Tagging Jets in Invisible Higgs Searches

Dear referee,

Thank you for the useful corrections.

We have looked through your suggestions and modified the paper accordingly:

1- The abstract mentions the importance of controlling single-top backgrounds. However if one examines a CMS analysis of this channel 1610.09218 (Ref.[19]), Fig.3, they have barely any background from top production. The authors should adapt and/or clarify their statements in this regard. -> The increased contribution from single top events that we see is due to the more inclusive signal definition used for machine learning approaches. However, we understand that the sentence could be misleading and therefore we have changed it from 'First, precision analyses of the central jet activity require full control of single top production.' to 'First, precision analyses of the central jet activity require full control of single top production in some analyses.'

2- In the description on p.5 of their simulation setup, some parts are carried out at LO (WBF signal), while others appear to be at NLO (given the reference to OpenLoops), such as gluon-fusion Higgs + 2 jets. It would be good to be explicit about the use of NLO for the latter. While for the former, I think it would be useful if the authors gave an indication of the expected effects of (N)NLO corrections, since these are known in many cases. -> The description of the simulation setup was unclear before. We modified the simulation setup description to clarify that our simulation is LO and OpenLoops was only used for loop-induced LO processes. We did not consider (N)NLO effects and feel that they are better left to a dedicated study.

3- p.7, two lines before Eq.(5), there's a typo "the the". -> fixed

4- On p.7, the authors state that between R=0.4 and R=0.7 the peak of the pT,j spectrum shifts by around 10 GeV. But in Fig.3 it looks closer to 5 GeV. -> fixed

5- in Eq. (8) (definition of substructure variables), the definition of pTD looks wrong. In the numerator of the first equation to the right of the equal sign the pT,i terms should appear squared, which also prevents the simplification in the right-most part of the equation. -> Thank you for pointing out this massive typo. However, the definition of pTD was only wrong in the text, not in the implementation of the variable. We have fixed the defintion in the text.

6- Still for Eq.(8) it would be better if Refs.[41,42] were replaced with references to the original articles that introduced the individual variables (rather than conference proceedings that just use them). -> We agree. The references were replaced by references to the original articles.

7- There's a typo in the last main sentence of the first big paragraph on p. 14: "even" -> "event" -> fixed

8- Relating to Fig.11(right), and also the statement in the abstract that subjet information [...] can be used to relieve some of the pressure on other critical observables: by this, the authors presumably refer to the fact that they've obtained the improvement in performance relative to the left/middle figures, despite the fact that while lowering the 3rd jet cut to 10 GeV, they've not used the 3rd jet pT as an input. However, I think an important comparison in this regard would be with a situation where they keep the lower pT cut and use the 3rd jet pT as an input (with and without jet substructure variables). I encourage the authors to add this. -> While preparing the paper this comparison was completed. However, there was no (visible) difference between including the 3rd jet pT as an input or not. Therefore we did not feel like it would add to the publication.

Thank you again for your helpful corrections.

Yours faithfully, Anke Biekoetter (on behalf of the authors)