Precise predictions for boosted Higgs production

Referee 1

1- I suggest to motivate the use of a given scale choice. It could be sufficient to provide references where the choice has been motivated.

2- The authors should clearly describe the technical aspect (e.g. the meaning of 3, 7 and 9 point scale variation or the merging scale). Again references to the literature should suffice.

We agree with both points 1 and 2, and have added a number of references and text throughout the paper to address these comments.

3- I suggest complete Table 3 with the missing uncertainties and Table 5 with the missing entry.

The fixed order predictions do no contain uncertainties as this is rather costly requiring 7 independent runs. The total of table 3, on the other hand, is identical to the total in table 4, hence the inclusion of uncertainties on the total. To make table 3 more consistent, we have removed the uncertainties on the total, and have added a sentence to the captions in table 3 and 4 stressing that it is only table 4 which contains the recommended predictions.

The 430 GeV point in table 5 was added at a late stage in the write-up of the manuscript. The HJ-MINLO authors did not provide this value due to time constraints. For simplicity we have removed that 430 GeV row.

Referee 2

1. While I agree that it is "well known that the pure EFT computation fails to describe the pt spectrum for transverse momenta larger than ~200 GeV," I believe the authors should still supply a reference for less familiar readers.

We have added a reference to this effect.

1. In Figure 1, the authors have uncertainty bands associated with scale variations and simply mention that it is the 7-point scale. It is not until later in the paper that this scheme is introduced. I recommend that this point be moved earlier in the paper to before the first reference to this scale.

We have added the definition to the caption.

1. In the comparison to event generators for gg fusion, Sherpa is not included. Is there an explanation for why Sherpa is not included in this section but is included in the later sections for non-gluon fusion processes and EW corrections? Since Sherpa is another major event generator, I think it is important to include it in the gluon fusion comparisons.

For the EW corrections and ttH production Sherpa has only been used as a fixed order generator. At this level the gluon fusion prediction agrees with the standard NLO result. The Sherpa authors were originally contacted when we started this project, but were unfortunately not able to provide any predictions before the note was finished. We agree with the referee that providing Sherpa predictions would be ideal. For this reason we are currently planning on setting up a more extensive study across all the sub-groups in the LHCHWG, taking into account recent progress in for instance EW corrections to ggF as well as a robust assessment of the top-mass scheme uncertainty. We will include predictions from Sherpa along with other major event generators in this study.

1. In Table 3, only the total column has uncertainties. This is the only table that does not include uncertainties on all the numbers. The authors should add those values into the table.

The fixed order predictions do no contain uncertainties as this is rather costly requiring 7 independent runs. The total of table 3, on the other hand, is identical to the total in table 4, hence the inclusion of uncertainties on the total. To make table 3 more consistent, we have removed the uncertainties on the total, and have added a sentence to the captions in table 3 and 4 stressing that it is only table 4 which contains the recommended predictions.

1. When discussing the results from MG5_MC@NLO, the authors switch to a 9-point scale with no motivation for the change just for MadGraph. This should either be justified or changed to the 7-point scale for consistency.

The apparent inconsistency in table 5 is due to the fact that we followed the uncertainty prescriptions that were used in the MiNLO and MC@NLO publications, and were recommended by the authors. We have added a footnote to clarify this.

1. Additionally, when discussing the VH production the authors only consider the 3-point scale variation without any justification for not using the 7-point scale. Again they should either justify this choice or use the 7-point scale.

For VBF and VH the 3-point scale variation has been found in previous studies to almost entirely contain the 7-point. We have added two sentences and references to this effect.

1. In the caption of Figure 4, it is unclear what is mean by "as a function of the lowest Higgs boson transverse momentum." I think it would be made more clear to change to "as a function of the Higgs boson transverse momentum cut".

We agree and have changed this.

The changes are as described in the "Author comments". Most are minor, e.g. adding of references and clarifications in the text.