Probing Proton Structure at the Large Hadron electron Collider

I would like to thank the authors for their replies and the implemented changes.

As the authors state, it appears that there is a basic difference in our views about what are the goals
and the potential of a new high energy electron-proton collider versus the current status for the resolution of proton structure and the development and test of QCD. The present PDF analyses essentially depend on HERA, complemented by a plethora of different, and partially incompatible LHC data. I of course fully agree with the authors that we
have to use the precious LHC data as best as we can also for constraints on the proton structure.

The LHeC, then, would have the goal to unravel not yet known secrets of the proton structure going very deep,
because of the theoretical and experimental cleanliness of DIS vs pp. The goal is to provide an ultimate
new set of PDFs with the LHeC and confront the pp data and PDF analyses of the kind the authors have been
successfully performing. This fundamentally and conceptually differs from establishing a complementarity
between ep and pp which is celebrated in the abstract and runs thru the whole paper. Like the authors
also state, there are different views, and I understand that we differ here, and acknowledge the validity of the fit results the authors present. One needs to understand that the LHC is real, HL-LHC a hopeful future and LHeC so far
only a concept one hopes will be realised. I fully acknowledge that the value of the LHeC data,
here still restricted to inclusive NC+CC and HQ simulated data, is made clear in the paper.

Please let me iterate for a moment why I am convinced about the special role of DIS vs pp. Here I like to bring forward e.g. the excellent talk by Stefano Forte in 2014 about the basic difference determine PDFs at a hadron collider versus an ep collider.
https://indico.cern.ch/event/183282/session/4/contribution/21/material/slides/0.pdf

In summary, I may also quote from the paper "On the Relation of the LHeC and the LHC"
by J. L. Abelleira Fernandez et al., arXiv:1211.5102

"In fact, because factorisation is most reliably established in deep inelastic scattering, it is the availability of precise parton distributions from lepton-hadron scattering which may allow detailed tests of the validity of factorisation for processes for which it is less well established. On the other hand, because lepton-hadron data are generally subject to smaller power-suppressed corrections, perturbatively more stable, easier to compute than most hadronic processes so results to the highest perturbative orders are available, and finally free of many complications which arise when dealing with hadronic initial and final states (such as jet definitions, or underlying event), lepton-proton data always provide a comparatively more competitive and theoretically reliable determination of parton distributions than hadron-hadron data. The natural scenario is one in which lepton-proton data are used to determine parton distributions, and the latter are then used for hadron collider processes, and there are strong reasons of principle why this is the case."

Hence I indeed request that you remove the statement about the 'complementarity of ep and pp data' e.g. remove the last sentence of the abstract and also later in the summary.

Further on the abstract it is important to realise that the high x potential of the LHeC data vs LHC has not been evaluated at the same footing because the LHeC jet data have not been available. Please add the word 'inclusive' in front of the LHeC data mentioned in the abstract (second last sentence) and elsewhere (e.g. in the summary p13) to make it very clear, in the abstract you correctly state the used data, however, the word "inclusive" will help the reader to understand clearer the origin when you present the low x and high x data results.

Minor comments are:
Table 2.1 : I see that the author of http://hep.ph.liv.ac.uk/~mklein/lhecdata/datlhecreadme
made here the comment of eta<5, however, if I check the tables of data, the actual eta of usable data is eta<4.4,
anyway, in the context of your cuts it may not matter
What I still do not understand, is if you used 1 ab-1 for e+p data or if this is a typo in the table. As Ref. [26] states, e+p luminosity is at most 0.1 ab-1. The availability of positrons in the linac-ring ep configuration is much inferior to electrons. Your results will not depend on this as you find that above a few 10 or so fb-1 the uncertainty is systematics limited.

Page 4, paragraph 2.1, line 14: In the current scenario, the charm e+p data would constrain strange like e-p would constrain anti-strange. It would be interesting to see how one may constrain s-sbar from these two measurements. One could probably use the same simulation also for e+ and consider the correlated systematics the same.

I thank for the clarification on the data simulation, while still believing that the person who provides all data would usually be a co-author of a publication. I believe this is for clarification in this case with Max Klein, and not for the referee eventually to decide.

I did not make comments to disappoint the authors but for the reason, as sketched and cited above, that with many theorists and experimentalists I hold a different opinion. In our discussion, which is known to be ongoing, it may only help if different views are expressed and explained.
To reflect and acknowledge the other view, I recommend that you add the before mentioned Ref. [arXiv:1211.5102] to your paper.

There also seems to be a misunderstanding w.r.t. used parameterisation: The parameterisation for LHeC will be determined by the LHeC data and, due to much higher statistics and range, it will surely differ, both from the HERA ansatz, also because ALL PDFs will be determined not just uv, dv, sea, c, b, xg, but as well ubar ne dbar, strange, top and all with much higher precision. It will be a "wonderful world" for QCD and PDFs and I sense there is no disagreement about that expectation with the authors.

I recommend the paper for approval with the small changes as suggested above (excluding the s,sbar fit which is a separate study) and would be grateful if the text was adjusted towards a recognition of the differences of ep and pp, which does not diminish the results currently obtained in global fit analyses such as the ones of the present authors.

See in Report box.

The authors have addressed all comments of the previous report in a satisfactory manner. I recommend publication.

I am now happy that this paper be published. I note a few 'typos' in requested changes below--basically the legends in Figs5.2,5.4 and 5.5,5.6 will not be obvious to a non-expert, or indeed if these figures are used alone, not with their companions 5.1and 5.3.
I am sure the authors will wish to correct this. I don't need to see the paper again.

I have one general comment and it concerns the authors' reply to referee 2.
The authors rightly note that T=1 may not even be applicable to HERA, with which I can- at least partially- agree, and from this deduce that it also would not be applicable to the LHeC, with which I do not agree.
The point is that at the time that HERA was running there was still a focus on finding new physics there and although measurements related to PDFs were considered very important, they were not the paramount aim. Hence insufficient attention was paid to the full consistency of methods of deriving systematic uncertainties both within and between the experiments. This is why it took until 2015 to disentangle all this information to the best of our ability- and some discrepancies remain. In the case of the LHeC the DIS cross sections needed for PDFs will/would be the paramount aim. We have learnt a lot from HERA and we would have accords as to how to handle systematics. The data will/would be analysed in a consistent manner across the whole kinematic plane, and from year to year. Hence T=1 really could be the correct tolerance.

Figs 5.2 and 5.4 have both lost the +LHeC from the second appearance of HERAPDF in their legends. Just compare to 5.1 and 5.3 to see what I mean.
In Figs 5.5 and 5.6 (and I thank the authors for aving added 5.6 as I requested..) I think the green line at unity is now the PDF4LHC profiling result (it was the pre-profling result in may previous figures) for comparison to the HERAPDF profling results. But the legend does not actually specify this. I think it needs to so that the figure can be used 'stand-alone'.