Higgs-Boson Decays: Updates

We would like to thank the referee for their careful investigation of our paper. In the following we respond to the individual points raised.

• We have extended the abstract to shortly summarize what has been done in this work. We left the introduction unchanged, since we believe that it is suitable.
• We have modified Section 2 to clarify the misleading description of details about the proper definition and implementation of the NLO quark-mass effects. We have only included top and bottom NLO mass effects, since charm mass effects will be too small. In this context it should be kept in mind that \Delta E parametrizes the NLO mass effects on top of the LO ones that are taken into account by the full LO width.
• We have rewritten Section 4.1 to make it different from the text in Ref. [79], while keeping the same content. Since both of this is our own work, we do not see a problem related to plagiarism, because Ref. [79] is a working group report as well. The main purpose of this section is to make the real meaning and relevance of the numbers given in Table 1 clear, i.e. they just correspond to the integrals of the red curves plus their end-point contributions in terms of the LO width and the virtual corrections. Without Section 4.1 the numbers in Table 1 will loose their precise definition which will be a major harm to our write-up. However, since this is just a working group report, we do not see a problem with the omission of the interference term in Fig. 3 for the weak Dalitz decay. This is ongoing work and will be published independently in a larger context quite soon so that this issue is beyond the scope of this work. There are many more details connected to the subleading contributions. The situation of being a status report should not be a problem for publishing this in Report 5.

We hope that we coped with and answered the comments of the referee appropriately so that the paper can now be published.

P.S. Following our understanding of SciPost guidelines, we are not attaching the new version of the manuscript to this reply, but of course it can be made available upon request.

Best regards, The Authors