Matteo Defranchis

- Which PDF is used in the MC?

The MC is centrally produced with NNPDF3.0. However, PDF uncertainties in NNPDF is estimated using replicas, which are not statistically independent and cannot be used as input to the fit. For this reason, in this analysis PDF uncertainties are estimated as the relative variations from the CT14 eigenvectors, which are independent.

- Section 3.2, Fig. 4: It seems the JES uncertainties and many of the modelling uncertainties are constrained quite a bit. -> In contrast, the b-tagging uncertainties are not constrained (while this was the goal of having the b-tag categories if I understood correctly). Are the b-tag categories constraining the Bowler-Lund fragmentation and/or JES flavor instead? -> I wonder which distribution/categories are constraining the color reconnection. Could you check this somehow? Is this also the case in the inclusive measurement? If so, then I wonder which categories or distributions are responsible. Maybe the pt of the fourth jet? -> The JES: Fragmentation nuisance parameter is pulled quite a bit, while the FSR scale is constrained a lot. This is a bit funny, because I would naively think that these two are giving similar effects. -> I wonder if the JES: Fragmentation is correcting most of the top pT mismodelling. The top pT is also pulled, but still within 1 sigma. Could this be verified?

- Section 3.5, Fig. 6: Why is mt(mt) set to 164 GeV? Could you add in Fig. 6 also some additional mt(mt) values (one below 164 and one above) according to some reasonable variation?

The theory prediction in this plot is just for illustration purposes. mt(mt) = 164 GeV is the value obtained by extracting mt(mt) at NLO from the inclusive cross section measurement of TOP-17-001, using Hathor. In principle, other values can be added without any problem. TODO

- L212: how are the correlations between the measurements in the different mtt^gen determined for Table 6?

These are the post-fit correlations estimated by minuit+minos

- For Tables 2-5: how is the total uncertainty obtained? Is this still in %?

yes

I assume it the quadratic sum of the uncertainty in the visible XS and the extrapolation uncertainties? I don't think it is explained in the text.

yes, exactly. It is explained at L158-159, but if it's not very clear I can try to rephrase

- Section 4: suddenly the fourth mtt^gen bin is dropped. It is nowhere discussed why this is the case. I wonder what Figure 8 looks like for the fourth bin.

It is explained at L236-237: in this bin, the centre-of-gravity if the mtt spectrum is not a representative scale of the process, since the range in mtt is too broad (even more, it's not limited from above). Initially I performed the fit with only 3 bins, and then I decided to introduce an upper cut on the mtt in the last bin, for the reason discussed above. The resulting 4th bin is consistently treated as a signal in the analysis, but it is not used in the extraction of the running. In addition, at higher mtt the sensitivity to mt decreases, and Figure 8 would look like a very mild dependence, resulting in a very large uncertainty in the extracted mass.

- Section 4.2: you use the asymmetric chi-2, but for the 2nd and 3rd mtt^gen bins, the uncertainty is quite symmetric, also after extraction the mt(mt) mass. As a consistency check, how do the results change if you symmetrize the uncertainty and use the regular chi2?

I could do it as a cross check, but I wouldn't expect the result to change. In fact, the uncertainties are symmetrized after the chi2 extraction (see L268-270).

- Fig. 9: why is only the experimental uncertainty shown for the mt(mt) masses you extract? Is it because you can not fit any dependency if the other uncertainties are included?

This plot too is meant for illustration only, and we don't plan to include it in the paper. It is an intermediate result used to guide the reader through the procedure. In particular, this is the uncertainty that one estimates from the chi2, described in the previous section. As a matter of fact, this plot is a graphical illustration of Table 8, which also includes only the experimental uncertainty (I made this explicit in the table's caption, will be available in the next version of the AN). Other uncertainties are propagated directly to the ratios. In principle it is doable to propagate all uncertainties in this plot, but it would require some additional explanation in the text, that in my opinion is not necessary and could confuse the reader.

- Fig. 9: Is it fair that mt^MC is chosen as scale mu for the inclusive XS measurement, while mtt^gen is chosen as scale mu for the exclusive points.

It is not mt^MC, it's the top mass in the MSbar scheme evaluated at its own scale. For example, mt(mt)=164 GeV means mt(164 GeV) = 164 GeV.

Wouldn't it be more fair to chose as scale mu for the inclusive XS measurement the weighted average of mtt^gen? Same question applies to Fig. 12/13.

It can certainly be done, but this does not really provide any additional information, for two reasons:
- in all cases, the procedure involves extracting mt(mt) and then using RGE to evolve to a different scale
- the weighted average of mtt over the whole spectrum is not a representative scale of the process. This choice only makes sense when the measurement is performed is a small enough range, as in the first three bins in mtt. Also, calculations of inclusive cross sections are normally performed using mu_r = mu_f = mt(mt)

- Section 4.4: L306-310 wouldn't it make more sense to put this closer to tables 2-5?

This is how we estimate the impact of extrapolation uncertainties on the ratios, i.e. the quantities r_12 and r_32. The procedure to extract the impact on the cross section is described in Section 3.3

- Fig. 11: I think it makes sense that the correlation in this figure is the same as between the XS in the mtt^gen bins, no? If so, this could be stated.

I also think it makes sense, but I am not sure that it is trivial a-priori. In fact, the transformation from the differential cross section to the mass is not linear, and the dependence on the mass is very different in the different bins.

- Section 4.6, last paragraph. You state that the modelling uncertainties cannot be reduced using more data. I tend to disagree, because apparently you are constraining the modelling uncertainties (see Fig. 4). I don't understand why. You are even constraining the JES, which is an important systematic. More data would therefore potentially help. However, this should not be a reason not to publish as soon as possible, since the analysis is really nice.

It is true that we gain from constraining modelling uncertainties in the visible phase space. However, we don't consider these constraints in the extrapolation to the full phase space, which is relevant contribution to the total uncertainty (see eq. 7 and 8). I can make this consideration more clear in the text. As for JES, things get complicated as one would have to carefully study the correlations between the different datasets. I am not sure that adding (e.g.) 2018 data would help much to constrain JES in the 2016 dataset. The precision would ultimately be driven by dataset with lowe prior uncertainties (currently 2016). The same holds for other experimental uncertainties, like luminosity and lepton IDs. My whole point here is: adding the full Run2 statistics would be a disproportionate amount of work compared to the gain in precision that can be reasonably expected.

Some minor textual comments:

- I identified some typos in the following lines: 30, 104, 132, 144 (this -> these), 150 (parameterS), 156, caption Fig. 8, 278, 287 (careful), 311 (uncertainties and estimateD), 325, caption Fig. 12 (includeS and iNclusive), 342, 357, 362 (2x), 365, 372 (studieD and benefit FROM)

thanks, I will fix TODO

- L351: the correlations ... are correlated -> please rephrase to something meaningful

yes sorry, that doesn't make any sense. I meant "since the contributions from the different nuisance parameters are correlated".