The Gauge-Higgs Legacy of the LHC Run II

1) Fit with new Run2 Data
2) The authors take the opportunity to re-discuss practices that have become common in the literature (in particular they quantify the extend to which operators that enter EW observables can be neglected in the context of Higgs physics)

1) Physics content not very innovative
2) Some explanations not very clear (see requested changes)

To be published after adressing comments below.

1) The authors mention Triple gauge vertices (TGV) in section 2, before including the operators of eq 8, some of which also enter diboson pair production and play therefore a role in the extraction of TGV. I did not understand whether these effects (eq 8 in dibosons and the extraction of TGV) has been taken into account?

2) In the context of Fig.1, the third and fourth diagrams are described as providing different energy growth (it is said that the third is accompanied by a propagator, while the fourth is not). It seems to me that, when included in the amplitude, diagrams 3-4 give exactly the same contribution (the momentum in vertex 3, and the one from a SM triple gauge vertex will compensate the $p^2$ in the propagator).
Moreover in the caption it is said that the scaling with $v$ is generated by the non abelian component; I don't understand this statement.

3) In the last paragraph of section 4: the authors say that the tG operator enters $tt$ production, which tests it much better than $tth$.
It is not obvious to me that this dominance will always persist: it enters $tt$ with the opposite chirality (helicity in the $E\gg m_t$ limit) w.r.t the SM, so it doesn't interfere at the leading order in $E/m_t$; moreover the $tG$ operator is suppressed by an insertion of $v$ in the $tt$ process. On the other hand this operator sources the same helicity as $tth$ in the SM and it represents a contact interaction for $tth$, so that it must grow as $E^2/Lambda^2$ w.r.t. the SM.
So I expect that, as the collider energy increases (as in Run 2), tth might play more and more of an important role.

4) In p.10 it is said that $h\to 4l$ can be neglected in a global analysis; are the authors referring to the differential measurement or even the branching fraction?

5) Figure 5: I find it confusing that the shaded band does not include the SM, which lies between the opposite signs of the coefficient. Also the units don't match (shouldn't it be TeV$^2$?).

6) top of p13: the authors mention that the error bars in fig 3 are not gaussian and symmetric: is there a quantitative way to relate these shapes to statements about, say, the relative size of linear and quadratic terms (I guess this is where the authors are heading)? Also, further down \emph{extremely successful} Run I measurements: is this for a statistical fluctuation?

7) Fig.6 and discussion in p14. I have similar comments as above for fig1.
It doesn't seem to me that the scalings in eq 20 can be used to conclude their impact on the amplitude: longitudinal vector polarizations have power of $E/v$ that also enter and compensates for the powers of $v$ at numerator in eq 20. It seems to me that these vertices have the same size in diagrams.

Moreover: what couplings are the authors referring to in the last paragraph of p 14?

1 Precise and careful reanalysis of experimental data.
2 Systematic approach in terms of operators

1 We already had bounds, the new ones don't have a significant impact
2 Simpler approaches give most of the information

The paper presents a detailed accurate updated analysis of precision bounds on extra dimensional operators, including data from the LHC collider. While experts can appreciate the systematic approach, the paper does not add much to what we already knew

In my opinion the paper can be published in its present form