A Journey into the Proton Structure: Progresses and Challenges

Round 1

Reviewer 1 Report

Very well written short manuscript describing progresses and challenges in the extraction of TMD parton densities.   

Two minor comments for the authors to consider:

The font on on the axis of Figure two is too small and should be increased to make them clearly visible.

This manuscript focuses on gluon dominated distributions (low x), which is great, but I think it would be appropriate to to add a few sentences about the current fixed target programs (e.g. CLAS12) that are providing the information about the valence quark region (high x) and of course it all needs to go together to get a complete 3D picture of the proton.

Author Response

I thank the Referee for her/his careful reading and for her/his valuable comments. 
I list here answers to points raised. 
For the sake of readability, the corresponding changes and/or additions in the revised version of the manuscript have been marked up in blue color by making use of the “Changes” package in LaTeX.

Answers to Referee's points:

1. The font size of axes in panels of Fig. 2 has been enlarged.

2. Two new sentences on future fixed-target programs at the JLab and the LHC, together with new Refs. [215-230] were added at the end of Section 3 (Prospects).

Further remarks:

A. I have added a new paragaph to Section 1 (please also note a slight change of the section title) emphaisizing the physical interpretation of TMD, shortly introducing GPD and addressing their mutual relations. Furthermore, new Refs.[26-46] have been added.

B. I have added two new paragraphs to Section 2 the TMD factorization status both in the quark and in the gluon sector. Contextually, new Refs. [66-84] have been added.

C. Some references, now published papers, were automatically updated via BibTeX.

D. Old Ref. [169] was removed, since it was a mere duplicate of old Ref. [170] (now Ref. [205]).

E. Added new Refs. [151, 213, 214] on the natural stability of the high-energy resummation.

Reviewer 2 Report

This is an interesting introduction to the TMD distributions

with a comprehensive list of References.

I recommend  to accept it after minor revisions. Namely, physical interpretation of TMD distributions would be useful for a reader along with comments on their relations with GPD functions. Also, the status of TMD factorization deserves further comments in view of the mentioned TMD process dependence. Some textual corrections are needed, e.g."bind us al"

Author Response

I thank the Referee for her/his careful reading and for her/his valuable comments. 
I list here answers to points raised. 
For the sake of readability, the corresponding changes and/or additions in the revised version of the manuscript have been marked up in blue color by making use of the “Changes” package in LaTeX.

Answers to Referee's points:

1. I have added a new paragraph to Section 1 (please also note a slight change of the section title) emphasizing the physical interpretation of TMD, shortly introducing GPD and addressing their mutual relations. Furthermore, new Refs. [26-46] have been added.

2. I have added two new paragraphs to Section 2 the TMD factorization status both in the quark and in the gluon sector. Contextually, new Refs. [66-84] have been added.

3. Thanks for spotting the misprint, which has been corrected now.

Further remarks:

A. The font size of axes in panels of Fig. 2 has been enlarged.

B. Two new sentences on future fixed-target programs at the JLab and the LHC, together with new Refs. [215-230] were added at the end of Section 3 (Prospects).

C. Some references, now published papers, were automatically updated via BibTeX.

D. Old Ref. [169] was removed, since it was a mere duplicate of old Ref. [170] (now Ref. [205]).

E. Added new Refs. [151, 213, 214] on the natural stability of the high-energy resummation.

Reviewer 3 Report

This paper is a timely and clearly written review of a subject that is becoming
increasingly active, both in theory and experiment, and which is unfortunately
still lacking high quality reviews of this type.   I therefore have no
hesitation of recommending it be published.  People entering the field need
manuscripts like this.

However, there is one issue that needs to be added and discussed.  TMDs
are not the only tomographic observables being currently investigated,
for they refer to the proton's "momentum structure".  The roughly
complementary spacetime picture is parametrized by GPDs.  These are investigated via different observables and
are in a rough sense unobservable together due to the equivalence
principle. Finding a clear explanation of this to outsiders is a very
challenging task.

I strongly recommend the author adds a paragraph to the introduction
discussing the
distinction between GPDs and TMDs, and gives appropriate references. I
say this because it would make this review a lot more useful for
outsiders interested in the field of which they are many.

Author Response

I thank the Referee for her/his careful reading and for her/his valuable comments. 
I list here answers to points raised. 
For the sake of readability, the corresponding changes and/or additions in the revised version of the manuscript have been marked up in blue color by making use of the “Changes” package in LaTeX.

Answers to Referee's points:

1. I have added a new paragraph to Section 1 (please also note a slight change of the section title) emphasizing the physical interpretation of TMD, shortly introducing GPD and addressing their mutual relations. Furthermore, new Refs.[26-46] have been added.

Further remarks:

A. I have added two new paragraphs to Section 2 the TMD factorization status both in the quark and in the gluon sector. Contextually, new Refs. [66-84] have been added.

B. The font size of axes in panels of Fig. 2 has been enlarged.

C. Two new sentences on future fixed-target programs at the JLab and the LHC, together with new Refs. [215-230] were added at the end of Section 3 (Prospects).

D. Some references, now published papers, were automatically updated via BibTeX.

E. Old Ref. [169] was removed, since it was a mere duplicate of old Ref. [170] (now Ref. [205]).

F. Added new Refs. [151, 213, 214] on the natural stability of the high-energy resummation.