Section I Line 122 : can you elaborate a bit on the longitudinal polarisation feature ? —> The original text is “... the off­shell Higgs (H*) decays to longitudinal Z boson pairs and interferences with non­resonance gg­­>ZZ productions.” We could modify this statement as below: “... the off­shell Higgs (H*) decays to longitudinally polarized Z­bosons, which becomes important and compensate for the decrease in the cross­section caused by the off­shell Higgs propagator. This leads to a sizable contribution to the invariant mass distribution that extends over a large mass range. The off­shell Higgs production has a large destructive interferences with non­resonance gg­­>ZZ productions.” Line124­126: may be you can rephrase: it looks puzzling that not having an NLO calculation makes things more interesting —> We rephrase the sentence to : “The direct estimation of the on­resonant 4l event production from gluon gluon fusion can improve the understanding of this process since its curent theoretical calculation of the cross section is only known up to leading­order (LO) . “ Line148: can you briefly recall why this is so…? —> We might have been not clear here, the single Z resonance is produced via qqbar production in the s­channel. There is no resonant production of a single Z boson via gluon­gluon fusion and the 4l events produced in this region are suppressed as they are coming from single Z production with lepton pair decays and one lepton has internal radiation decays to another lepton pair. Section II Line 211­212: what is the origin of the PTZ>2 GeV cut? —> There is a generator cut in gg2VV and MCFM when producing the gg events in order to have stable numerical calculations in MC programs. ­line 219 2.5 or 2.47? —> For simplicity, we’re using 2.5 for the truth level selection for fiducial volume requirement. In the recon. level, we used |eta|< 2.47 for electron selection. The difference should be taken into account from the Correction factors (C_4l). ­line 221­223 look inconsistent —> Thanks for pointing it out, we rephrase line 222, 223 to : « m(l+l­) > 50 GeV for the primary Z boson, which has lepton pair invariant mass closer to the PDG Z mass value. « m(l+l­) > 12 GeV for the secondary Z boson. Section III ­line 354: can you be more specific on the Pythia version being used? —> Pythia8. We’ll update the text accordingly in the next version. Section IV ­line 465­468: One may wonder if what you do here is fully legitimate. As the ratio of accepted events between phase­space and fiducial is different for qqbar and gg initial states, it may be that the tau acceptance is different as well..(at least the opposite is not proven) → Agree. For now, we donot have the gg­­>ZZ­­>tau+l MC samples. We can ask for the new MC samples to make accurate corrections. If the full simulation samples are not available, we will use the generator level (with parton shower) samples to estimate the tau contributions. ­table 7: it is not clear (to me) what is the distinction between “on­shell gg”and “off­shell gg” . I thought the largest cross­section correspond to two “on­shell Zs “ ? Also this terminology is not used in the text… —> in line 254, we stated that for mZZ < 140 GeV, the interference between the on­shell Higgs production and the continuum gg→ ZZ production is negligible, so in mass range MZZ<140 GeV, we calculate the on­shell Higgs production cross section (NNLO) and the gg­­>ZZ cross section (LO) separately without including the interefence. → We should modify the wording in Table 7 “on­shell gg” and “off­shell gg” to “gg continuum with mZZ < 140 GeV (> 140 GeV)” ­­­> We separate gg processes in such a way since we have MC samples that are known to NLO for the on­shell Higgs and to which we can correct for NNLO while we only have samples with LO for the gg processes coming from continuum (box) in general and for any gg —> ZZ where both Z’s are on­shell. We will try to rephrase the 1st column of table 7 in the next version. Section VII: results Fig 32­d : is there an indication that the number of fakes is underestimated? —> We guess you mean data excess in low pT region of the 4th lepton. This is the region of the lepton pT region from Higgs signal. We used the SM Higgs cross section for normalization. From H­­>4l analysis, the signal strenth should be 1.6 SM Higgs cross section. Another possible source of the contributor to the data/MC descripancy is that the ZZ*, Z*Z* calculations are not included the high order QCD/EW corrections, which could also increase the low pT lepton rate. As for background estimation, we have used two methods (with three independent studies) and obtained consistent background estimations. For your information, those plots contain background estimations from one of our estimation procedures (FF I), which actually is not the current baseline background estimation. In any case all three background estimation procedures provide compatible bkg estimations. Also, there are no systematic uncertainties added in the error bars. Line 939: might be useful here to recall that the expected value of sigma_Delta is not exactly zero (table 2 and 3) —> OK we’ll point this in the next version. Section VIII: Unfolding You have chosen to unfold the distributions in the “fiducial volume”with the argument that there are less experimental errors. On the other hand, if you unfold it is to ease comparison with theory, and in this case the “phase space”would look more appropriate. Is there a comparative study of the two approaches? —> In fact, unfolding in the “fiducial volume” should have less theoretical uncertainties. Not “less experimental errors”. For your information, all the SM EWK measurements for the unfolding part are done in fiducial volumes only. → We agree that for theorists, unfolding in final phase space would be more approriate. We in fact has also performed the unfolding in final phase space as well, which can be included in the appendix for comparison. Also can you justify the chosen binning?Was that optimized in some way? —> The binning for the mZZ differential cross section (unfolding) is chosen by two considerations: (1) the mZZ line shape structure including two resonances (Z and H) and the both ZZ on­shell ‘bump’ should be retained; (2) the statistics (based on MC) in each bin should be around or > 10 events to have a reliable fitting and to control the statistical uncertainties. Section IX: ggtoZZ cross­section. In the analysis presented you limit yourself to extracting the ggtoZZ cross­section by subtracting from the total sample(­backgrounds) the qqbartoZZ calculated at NNLO. Have you thought/tried an approach similar to that used for placing a limit on the Higgs width (ATLAS­CONF­2014­042), ie building a BDT (or equivalent) from all relevant kinematical variables in order to separate ggtoZZ from the rest? From the figures 33 to 45 it looks like some discriminating power exist in the plotted variables, and there are a few more to be looked at…. —> Our primary goal is to use the most robust variable, the 4­lepton invariant mass distributions, to extract the gg­­>ZZ­­>4l component by a simple likelihood fitting. This variable has the advantage in a sense since it is less sensible to modeling issues than other variables presented in those plots. Furthermore, the NNLO and EW corrections to the qq­­>ZZ­­>4l are a function of the on­shell ZZ mass only. There is no corrections for other kinematic distributions. → We know that the Higgs width measurement used both cut­based and multivariate (MELA) analysis to set the limits on Higgs width. The variables used there are masses and Higgs decay angles. No other variables, like pT and eta distribtuions since these variables could have large uncertainties in modeling (particularly, the gg→(H*)­­>ZZ, where only LO modeling exist). → On the other hand, we have an ongoing study with MELA method to check whether we can gain significant improvement in the separation between processes using a method based in Matrix Element Methods. The current status (very preliminary studies) are shown in the appendix P. The key issue here is to understand the systematic uncertainties in the fitting process if using pT(ZZ) and eta(ZZ), which are modeled by LO calculations only. → We like to emphasize here, the MVA (BDT,MEM, etc) are complex approaches (particularly in understaning the systematic errors) we shouldn’t not delay the accomplishment of this analysis. Our baseline method for extracting the gg component is to use the m4l variable only.