OPT-IN: Measurement of (double-)polarization observables in the photoproduction of π+π− meson pairs off the proton using CLAS at Jefferson Laboratory

[Daniel Carman]

Dear Volker et al.,

I have read through the draft of your new paper on CLAS 2pi photoproduction data from the
FROST experiment. I detail my comments below. Mainly they are focused on improving the
grammar/style. If you have any questions, let me know. Good luck with the submission process.

Regards,
Daniel
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General:
 - Minor grammar point. You should not use a hyphen after an "ly" modifier. Proper usage is
   "transversly polarized target" not "transversely-polarized target". Please review throughout.
 - 
   
Page 1:
 - Title. I am not sure I understand the title that you have chosen. Why is "double" in parentheses?
   This form is awkward to me. Why not "Measurement of polarization observables in the ..." or
   "Measurement of single- and double-polarization observables ..."?
 - Paragraph 1. Line 23. Capitalize "Quantum Chromodynamics" for consistent usage.
 - Paragraph 2. Line 11. Use "... additional pion, resulting ...".
 - Paragraph 2. Line 15. Use "... $N(2000)5/2^+$, and ...".
 - Paragraph 2. Line 23. Use "... $({\bf 70},2_s^+)$ multiplet requires ...".
 - Paragraph 3. Line 5. The sentence "The large width ... makes the preparation of a pure ... almost
   impossible ...". I cannot understand what you are trying to say here. It seems like a word is missing
   or your thought is not complete. Please review.
 - Paragraph 3. Line 8. Do not include the parentheses about the final hadron pair listings.
 - Paragraph 3. Line 12. Use "... the evidence for an nucleon or $\Delta$ is either ...".

Page 2:
 - Paragraph 2. Line 2. Use "... the linearly polarized beam asymmetries ...".
 - Paragraph 2. Line 16. Use "... a discussion of the observed resonance contributions ...".
 - Paragraph 4. Line 14. Use "... the helicity dependent ${\bf E}$ observable ...".
 - Paragraph 4. Line 15. Use "... target polarization) for the ...".
 - Fig. 1 caption. Line 6. Use "... as the green-shaded area) ...".
 - Fig. 1 caption. Line 9. Use "... as the orange-shaded area) ...".
 - Fig. 1 caption. Line 16. Use "... permission from Ref. [29]; copyright ...".

Page 3:
 - Paragraph 2. Last line in left column. Use "... energy spectrum, known as the ...".
 - Paragraph 3. Line 5. Broken reference here.
 - Paragraph 3. Line 9. Broken reference here.
 - Fig. 2 caption. Line 1. Use "beamline".
 - Fig. 2 caption. Line 12. Use "Use "... permission from Ref. [29]; copyright ...".

Page 4:
 - Paragraph 3. Line 2. Use "... spectrometer [26] based on a toroidal magnet that provides a
   non-homogeneous magnetic field, ...".
 - Paragraph 4. Line 2. Use "... counter [36], which was ...".
 - Paragraph 6. Line 3. Use "... and, therefore, photon selection ...".

Page 5:
 - Paragraph 1. Line 9. Use "... 0.01 were measured for the ...".
 - Paragraph 1. Line 14. Use "(see Fig. 3).".
 - Paragraph 2. Line 4. Broken reference here.
 - Paragraph 2. Line 6. Use "... such as imperfect knowledge of the magnetic field ...".
 - Paragraph 3. Line 2. Use "... and, thus, considerably ...".
 - Fig. 4 caption. Line 3. Broken reference here.

Page 6:
 - Fig. 5 caption. Last line. Remove the blue text with the editing remark.
 - Paragraph 1. Line 7. Use "... and, therefore, led to ...".
 - Paragraph 1. Line 11. The term "$\beta_z$" is not defined.
 - Paragraph 1. Line 13. Use "... [39]. Figure 5 shows ...".
 - Paragraph 2. Line 4. Use "multi-variate".

Page 7:
 - Fig. 7 caption. Line 2. Use "$Q$". (math mode)
 - Fig. 7 caption. This is the only place where you used color text for "green", "red", and
   "magenta". It is not needed.
 - Paragraph 1. Line 12. Spurious "energy" should be removed.

Page 8:
 - Eq. (4). Explain the "s" and "c" superscripts on your polarization terms.
 - Paragraph 1. Line 5 after Eq.(4). Use "... beam polarizations), and the ...".
 - Paragraph 1. Line 6 after Eq.(4). There is no phi angle in Eq.(4). Please review this text.
 - Paragraph 4. Line 12. Use "... angular modulations to extract ...".

Page 9:
 - Paragraph 1. Line 1 after Eq.(8). Use "... into Eq. 7 gives:".
 - Paragraph 1. Line 1 after Eq.(9). Use "... was defined as $\overline{\Lambda}_t^+/\overline{\Lambda}_t^-$.".
 - Paragraph 3. Line 1. Use "... data can then be expressed as:".
 - Paragraph 3. Eq.(12). Add a comma after the second line of A', a comma after \Delta \Phi, and move the word
   "and" after \tilde{\delta_l}.
 - Paragraph 4. Line 2. Use "... using $A$ from Eqs. 11-12, was given by:".
 - Paragraph 4. Eq.(13). Put subscript i on event in math mode.
 - Paragraph 4. Line 2 after Eq.(14). Use "This was performed for every ...".
 - Paragraph 5. Line 3. Use ".. incident linearly polarized ...".
 - Paragraph 6. Line 2 after Eq.(16). Use "... using Eqs. 4 and 6, ...".
 - Paragraph 6. Eq.(17). Either add units of radians to "2.025" in the second and third lines or replace with
   $\phi_{offset}$ that you have already defined.
 - Paragraph 6. Line 2 after Eq.(17). Your left parenthesis on the \para symbol is incorrect.

Page 10:
 - Paragraph 1. Eq.(18). Either add units of radians to "2.025" in the second and third lines or replace with
   $\phi_{offset}$ that you have already defined.
 - Paragraph 1. Line 2 after Eq.(18). Your left parenthesis on the \para symbol is incorrect.
 - Paragraph 2. Line 1. Use "... data can then be expressed as:".
 - Paragraph 2. Equation between (19) and (20). Same comment here about unitless 2.025. Also use a comma after
   \Delta \Phi expression and move the "and" until after the \tilde{\Lambda} expression.
 - Paragraph 3. Eq.(20). Put subscript i on event in math mode.
 - Paragraph 5. Line 1. Use "data sets" for consistent usage.
 - Paragraph 5. Line 2. Do not hyphenate "beam polarization" or "target polarization".
 - Paragraph 5. Equation between (22) and (23). Add "and" after \overline{\delta_R} term.
 - Paragraph 5. Line 2 after unnumbered equation. Your left parenthesis on the \para symbol is incorrect.
 - Paragraph 5. Last line. Same comment here about "2.025".
 - Paragraph 6. Line 3. Use "Then $N_1$ was simplified to ...".
 - Paragraph 6. Eq.(23). End with a period for proper punctuation.

Page 11:
 - Paragraph 1. Line 1. Your left parentheses on "1" and "2" are incorrect.
 - Paragraph 2. Eq.(26). Put subscript i on event in math mode.
 - Paragraph 3. Line 3. Use "... as well as the ...".
 - Paragraph 4. Line 14. You state that the pi+ meson is chosen for the representation of the results. I believe
   that you need to say a bit more. In this analysis do you get additional information if you choose the pi- or
   the proton? If this is not the case in photoproduction, make an explicit statement to make this clear.
 - Paragraph 5. Line 15. Here you begin to use notation of $\cos \theta$ and $\phi$ without the pi+ subscript. I
   think that you should use $\cos \theta_{\pi^+}$ and $\phi_{\pi^+}$ for this notation consistently in the text
   and in the figures.
 - Paragraph 5. Line 21. Here you change notation and begin to list your observables not in bold font but in
   regular roman font or non-bold italics font. Please review your notation carefully and be consistent throughout
   the paper.
 - Paragraph 5. Line 25. Use "... rich structure and, in particular, the beam ...".
 - Table I. This table is confusing to me. Different observables have different systematics but you have not clearly
   differentiated them. That makes a straightforward assignment difficult and needlessly confusing. Please review.

Page 12:
 - Fig. 9 caption:
   - Line 3. Use "... other energy bin in ...".
   - Line 4. You state "Note that the energy range ... (second row) had poor statistics ...". However, the data points
     in the second row have error bars that same same as all of the other data points. Your statement does not seem
     justified.
 - Paragraph 1. See above comment on Table I.

Page 13:
 - Fig. 10 caption. Line 5. See above comment about statistical uncertainty called out for points in second row.
 - Paragraph 1. Line 2 after unnumbered equation. Use "... polarization observable, and ...".

Page 16:
 - Paragraph 1. Line 10. Why is "zero" in italics? This seems unnecessary.

Page 18:
 - Paragraph 1. Line 7. Use "... and several cascade decays ...".

Page 19:
 - Paragraph 1. Line 7. Use "... discussed in a forthcoming publication.".

Page 20:
 - You mentioned some information would be included in "supplementary" material, however, this was not provided as
   part of the review. If you have material that will be submitted in addition to the manuscript, please send it
   around of review.

Bibliography:
 - [2], [15]. Theses are the only references for which you have given the page range. Be consistent with your style
   throughout.
 - [20]. Remove spurious dash after the journal page number.
 - [40]. Use "... M. Bellis, and C.A. Meyer, ...".
 - [45]. Is listed out of order. It should go after [47].