]; L248: add a comma before "and"; LL248-249: Note that all the theoretical shapes; L250: add a comma before the second "and"; L253: {\sc PYTHIA} 6, tune Z2'; L254: in Fig. 4 [add space]. Fig. 4 caption, L2: add a comma before "and" and finish the line with a comma; L3: replace the period with a semicolon; L4: with the tunes Z2' and Z2∗, respectively. L6: lower panels show the ratios of theory predictions to dat. L7: statistical and systematic components.

> Done.

5) Conclusions, L264: finish the line with a comma; L268: away from data. All the; L270: The next-to-leading-order dijet; L271: and the leading-order calculation; L272: in the matrix elements ({\sc SHERPA});

> Done.

6) Acknowledgements: suggest using shorter version, appropriate for long letters.

> Done.

7) References. Swap the order of Refs. [1] and [2]. Add spaces between the parts of journal names in Refs. [1,2,4,5,7,12,13,15,16,25,32]. Refs. [1,24,25]: Collaboration is spelled twice. Ref. [3]: JHEP {\bf 06} (2012) 036. Refs. [5,12-16,32]: give just the first page, not the full range. Ref. [10]: suggest to replace with the jet energy scale paper (Ref. [31]). Ref. [11]: fix "sqrt(s) = 7 TeV". Ref. [17]: JHEP {\bf 01} (2010) 035. Ref. [18]: Eur. Phys. J. {\bf C52} [put the volume letter in boldface]; add the doi and arXiv references. Ref. [20]: JHEP {\bf 03} (2011) 032. Ref. [22]: JHEP {\bf 11} (2004) 040. Ref. [23]: JHEP {\bf 11} (2007) 070. Ref. [24]: JHEP {\bf 09} (2011) 109. Ref. [25]: fix "900GeV". Ref. [26]: JHEP {\bf 02} (2009) 007. Ref. [28]: not needed - replace it with the proper Ref. [12] in the text on L119.

> Done.

That's all. Good luck with the final editorial steps and timely submission!

Dear drafting committee,

Thank you for this nice paper. Please find below our suggestions for improvements.

Kind regards, Michael Tytgat on behalf of the Ghent group

Comments Type A

General:

Please use a hyphen for things like "high-pT or low-pT jets"

> Done.

Please use consistent notations for variables, like Δϕsoft and η (instead of sometimes ηjet), throughout the entire paper

> Done.

Detailed:

l.7: QCD is mentioned here, but not defined until line 12.

> Done.

l.37: the antecedent of the phrase “because of smaller systematic uncertainties” is not clear--what exactly is motivated because of systematics?

> Sentence rephrased. The systematics are smaller (mainly for the jet energy scale) because only the migrations inside the phase space affect the shape distributions not the ones from outside it.

l.43: tree-level (add hyphen)

> Done.

l.65-66: ... muons are reconstructed using tracks only; ... (add only)

> Done.

l.86: insert comma between "PYTHIA6.426 [14], HERWIG++ ..."

> Done.

l.160: [32] can go after unfolding instead of before.

> Done.

l.248-250: The sentence is incomplete as it lacks a clear subject

> Changed.

There are a lof of numbers repeating in Table 1 - can’t it be presented in a more compact way?

> Rounded to three digits.

Refs: Maybe an artefact of different journal conventions, but it looks funny that the same authors show up differently (e.g. Ref [14] vs. [16]).

> Fixed in the new version.

Comments Type B

* abstract: last but one line, "... provides a baseline for future ..." (remove useful, since it is not demonstrated here that it actually is)

> Done.

l.71-84: is the detailed description of the jet corrections really needed, i.e. is the reference not sufficient ?

> It was requested by the ARC to be a bit more extensive in the description of the physics objects.

l.80: in any case, please remove the sentence "This analysis uses the full 2010 data sample", since this is repeated several in the paper

> Done.

l.91: if possible, please provide a reference describing these tunes for MPI parameters

> We have added a reference to the Professor paper where the tune machinery is described and tested.

l.91-99: this part is somewhat hard to read, can it be re-ordered such that the different generators are described one after the other, i.e. PYTHIA6, PYTHIA8, HERWIG, instead mixing their description ?

> Order has been changed.

l.105: can this improvement when the parton shower contribution is changed be quantified ? perhaps add a reference ?

> There is no reference for these settings because it has been included in this analysis for the first time. These parameters are mainly sensitive in a multijet scenario where the forth jet is expected to come from the hard radiation in the POWHEG sample. A quantity is provided in line 244.

l.111: "... by the PYTHIA6 tune ..." (add 6)

> Done.

l.116-117: different parameter values are used for the Pythia6 MPI model in Sherpa; to disentangle the actual effect of these MPI parameters from the generator choice, might it not have been useful to use also Sherpa with the Z2 tunes ?

> In principle it could be interesting but the parameters we used are the recommended ones from the SHERPA authors. The issue you are mentioning has been checked by switching off the MPI contribution in MADGRAPH and SHERPA and observing a good agreement between the two with these settings. This motivates also the sentence written in the paper that the number of partons in the matrix element does not play a big role. It is not possible just to plug in the parameters of the Z2 tune in SHERPA, since it uses a different parton shower model.

l.122-123: this has already been mentioned in l.24-25, please remove

> Done.

l.124-126: if possible please provide a reference describing this reweighting procedure

> The sentence has been dropped. This corresponds to the usual procedure with 2010 data which the instantaneous luminosity is not available for and which the standard reweighting procedure can not be applied for.

l.130-132: it is not really clear why trigger efficiency correction is applied only for this limited 50-80 pT range

> This depends on the trigger used for the measurement. In this region HLT_Jet30U has been used and it starts to be fully efficient starting from a pT of the leading jet equal to 80 GeV. Small explanation added.

l.133-145: this paragraph has been discussed before in Section 2, please remove either part

> Removed.

l.150-167: this systematic uncertainty is described again on p.6, please remove it here

> To mention the jet energy scale here is relevant to explain the discrepancy at high eta for the leading jet. We have kept that, since it helps to understand the disagreement.

l.170: "individual contributions" instead of "single contributions" ? same remark for the caption of Table 1

> Done.

l.193-194: please remove these lines, as this has been mentioned several times before

> We think that it's useful to have an introductory sentence for the section. We have kept the sentence in order to have a place in the result section where we have the phase space of the measurement specified.

l.206-215: this paragraph is hard to read, please rewrite it and e.g. describe each generator one after the other, for each mentioning the pT and eta dependence, instead of mixing all the information

*> Some changes have been applied. "Measured cross sections are also compared to theoretical predictions. The MC event generator PYTHIA 8 predicts a higher cross section than the data mainly in the low-pT region, while it is able to reproduce the η dependence; POWHEG and MADGRAPH show some differences with respect to the measurements: in particular, POWHEG with the Z2’ tune, is in a good agreement with the data while M AD G RAPH has a deficit, mainly in the low-pT region. The disagreement between data and M ADGRAPH predictions is around 30 − 50 %. Both of them can reasonably well describe the high-pT region. The cross sections as a function of η are well described by all the predictions. Predictions obtained from POWHEG tend to overestimate, while MADGRAPH predicts a lower contribution of the four-jet scenario. Good agreement is achieved by SHERPA for both the pT and the eta cross sections within uncertainties.*

l.222-224: can one prove that the MADGRAPH and SHERPA difference really comes from the different MPI contributions only ?

> We tested that, by switching off the MPI contribution in both and observing that they agree quite well. When the default tune with MPI is set, the disagreement comes up.

Table 2, caption: please explicitly mention the final state, instead of writing the "selected final state"

> Done.

l.230: please remove the sentence "The data are reasonably well described by theoretical predictions", since this is discussed in detail from l.239 onwards

> Done.

Figure 2: Please add the sentence about the error bars and the yellow band, like in the other figure captions. Perhaps also add a sentence to say that the markers in the ratio plots are simply indicating the ratio equal to 1. In the upper plot (a), what is this shaded area below the data point around pT=350 ?

> It is the total uncertainty for that region where we have low statistics.

l.256: remove "useful"

> Done.

l.263: please remove "\sigma(four jets)=" and add the units (nb)

> Done.

l.265: With the "NLO theoretical predictions", do you mean POWHEG in this case ? If so please write this explicitly.

> Done.

• Lines 132-142: Since jets in HF are also used, it must be mentioned that these requirements are valid only for jets in the tracker region.

> Added a short sentence about the presence of HF and the coverage. Reference provided.

• Also the jet energy corrections for the jets in HF should explicitly be explained.

> We think that to provide the reference is sufficient in order not to increase the length of the letter.

• Lines 151-153: Have you checked with HCAL people that the detector simulation is OK? At least for |eta|>4, there might be some problems in the detector simulation itself. Then the discrepancies can not be only due to large scale uncertainties.

> See discussion with the ARC. (https://twiki.cern.ch/twiki/pub/Sandbox/FSQ12013ARCAnswersPaper/ARCmeeting.pdf)

• Lines 160-162: Here the agreement should is only in the central values not the uncertainties, right? Also, one can say something about the magnitude of the correlations looking at the response matrix used for iterative unfolding.

> The sentence is related to the central values. The uncertainties are the ones from the Bayes unfolding.

• Table 2: It would be nice to provide the cross sections within |eta|<3 and |eta|>3. Otherwise the differences between different MCs and data are mixed with inaccuracies in the HF simulation.

> This is documented in the PAS but it does not add any further information. The conclusions for the generators are basically the same.

• It will require additional work but some kind of DPS cross-section can be calculated and quoted in this paper which will make it much more valuable.

*> We would not like to enter the discussion of the DPS contribution since this would imply to measure sigma effective. The discussion about how to do it is still ongoing and we would like to have just the data points released. A sentence has been added in the abstract and in the conclusions, but it is not quantitative. *

• In the second paragraph, it is unclear if the two processes mentioned in line 13 are the two parts of SPS or are SPS and DPS. If DPS is not one of these processes, is it considered a background?

> It is referring to the hard scale process producing the hard pair and the soft scale process producing the soft pair. DPS and SPS are not yet mentioned.

• The discussion of pile-up in the first paragraph of section 3 seems incomplete. This study was done on a sample of events with low pile-up, so presumably pile-up is a problem, but this is not discussed. The pile-up reweighting procedure is not described or reference directly, though an indirect reference is made on line 186.

> We removed the discussion about the pileup, just saying that it is included in the simulation and a correction for pileup effects has been implemented. The pileup has not an issue in this analysis, even though we are dealing with a multijet sample, since the mean pileup value was quite low in the considered samples (as specified in the text).

Dear editors

thanks for your paper on the studies of four jet production in pp collisions. It is somewhat surprising that still papers are produced on the the 2010 data but this analysis does not need large statistics and the experimental conditions were no doubt much better for this measurement in 2010 (pile-up). By itself the paper contains useful measurements and should be published. I have some comments on the data interpretation and some details on the text, given below.

General comments

- We go out to eta = 4.7 for the jet measurements. Can we just do that without any discussion or mention of the HF specific calibration/special features in this paper? I would suggest to address that to give more confidence in the results.

> HF description included.

- Conclusions of the study: my observations are somewhat different than what is written right now in section 4. I see more discrepancies than what is reported. At the end of course it depends on what one calls 'reasonable' but I am more pessimistic, as I will detail below in the detailed comments. At the end what exactly did we learn on the physics with these measurements? It seems you need a right mix of tunes and MEs to do the job, or is there something more fundamental? Is it by chance Sherpa does so good or is there more to it. It would be interesting to spell that out if we know why it works well.

> I agree that the interpretation of the conclusions depends on what we call "reasonable". What we want to emphasize in the conclusion, is that PYTHIA8, considering that it is a leading order MC generator, gives already a good description of the measurement. Then, if we include a harder emission at NLO (looking at POWHEG), the agreement, as expected, improves. The agreement is not perfect, since we still have one jet coming from the parton shower that contributes to the final state and it is not accurate for a jet final state. From MADGRAPH and SHERPA, we basically learn that the UE model is the crucial point. MADGRAPH with the MPI parameters taken from the default tune fails to describe the data, while a higher MPI contribution included in SHERPA helps to get a better agreement. So basically what we would like to convey is that we need a proper SPS description and then we can improve the MPI.

A number of details: - abstract: I think we should add the distance parameter we used in this anti-Kt algorithm?

> Done.

- line 18: How is this compatible with the fact that we see no rise of sigma_eff in the other in CWR paper on DPS? Why should we see more at higher energies? (it may have to do with my question on the exact meaning of sigma_eff in 12-028 in comments to that CWR)

> Sentence rephrased. The fact is that the low-x region becomes accessible and then MPIs are more relevant for any measurement.

- Section 2 detector description: I would we give the detector pseudo-rapidity coverage here

> The detector description has been rearranged a bit.

- line 59: phi and eta are in principle already used/defined before on page 1

> The detector description has been rearranged a bit.

- line 110: I would suggest to add "LO" in here for the matrix elements.

> Included.

- line 117: Perhaps we should have a pointer to some twiki pages (or have an appendix) where these parameters can be found…? Just for people to be able to look that up.

> This Z2' tune has been used for the first time in this paper, and there are basically no references for that.

- line 133: How do you define the primary vertex? the one with largest sumpT? I think it is not mentioned now

> Yes, this is the definition. Sentence included.

- line 136 is a repeat of what is already said before, and by itself and not accurate description: We use PF particles to build the jets, and this was said already in section 2.

> This part has been removed.

- lines 142-145 are also a repeat of what was discussed in section 2. Note that here we seem to use a different baseline reference [31] than the one in section 2 which was [1]

> Changed.

- line 149: "THE pseudorapidity…"

> Done.

- line 153: "A big dependence on the matrix element used…" what does it mean exactly? This needs to be explained better.

> Changed. We meant generator.

- line 163: "stable results are obtained" please quantify this: do you mean to within 5%, 1%, better...?

> Done.

- line 164: What correction factors are discussed here? Or do you mean the unfolding factors?

*> We mean the unfolding factors. We changed in "final correction". *

- Fig 1 (b): some serious differences at the extreme edges in pseudo-rapidity. Is this not a worry? Do we control all experimental issues there for that region? (related to my general HF question above)

> See discussion with the ARC at https://twiki.cern.ch/twiki/pub/Sandbox/FSQ12013ARCAnswersPaper/ARCmeeting.pdf.

- Table 1 is a bit bizar with much repeated information. I encourage to look for a better presentational solution.

> Changed.

- line 204: is this not simply due to trivial energy-momentum conservation?

> Basically it is due to the different pt thresholds applied.

- lines 222-224: these seem like rather firm statements. Did we actually test that or from where do we have that knowledge?

> We tested for this analysis the agreement of the sample without the MPI contribution for SHERPA and MADGRAPH and we observed agreement. We changed the sentence in "We have verified that...".

- Table 2: I suggest to give also the phase space for which these cross sections are given, in the table caption (for completeness)

> Included.

- lines 225-230: are there effects of DPS that one can see here? Then I would mention that > We are not referring to the DPS effects here but just we describe the measurements in those lines. Some cross sections are really far off in table 2...

> Pythia8 is the one that is mostly far off but this is expected, since it has only a 2->2 process included.

- lines 239-240: I am not so optimistic as the authors here in the description of the results: powheg an madgraph have the wrong shapes in Fig 3c. Also the normalisation is way out of the error band for pythia, madgraph and powheg in all cases. So I do not really see a 'reasonable agreement' here. Only Sherpa seems to do reasonably for all distributions.

> the sentence "reasonably well described" has been removed. But still, it depends on what we mean with "reasonable".

- line 246 "a factor of 30%" does not look god english. For the LE to look at.

> Removed.

- fig4 Again I do not agree here: none of the curves describes fig 4c (the other two figures seem less discriminating/contraversial). You mention that madgaph, sherpa and powheg describe these data reasonably well, but pythia is not particularly worse, but is not mentioned. Powheg is actually the worst (apart from the pyhtia without MPI) for figs 4a/b (all are bad for fig 4c as said above)

> the sentence "reasonably well described" has been removed. But still, it depends on what we mean with "reasonable".

- line 268: further away… For the LE to look at.

> It was suggested by the LE.

- line 273-274: would we not need to show the powheg+pyhtia Z* curve as well to make that point?

> In principle yes, but we checked that and we observe that the Z2' tune is more appropriate for POWHEG since the hard radiation needs to be reduced.

Dear Editors

a very nice paper and well written.

Please find our detailed comments below.

Good luck with the next steps,

Ivan Asin, Samantha Dooling and Panos Katsas (DESY)

Type A (grammar and style):

general: check using \PT and all text in formulas not in math mode

> Done.

check british vrs american spelling -> be consistent

> Done.

check spacing before and after '=' (eg. L.26, 27), “>”, “~” (eg. L.204-205), “Fig.4” (eg L.247,254) symbols → be consistent

> Done.

Title: better: “Measurement of

> Done.

Abstract: “Measurements of four-jet production …. are presented ..”

> Done.

5 “ … with the density function of …” > Done. 10 “ …strong coupling alphas^4”. -> alphas is not a constant > Done. 12 “ … features of QCD .” since QCD is already defined in 4 > Done. 21 “…. discussed in Ref. [4].” > Done. 29 “... while the two subleading jets ...” > Done. 36 “ … and the hard first (second) jets respectively.” > Done. 37 “Distributions normalized to the visible x-section, which have smaller systematic uncertainties compared to -section measurements, are also presented.” > Done. 40 “… with parton showers and MPI.” (remove “ which ….”) > Done. 51 “... volume are located/placed/installed a silicon...” > It is taken from the official CMS description. 57 “ … centre of the LHC ring” > Done. 80 remove “This analysis …” > Done. 86ff make consistent PYTHIA6, PYTHIA 6, PYTHIA6.426 etc > Done. 86 “ …[14], …” insert a comma > Done. 101 102,113 ([1]), no bracket around [1] > Done. 103 “ with the POWHEG BOX” > Done. 105 Missing space before reference [18] > Done. 112 remove “initially” > Done. 136 “… with the PF algorithm,…” > Done. 157 “CorrectionS ..” > Done. Fig 1 axis (GeV) instead of [GeV] > Done. pseudorapidity instead of pseudo-rapidity > Done. 193ff “four-jets”: check in general > Done. Tab1 add % after (2) > Done. 203 “… distribution of the soft jets …” > Done. 207 “The prediction of PYTHIA8 is higher than the data mainly …. > Done. while the …. to THE measurements”. > Done. 211 “ 30—50% “ > Done. 214 “Agreement is achieved with SHERPA for both the \pt …” > Done. 216 “… 327 \pm (stat) \pm (syst)..” > Done. 224 “…. while both agree if MPI is turned off.” > Done. Fig 2 caption: “…. 3rd jet, respectively”. > Done. axis (GeV) instead of [GeV] > Done. Figure a), missing ticks in y-axis (comapre to figure b) > Done. DATA or data ? > Done. remove DATA from legend (also in other figs) > Done. MC/data or MC/obs ? > We have kept MC/data for consistency with other measurements. why are the ratio plots starting with 4th jet and not with 1st jet ? > Changed. in the plot write: pp-> 4j +X, also in the other figs > Done. is the box the total uncertainty or only systematic ? > It is the total uncertainty. put the uncorrelated (stat) error bars also in ratio > The ratio gets a bit too full with further vertical lines. We have kept the current format that gives already information about the total uncertainty for each bin. what are the correlated and uncorrelated uncertainties _> add this also in the text. In ratio plot, when prediction is at 0.6, is it then exactly at 0.6 or even smaller ? > Fixed in the plot. 231,239,264 Check consistency of symbol '\Delta^{rel}_{soft} \pt' vs '\Delta^{rel}\pt' > Done. 232 “It covers an order of magnitude … and has its largest value around one”. > Done. 246 20—30% > Done. 255 30—50% > Done. 263 sigma(pp-> 4j+X) = …. > Done. References: Collaboration Collaboration

Type B comments (content and clarity). 61ff HF should be mentioned and described since it is used. Why not using the standard detector text ? > HF part added. 61 “This measurement …. clustering algorithm [5-7]” Place this sentence later in L.69 after discussing which particles come into jet clustering algorithm > Sentence rephrased and structure changed. 62 Muon chambers are not mentioned. But they are extensively used for muon reconstruction. Similar argument for description of muons in L.66 > We do not use the muon. We mention them only for a general description of the detector. 96ff use standard description for Z2* (including PARP(82) and PARP90)) 98 Isn’t the tune 3C using CTEQ instead of MRST ? > It is the tune LHC-UE-EE-3. Fixed. 101 “… with the POHEW-BOX…” > Done. 101 give also reference for POWHEG box for dijets > Done. 153ff what is the reason for this discrepancy? Are the individual jets well described, how is it for inclusive and leading jets ? > A detailed discussion of these effects can be found in https://twiki.cern.ch/twiki/pub/Sandbox/FSQ12013ARCAnswersPaper/ARCmeeting.pdf. 153 What does it mean: “…. matrix element used…” Is it really the dependence on the ME or rather of the generator including parton shower and MPI ? > Done. 186 “... last iteration of the pile up reweighting procedure...” Are there several PU reweighting iterations? > There are 5 iterations for the pileup reweighting. This is the usual standard procedure for 2010 data where the instantenous luminosity is not available. Mention to the reweighting has been removed. 230ff what about a prediction from herwig++ ? > Adjusted. at least say in the text what the general behavior is…” 235 is it really balanced ? It they were balanced, they should have \Delta pt = 0 Just remove the whole sentence, as it does not really help. > Done. 274 Isn’t it more a difference in MPI rather than in parton shower ? Maybe put more emphasis on this > Sentence removed it seems to be in contradiction with the previous statement (line 223).

Dear editors,

Thanks a lot for your paper on the studies of four-jet production in proton-proton collisions at sqrts = 7 TeV. The following is our suggestions and comments for the paper.

Comments Type A

24 Line : Four-jet production ---> Four jets production

> Done.

34 Line : the vectorial momenta ---> the vectorial transverse momenta

> Done.

43 Line : tree level ---> tree-level

> Done.

46 Line : is described ---> are described

> Done.

86 Line : PYTHIA6.426[14] ---> PYTHIA6.426[14],

> Done.

149 Line : Pseudorapidity ---> The pseudorapidity

> Done.

157 Line : Correction ---> Corrections

> Done.

171 Line : systematic effects ---> systematic uncertainties

> Done.

202 Line : present ---> presented

> Kept as before because we mean "presence" not "presentation".

218 Line : higher value ---> higher value than data

> Sentence rephrased.

232 Line : and it ----> and

> Sentence rephrased.

Comments Type B

I think that most parts of the paper have been described in good format and have suitable structure. Even though some limitation of pages for publication should be considered, I point out only a weak description in the introduction. I have known that an introduction section is the most important part of a paper, which should explain why and how we study a subject. So the section should clearly show why we focus on the subject. In this point of view, the first and second paragraphs on the introduction section seem not to be connected reasonably. for example, the meaning of statement at line 8, “....jet in the central region of the detector is not very well described[3]” is not connected to second paragraph explicitly. Hence I suggest that some statements which connect between the first paragraph and the second paragraph in brief are need. It may help for people outside CMS to understand what and why we study this subject.

> This is a very valuable comment. Basically what we want to present in the first paragraph is the current status of the jet measurements (CMS and ATLAS) that agree in the central region but in the forward one and to claim why the measurement of the 4-jet scenario is useful and what it adds to the current status (line 8-10).

Dear Authors, Congratulations on the interesting paper. Our comments are the following:

Type B (analysis, physics) - Although every single observation is stated in the text, one could have added a discussion about possible reasons why a MC event generator did a good job describing the data, and anothers did not.

> We explain the different MC predictions when discussing the results. We say that the difference between MADGRAPH and SHERPA comes from different MPI parameters (in SHERPA it comes from the recommended tune suggested by the authors), PYTHIA8 fails because of missing higher order matrix elements, POWHEG is doing a good job even though the PYTHIA6 interfaced tune is not optimized.

- Also, the reader may want to have a discussion or statements if effects connected to double parton scattering are indeed seen in the data.

> We wouldn't like to enter the discussion of the DPS contribution since we don't measure the sigma effective of this process. The information we give is that samples without the MPI contributions fail to describe the shape of the observables. This fact is a baseline for DPS studies that we don't perform at this stage for the paper. We have added a sentence about the DPS, just when commenting the final results of the correlation observables.

L 13: not clear what "two processes" corresponds to: hard vs soft, or SPS vs DPS?

> These two processes are hard and soft. We have not yet mentioned SPS and DPS and we talk about a 2->4 process.

please clarify L 14: how can partons evolve resulting in additional jets?

> We are referring to hard radiation coming from parton shower.

L 37: what is a visible cross section? not defined

> Change applied: visible -> measured.

L 139: how can noise in ECAL and/or HCAL result in >30 GeV reconstructed jets? do we have such a high level of noise in the calorimeters? L 142: you talk about jet efficiency here; what about purity? should give a number L 153: why are the data-MC discrepancies start at eta > 4? why is that region so special?

> We include also jet purity that is of the same order of the efficiency. We have studied the discrepancies at high eta and the effects are summarized in these slides (https://twiki.cern.ch/twiki/pub/Sandbox/FSQ12013ARCAnswersPaper/ARCmeeting.pdf). The main effects are: - high jet energy scale uncertainties in the forward region; -dependence on the used generator (pythia and herwig are not the best in describing multijet scenarios).

L 159: not clear why you need "stable particle level" and ctau cuts; the reconstructed objects are jets and not particles;

> This is needed to define a particle level in the MC when doing the unfolding. These are the standard cuts applied. You are right that we deal with jets but they are made by clustering particles that might decay for which the detector response is different.

please clarify or fix Fig 1: what is meant by "Points are not normalized to the bin width"? on the vertical axis dsigma/deta is shown; these two seem contradictory; Also the big discrepancy seen at eta > 4, can it come from not properly dividing by the bin width (4.7-4 vs 5-4)?

> Fixed in the label.

Type A (general) - in math mode textual sub- and superscripts should not be in italic, but as plain text, e.g. \Delta_\text{soft}^\text{rel} \pt please check other cases as well

> Done.

- not sure if "S" for an angle is a good choice of notation; is it widely used in the literature?

> This is the usual name used for this variable (see W+jets paper, using the same notation).

- generator names are in small caps (I think that is standard), but MadGraph has a slightly different look (capital M and G); is it the CMS convention? Also Herwig and is ++ are too far from each other

> Fixed with CMS convention.

- all figures: the mention of the year (2010) is not needed since integrated lumi is given

> Removed.

Type A (details) L 12: QCD was already defined at L4,

> Done.

remove L 12: "at different thresholds" -> "above different thresholds"

> Done.

L 24: would put \pt in parenthesis

> Done.

Eq 3: pt(jhard1, jhard2) and others do not seem to be defined

> They are defined after the equation.

L 103: references should not be in parenthesis

> Done.

L 113: reference should not be in parenthesis

> Done.

Table 2: MC cross sections have too many SF, rounding to integer would be fair enough

> Done.

L 247 and L 254: Fig._4 (space)

> Done.

L 264: "four jet" (even better "4j"), stat and syst should not be italic but plain text

> Done.

L 267: for SHERPA the CMS macro (small caps) should be used

> Done.

Type A (references) [1] remove extra "Collaboration" - The bibtex file should be edited: in general journal names should not be glued, also, the journal letter should be part of the journal name and not of the volume, e.g. Phys.Rev. D87 -> Phys. Rev. D 87 This applies to [1,2,5,7,12,13,15,25,32] - JHEP volume numbers are usuallt incorrect in inSpire bibtex; they should only have 2 digits (instead of four): the other two are redundant repetition of the year; please check them: [3,17,20,22,23,24,26]

> Fixed.

Dear authors,

congratulations with a great work did! The analysis is very interesting and well written. Nice to see a lot of studies to understand the MC description!

Here are our comments:

L17) "At high centre-of-mass energies the parton densities become large..." we propose to replace to "At high centre-of-mass the low x region is accessible where the parton densities become large" (PDFs do not depend on cms energies it just opens the phase space)

> Done.

L33-34) Would be nice if you write a sentence explaining why only correlations between soft jet pairs are consider and why Delta_rel_pt between two jet systems is not shown in the paper.

> There are two main reasons to do that: the first is just the result of the compromise between number of plots and sensitivity to the dps (the most sensitive observable is DeltaS anyway). We wanted to focus in a few variables that could give a picture of the sensitivity to dps instead of just adding a long set of plots. The second one is that we wanted to unify the measurement with the W+jets analysis that is concentrated in the same DPS-sensitive variables.

L34) "...are the vectorial momenta for..." -> "...are the vectorial momenta in the transverse plane for..."

> Done.

L106) - If you change PARP(67) and PARP(71) in Pythia PS do you also change the parameters accordingly in Powheg to do a matching? - If you use Z2' tune for MadGraps does the description get better?

> In Powheg there is no real matching. A matrix element at NLO is generated with the hardest emission included and what Pythia6 performs, is the shower of these three partons. The parameters we are referring to are the ones that rule the evolution and, in particular, the phase space for the emitted hard radiation. Since a hard emission is already included in the Powheg method, this phase space should have been reduced with respect to the default set of parameters tuned in Pythia standalone. The agreement in the four-jet scenario improves with the new set of parameters. The new set of parameters does not play a role in Madgraph, since it produces already 4 partons in the matrix element and an additional hard radiation is cut off by the merging scale.

L152-153) Some explanation on why the dependence on ME is expected at large eta (eta>4) would be useful.

> "ME" has been changed to "generators".

Fig.1) - We propose to change the x-axis labels: Jet pt -> Leading jet pt, Jet eta -> Leading jet eta, etc.

> Done.

- In the caption it is written "points are not normalized to the bin width", but on the y-axis it is written [pb/GeV]. Inconsistency.

> Done.

- In the legend it says 'PYTHIA6 Tune Z2'. Should it not be Z2*?

> Done.

L202) " ...hard jets are mostly present in the central region to eta ~ 4..." -> "...hard jets are mostly present in the central region, and up to eta ~ 4..."

> Done.

Fig.2) Why does the Pythia8 describe 3rd and 4th jets? Is it a purely LO model or there is some reweighting to compensate for the missing higher orders?

> No reweighting has been applied for the Pythia8 sample. The agreement is quite good (but not the best..we do need NLO and higher order matrix elements!) because we are selecting basically a DGLAP scenario with a hard scale process accompanied by additional softer radiation; and this is basically the model which Pythia is based on and it can therefore describe this scenario reasonably well.

The Bristol group congratulates the authors on a clear, interesting and well-balanced paper. We have some minor comments and suggestions for improvements below. These are all of Type A unless indicated by *.

Regards,

Joel (on behalf of the Bristol CMS group)

First sentence of the abstract is quite long, I would break it up. Also need to mention pp collisions here

> Collisions added in the sentence. One sentence has been kept because it is a bit difficult to split it in two without having repetitions.

Line 2 (and line 24) large transverse momentum (singular)

> Done.

Line 3 “a scattering” should be “the scattering”

> Done.

Line 4 “quantum chromodynamics” (no capitals or hyphen)

> Done.

Line 4-5 “The partonic process is convoluted with the density of partons inside the protons.” What does this mean? It’s a description of the mathematical procedure used to obtain the cross section – but it sounds like it’s describing something physical? Rephrase

> Done. Rephrased by mentioning the low-x region.

***Line 7 Provide reference for the good agreement mentioned

>These are the references that are already mentioned.

***Line 9-10 “… provides additional and new information of the production process as it involves terms of fourth power of the strong coupling constant” So many comments. I don’t understand what this is trying to say. Why do terms in alpha_s^4 provide new information? More trivially, “additional AND new”? And too many “of”s.

> What we are trying to say is that we might get additional information by looking at a process with a hard scattering with two additional hard emissions (terms in alpha_s^4) in order to understand how different models can describe this higher-order measurement. This is what we call a 2->4 process (or specifically, single parton scattering in the text). We think that "new" refers to the fact that we investigate multijet final states (in particular four-jet final states) and "additional" refers to the fact that the available measurements (CMS and ATLAS cited in the paper) show that MC predictions are able to give a good description of inclusive jet cross sections and we want to check if this is still valid for higher jet multiplicities.

Line 12 QCD already defined

> Removed.

Line 12 "requiring....at different thresholds" is poor English

> Changed in "above different thresholds".

Line 14 "their evolution" needs clarifying/explaining

> We want just to say that the parton evolution .

Line 15 and 19, no “a” before “single/double parton scattering”

> Done.

***Line 21-23, last sentence of the paragraph, what is “a strongly correlated configuration in the azimuthal and pt-balance between the two jet systems”? What does "preferered uncorrelated" mean? Indeed, is it clear what “the two jet systems” are? Rewrite and clarify (probably using more than one sentence).

> We have rephrased the sentence. "Preferred uncorrelated" referred to the fact that a double parton scattering is expected to produce two pairs of jets (what we call "jet systems") that are back-to-back in the transverse plane: this is what we would call "uncorrelated topology of the jet systems". We had added the word "preferred" because from a preliminary MC studies, we have realized that this back-to-back configuration is smeared by the parton shower and hadronization effects. So at the end, for a DPS event, we don't have exactly an exact back-to-back topology but a more smeared one.

Line 24: Again, pt has already been explained in line 2, so perhaps no need for both the words and the 'pt' here?

> Done.

Lines 25-27 Sentence has too many commas and is therefore very confusing

> Two sentences have been chosen for that.

Line 27 (and elsewhere) Roman font for subscripts

> Done.

Line 26 "R=0.5" needs spaces

> Done.

Line 28 "Leading" is jargon and should be changed or explained

> Explanation of leading (highest pt jet) has been added in the first place in the paper.

***Line 30 This paragraph should say somewhere that the selection is exclusive.

> Done.

***Equations defining correlation variables: (i) words used as subscripts/superscripts should be in text font (eg all the “soft”s look odd) (ii) in equation 2, the pTs inside modulus signs in the denominator should be vectors (iii) also in equation 2, why are the “rel” and “soft” labels attached to the Delta, rather than the pT? (iv) in equation 3, what do the capital Ps mean? (v) arccos should be cos^{-1} (vi) do we really need all these equations? Only eq 2 would not be obvious from a text description

> The equations and the notation used has been chosen for consistency with the W+jet paper. The font has been fixed.

***Lines 35-36 It’s not explained what first and second jets mean.

> Terminology changed.

Lines 37-39 Horrid sentence, please rephrase

> Done.

***Lines 37-44 actually, horrid paragraph. In line 40 we have O(alpha-s^2) matrix elements; in line 42, dijet production at NLO; line 43, higher order tree level diagrams. Not at all clear how these are related to each other. Also on line 40 “which can be used in the future to study …” What can be used? The O(alpha_s^2) Monte Carlo? When in the future?

> Removed "in the future". About the sentence you mention, basically this is the point of the analysis. We want to compare the measurement with predictions of different generators that make use of different matrix elements to check which one performs better. In particular, we want to understand which are the effects of going from a Leading Order MC generator, like Pythia, to more sophisticated ones like Sherpa and Madgraph, until NLO matrix elements implemented in Powheg.

Line 46 “the detector and Monte Carlo … ARE described” (replace “is” with “are”)

> Done.

Line 52 “brass/scintillator” I think needs to be changed to “brass and scintillator”

> Kept as it was. It means alternate layers of brass and scintillators. It was taken by the standard detector description.

Line 61 “This measurement uses …” Why are we talking about clustering before the PF algorithm? Also, we should say “Particles are grouped together to form jets using” in preference to “This measurement uses”. Also, we already mentioned jet clustering and anti-kT in line 26, so doesn’t need to be repeated.

Line 64: I think the sentence beginning "Electrons are reconstructed..." explaining PF could be rephrased to read a little more clearly.

> Standard detector description.

Line 66 “in case of charged ones” is odd – rephrase to avoid this. Anyway: “in case of” is misused here - it means “as a precaution”.

> Standard detector description.

Lines 69-70 “response … close to unity” Very odd phrasing. Should be a new paragraph? How about “The momentum of jets is corrected by a number of factors. Because the reconstruction makes optimum use of the tracking detectors and calorimetry in the measurement of individual particles, the corrections applied are small, at the level of 5-10%.”

> Standard detector description.

Line 73 "back-to-back jets in azimuth" is odd - suggest "jets that are back-to-back in \phi"

> Standard detector description.

Line 77, again “restores the response to unity” is odd.

> Standard detector description.

Line 77-78 “further corrected for the pileup of multiple proton-proton collisions” – rephrase

> Removed.

Line 80: Already stated on line 25 full 2012 data sample is used. Also repeated on line 122.

> Removed.

Line 85: If MC is going to be introduced for Monte Carlo, should probably be the first time it is used on line 39.

> Done.

Line 86 Use semi-colons are separators in list

> Done.

Line 89 Either "the" or "a" is required before "cluser framgentation"

> Done.

Line 91: "tunes" is probably jargon and should be clarified/avoided

> Is it not widely used in the literature? We provide references for every tune we mention and when we introduce the word for the first time, we added a reference to the Professor paper where the tune machinery is described.

Line 91: "collision" should be "collisions"

> Done.

Line 92: remove "the" before "MPI" and comma after "Pythia 6"

> Done.

Line 93: say "color" to be consistent with other US spellling

> Done.

Line 93: PYTHIA6 has a space before the 6 in the line above.

> Done.

Line 96: "has been"->"was"

> Done.

Line 97: Remove "as" before "parton distribution functions"

> Done.

Line 102,113: are both square and normal brackets necessary for the references?

> Removed the normal ones.

Line 105: no need to repeat reference 18

> Done.

Line 106-107: try and avoid using "PARP" if possible. Should be fine to say "...by changing the parameters that control .....by a factor of four..." or similar

> We would like to keep that since it is the first time that this particular tune has been used and we would like to give technical information.

Line 109 Rephrase "from here on"

> Done with "henceforth".

Line 110-111: ME should be introduced on the first occasion it is used on line 40.

> Done.

Line 112: "has been"->"was"

> Done.

Line 117: "the" before "PYTHIA"

> Done.

***Line 123-126: include this in the previous section

> Done.

***Line 127: move to detector section

> Done.

Line 124: "reweighting" is jargon, prephrase

> Removed.

Line 135 "hardest" is jargon

> Done with "highest pt".

Line 136-137 repetition of PF intro

> Removed.

Line 140 comma after "hadron"

> Done.

Line 142-145: Jet correction section is repeated, this time with introduction of Z+jets???

> Removed.

Line 146-147: Repetition of earlier discussion

> We start to discuss the detector level distribution of the four-jet scenario that were not previously mentioned.

Line 152 "rather big" reads too colloquially. Suggest "large"

> Done.

Line 154 Reference needed for observation of discrepancies

> The discrepancies have been observed for further checks related to these analysis and they are not published. The discussion is widely treated in https://twiki.cern.ch/twiki/pub/Sandbox/FSQ12013ARCAnswersPaper/ARCmeeting.pdf

Line 158: "kinematical variables" is not normal English

> Done with "pt and eta" extensively.

***Line 159: Need to explain more what is meant by "correcting to stable particle level"

> It refers to the definition at the generator level which the data are corrected to.

***Line 162: rephrase, especially "...and it has been checked as closure test..."

> Done.

Line 166 "deviation from average" is unclear, rephrase

> Done with "mean value".

Figure 1: (i) Yellow uncertainty bands are completel invisible in monochrome print. (ii) Can ratio plots be done in the same format as later figs, i.e. data points on line=1 (iii) Can line styles be made consistent between plots? (iii) If values are not normalised to bin width, is it OK to label y axis as "dsigma/dpT"?

> Fixed.

***Line 172: Would help to emphasise that this is just the difference in the response matrix

> Yes. We just wanted to give more insights how it is actually evaluated. Included.

Line 179-180: Rephrase "Regarding the normalized distributions...."

> Done.

Line 186 "Pileup reweighting" is jargon

> Removed.

Table 1: (i) caption: parenthesis -> parentheses (ii) first eight lines could be condensed to one or two

> Done.

Lines 193-195: Paragraph up to "detector effects and efficiencies" is not really necessary

> Removed.

Line 196 pT already defined

> Removed.

Line 197 use \eta for pseudorapidity

> Done.

Line 201 specify fig 2b

> Done.

Line 203 "edges" and "quite flat" are too colloquial

> "edges" has been kept while "quite flat" has been changed to "more flat".

Line 204 suggest joining sentences with a semicolon

> Done.

***Lines 206-215: Very confusing to follow. Suggest separating out into discussions of pT and eta separately in different paragraphs

> We would like to keep the discussion by generators not by distributions.

Line 221 what is meant by "increase its contribution" - clarify

> The different parameters used by Sherpa tend to increase the MPI contribution: it is basically related to the high overlap function of the two protons.

***Line 222-224: Need to present evidence or reference that difference is due to MPI

> It has been shown in the working group that by switching off the MPI in MADGRAPH and SHERPA, we get agreement between the two matrix elements. This was a private work related to the understanding of the behaviour of the predictions for this analysis.

Line 228-229: the angle is \phi_{soft}

> Done.

Line 229: decorrelated -> uncorrelated?, "bump" is colloquial

> Done. Bump-> local maximum.

Line 232-233 write "one" or "unity"

> Done.

***Line 235: why is "balanced configuration" at phi=0.2? Needs explanation

> Removed.

Line 237: "is falling"->"falls"

> Done.

Line 240: remove "we" before "considered"

> Done.

Line 241: "data by less than"

> Done.

Line 242: "in LO \alpha_s"->"at LO"

> Done.

Line 244: "bringing a differnece up to"->"giving a difference of up to"

> Done.

***Line 244-245: "This is due to the additional hard contribution of the parton shower" is an odd statement as the POWHEG is matched to the PS, isn't it?

> Powheg has only an additional hard emission included in the matrix element and the forth jet must come from the parton shower provided by pythia6.

Line 248-249: should be "'It is interesting to observe that all...."

> Done.

Line 254 "While the \Delta\phi..."

> Done.

Line 263 use roman font for "four jet" and official macros for syst and stat

> Done.

Line 266 Break sentence "...agree with the measurements. A good description..."

> Done.

Line 269-274: Phrasing is awkward in several places.

> Rephrased.

In general

(1) Throughout the paper (including in formulas, figure captions and Tables), sometimes the subscript "T" in "pT" is expressed in italic, sometimes in non-italic. They may should be consistent, i.e. either

all as pT(italic) or all as pT(non-italic)

instead of a mixture.

> Done.

(2) In all figures

(a) At the top line above each plot, a comma should be added after the luminosity numbers, and two spaces should be added before and after the sign of "=", i.e.

"L=36 pb-1 pp-> 4j" --> "L = 36 pb-1, pp-> 4j"

(b) In the legends of plots,

(i) at the top-left corners, two spaces should be added before and after the sign of "<", i.e. "|eta|<4.7" --> "|eta| < 4.7"

(ii) in the right column, the bottom lines (of Figs.1, 3 and 4) or bottom 4 lines (of Fig.2), the "DATA" should be changed from "DATA ..." --> "Data ..."

(c) The plot labels (a), (b), (c), (d), ... should be moved upward by a line, so that they can be closer to the indicated plot than to something below.

(d) In the captions of all figures (except Fig.1), the 4th lines of Figs.2 and 3's captions and the 6th line of Fig.4's caption, it may should be changed from "the ratio of theory prediction to data" --> "the ratio of theoretical prediction to data"

> Done.

Page 0, in Abstract

(3) In the 8th line, the "NLO" may should be spelled out, i.e. "with NLO calculations ..." --> "with next-to-leading-order calculations ..."

> Done.

Page 1

(4) L7, the "NLO" should be explained at its 1st appearance in text here instead of on L42, i.e. (also, a hyphen should be added) "at next-to-leading order QCD." --> "at next-to-leading-order (NLO) QCD."

> Done.

Correspondingly, L42 can be shortened from "for dijet production at next-to-leading-order (NLO) matched to ..." --> "for dijet production at NLO matched to ..."

> Done.

(5) L9, as "pT" has been already introduced on L2, thus here it can be shortened from "jets at large transverse momenta provides ..." --> "jets at large pT provides ..."

> Done.

(6) L11-13, as "QCD" has already been introduced on L4, thus here it can be shortened from (also for pT)

"the features of Quantum Chromodynamics (QCD). By requiring pairs of jets at different thresholds in transverse momentum," -->

"the features of QCD. By requiring pairs of jets at different thresholds in pT,"

> Done.

(7) L17, it seems better to add a comma, i.e. "At high centre-of-mass energies the parton densities become large" --> "At high centre-of-mass energies, the parton densities become large"

> Done.

(8) L24, similar as the item (5) above, it can be shortened from "Four-jet production at large transverse momenta pT is measured ..." --> "Four-jet production at large pT is measured ..."

> Done.

(9) L25, the "CMS" (instead of on L49) and "LHC" should be explained at their earlier appearances in text here, i.e.

"collected with the CMS detector at the LHC during 2010." --> "collected with the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) during 2010."

Correspondingly, L49 can be shortened from "The central feature of the Compact Muon Solenoid (CMS) apparatus is" --> "The central feature of the CMS apparatus is"

> Done.

(10) L26,

(a) the "kT" here is expressed differently in the titles of [5] and [6] (where it is "kt"), I'm not sure whether they should be consistent or not.

The other places where also need to be considered are L61 and L193.

> Done.

(b) Two spaces may should be added before and after the sign of "=", i.e. "with a distance parameter of R=0.5," --> "with a distance parameter of R = 0.5,

> Removed "R =".

(11) L29-31, similar as the items (5) and (8) above, two places can be shortened from

"must have a transverse momentum pT > 50 GeV while ... 20 GeV. The cross section as a function of the transverse momenta and ..." -->

"must have a pT > 50 GeV while ... 20 GeV. The cross section as a function of pT and ..."

> Done.

(12) The line below L34, I'm not sure whether the "Delta(S)" should be swapped forward by a few words, i.e. "the azimuthal angle between the two dijet pairs Delta(S) defined as:" --> "the azimuthal angle Delta(S) between the two dijet pairs defined as:"

> Done.

(13) Eq.(3), I'm not sure about the reason why the transverse momentum in this Equation uses the capital "PT" instead of "pT" as used elsewhere in this paper.

> Changed.

Page 2

(14) L45-47, at 3 places (one on each line), the "section"s should capitalize the 1st letters, i.e. "in section x" --> "in Section x"

> Done.

(15) L57-58, as the center of the LHC may refer to different things, it may be slightly clearer if two words of "ring" are added, i.e.

"the x axis pointing to the centre of the LHC, the y axis pointing up (perpendicular to the LHC plane)," -->

"the x axis pointing to the centre of the LHC ring, the y axis pointing up (perpendicular to the plane of LHC ring),"

> Done.

Page 3

(16) L113, the round brackets seem extra and can be removed, i.e. "to inclusive jet cross section ([1])" --> "to inclusive jet cross section [1]"

> Done.

Page 4

(17) L130 and L134-135, three "transverse momentum"s may be shortened as "pT", i.e.

> Done.

L130: "In the region of transverse momentum between 50 and" --> "In the region of pT between 50 and"

> Done.

L134-135: "with a transverse momentum pT > 50 GeV and two with a transverse momentum pT > 20 GeV." --> "with a pT > 50 GeV and two with a pT > 20 GeV."

> Done.

(18) L136, as the "PF" has been introduced on L62, here it can be shortened from "The jets are reconstructed with the Particle-Flow algorithm," --> "The jets are reconstructed with the PF algorithm,"

> Done.

Page 5, Fig.1

(19) In the caption, the lower panels of plots may should be explained.

> Done.

Page 6

(20) L175-187, all of those systematic uncertainties percentages (e.g. 3-5%, 15-18% and 6-19%, etc.) may should be given some reference articles, so that readers would not wonder why these percentages are chosen, why not any other arbitrary percentage numbers.

> These uncertainties have been measured for this specific analysis. The numbers that are reported in the table are the results of an average over the whole range of the total systematic uncertainties. For the shapes, where some statistical fluctuations are observed for the uncertainties, two adiacent bins have been merged and the same procedure has been applied.

(21) L191, the "table 1" may should capitalize the 1st letter, i.e. "is given in table 1." --> "is given in Table 1."

> Done.

(22) Table 1

(a) In the header row and header column, the 1st letter of 2nd word should be in the lower case, i.e. "Measured Observable" --> "Measured observable"

(b) In the 5th column and all rows under the header row, a space may should be added after the sign of "<", i.e. "<0.1%" --> "< 0.1%"

(c) In the 2nd-4th columns and the bottom 3 rows, I'm not sure whether the "%" symbols should be added in 6 cells, i.e.

"3% (3%) 14% (3) 2% (2) 3% (3%) 13% (3) 1% (2) 5% (4) 15% (3%) 4% (3)" -->

"3% (3%) 14% (3%) 2% (2%) 3% (3%) 13% (3%) 1% (2%) 5% (4%) 15% (3%) 4% (3%)"

> Done.

Page 7

(23) L196-197, the two lines may be combined into one and be shortened from

"as a function of the transverse momenta pT of the four jets are presented in Fig. 2(a). The cross section as a function of the jet pseudorapidity are shown in Fig. 2(b)." -->

"as the functions of pT and eta of the four jets are presented in Fig.2."

> Done.

(24) L201, a plot label seems missing, i.e. "The cross section as a function of h (Fig. 2) is ..." --> "The cross section as a function of h (Fig.2(b)) is ..."

> Done.

(25) L217, similar as the item (21) above, "in table 2." --> "in Table 2."

> Done.

(26) Table 2, the left column and the row above the bottom row, as the "LO" has not been explained in text yet, it may should be spelled out, i.e. "SHERPA LO" --> "SHERPA Leading Order"

> Removed.

(27) L227, similar as the item (14) above, it may should be changed from "section 1." --> "Section 1."

> Done.

Pages 9 and 10

(29) Figs.3 and 4, the horizontal axis labels of all plots should have units, i.e. "Delta(phisoft) Delta(relpTsoft) Delta(S)" --> "Delta(phisoft) (radians) Delta(relpTsoft) (GeV) Delta(S) (radians)"

> Done.

(30) L242, the "LO" should be explained at its 1st appearance in text here, i.e. "although the prediction is only in LO ..." --> "although the prediction is only in Leading Order (LO) ..."

> Done.

Page 11

(31) L276-324, this paper is not too long, thus may choose a shorter version of Acknowledgments Section.

> Changed to the short version.

Pages 12-14, in the References Section,

> Implemented all the comments in the reference section.

(32) L326-326, in [1],

(a) obviously "[1] CMS Collaboration Collaboration," --> "[1] CMS Collaboration,"

The others which also need to be changed by the similar way are [24] and[25].

(b) a space should be added between words in the journal name, i.e. "Phys.Rev. D87 (2013)" --> "Phys. Rev. D87 (2013)"

The others which also need to be changed by the similar way are [2], [4], [5], [7], [12], [13], [15], [16], [25] and [32].

(33) L329, in [2], to be consistent in this paper and in this Section for the expression of "pp" (e.g. [25], etc.), it may should be changed from "ppbar(italic) collisions" --> "ppbar(non-italic) collisions"

Another one which also needs to be changed by the similar way is [3].

(34) L334, in [3], to be consistent with other JHEP Refs. (e.g. [6] and [14], etc.) in this Section, it should be shortened from "JHEP 1206 (2012) 036," --> "JHEP 06 (2012) 036,"

The others which also need to be changed by the similar way are [17], [20], [22]-[24] and [26].

(35) L338-339, in [5], to be consistent in this Section, all references should have only one page index instead of two, i.e. (together with the item (32b) above) "Phys.Lett. B641 (2006) 57®C61," --> "Phys. Lett. B641 (2006) 57,"

The others which also need to be changed by the similar way are [12], [13], [15], [16], [25] and [32].

(36) L347, in [9], the 1st letter of "reconstruction" may should be in the upper case, i.e. "Commissioning of the Particle-Flow reconstruction in" --> "Commissioning of the Particle-Flow Reconstruction in"

(37) L352, in [11], two spaces should be added before and after the sign of "=", i.e. "Jet Energy Resolution in CMS at sqrt(s)=7 TeV" --> "Jet Energy Resolution in CMS at sqrt(s) = 7 TeV"

(38) L354, in [12], the 1st letter of "toolkit" may should be in the upper case, i.e. "GEANT4: A Simulation toolkit" --> "GEANT4: A Simulation Toolkit"

(39) L362, in [16], an author name should be corrected from

"[16] T. Sjostrand," --> "[16] T. Sjo(with two dots on the top of "o")strand"

The others which also need to be changed by the similar way are [17] and [20].

(40) L368, in [18], to be consistent in this Section, a space before the volume index may be removed, i.e. "Eur. Phys. J. C 52 (2007) 133." --> "Eur. Phys. J. C52 (2007) 133."

(41) The "year" number should be given for Refs.[21], [27] and [33]. If there would be problems to display the year number with the default bib file, it may be fixed by changing from "article" to "unpublished" in the bib file.

(42) L374, in [22], the 2nd word in the article title should be in the lower case, i.e. "A New method for combining NLO QCD with shower ..." --> "A new method for combining NLO QCD with shower ..."

The others which also need to be changed by the similar way are [27], [28] and [32].

(43) L377-378, in [23], two words in the article title may should be in the lower case, i.e. "Matching NLO QCD computations with Parton Shower simulations:" --> "Matching NLO QCD computations with parton shower simulations:"

(44) L384, in [25], to be consistent in the article title, it should be changed from "= 900GeV(italic) and 7 TeV with the ATLAS" "= 900 GeV(non-italic) and 7 TeV with the ATLAS"