HEJ 2.2: W boson pairs and Higgs boson plus jet production at high energies

We again thank the referees for their reports. Following their
comments and suggestions we have changed the manuscript as follows.

- The requested change 1) in Report 1 is to clarify the momentum
assignment for the outgoing partons with flavours fa, fb. To this
end, we have added the following sentences to the paragraph before
equation (2): "This implies that the outgoing parton with flavour fa
has momentum p1 and the outgoing parton with flavour fb has momentum
pn. However, note that this identification does not necessarily hold
at NLL. For example, if there is an unordered gluon in the backward
direction then the outgoing parton with flavour fa has momentum p2."

- In the same report, requested change 2) is to comment on the number
of active flavours and the role of the top-quark mass. We have added
the sentence "We use a diagonal CKM matrix and do not include
third-generation quarks/anti-quarks, i.e. the number of active
flavours is 4." to the first paragraph of section 2.2. We have
further verified that this statement is consistent with the run
cards in section 3.1.

- In their requested change 3) the referee suggests defining the scale
H_T. We have added the definition at the start of section 3.1.

- Requested change 4) in Report 1 and requested change 1) in Report 3
is to add labels on the y axis of Figure 2 (left). We have extended
the plot range such that labels are shown.

- Following the SciPost requirement of benchmarking tests pointed out
in Reports 1 and 3 we have added reference cross sections to all
examples in section 3. We also show reference distributions for each
example in sections 3.1 and 3.2. To facilitate reproducing these
results, we have slightly modified the examples and extended the
explanations, in particular the discussion of the separate low and
high transverse momentum runs at the end of section 3.1.3.

- As further pointed out in Report 1, SciPost requires detailed
instructions on downloading, installing and running the software. We
have added a new appendix A with these instructions.

- In Report 2 it is pointed out that the integrated cross section in
Figure 2 is much smaller than expected. In order to explain this
seeming discrepancy we have added the sentence "We observe that the
bulk of the events does not pass the analysis cuts." at the end of
section 3.2.1.

In addition to these requested changes we have modified the document
as follows.

- We have added a reference to version 2 of OpenLoops at the start of
section 3.2.1.

- We have added the following open access statement to the
acknowledgements: "For the purpose of open access, the authors have
applied a Creative Commons Attribution (CC BY) licence to any Author
Accepted Manuscript version arising from this submission."

- We have corrected the ordering of the authors.

- In the NLO reweighting example in section 3.2.2 the leading-order
contribution for Higgs plus dijet production was missing from the
truncated HEJ prediction. We have added an explanation and a
description for adding this component.

- We have corrected various typographical errors, including
inconsistent file names in the examples.