OPT-IN:Exclusive π− Electroproduction off the Neutron in Deuterium in the Resonance Region

[Daniel Carman]

Dear Ye, Ralf et al.,

I have read through the updated draft of your paper on exclusive pion production off the neutron.
My comments are included below. This version of the paper is in much better shape than the first
version. However, as you can imagine, with so many comments marked in the first draft, some things
were missed and some new things arose. If you have any questions, let me know. I appreciate that
you are taking my comments seriously. It is important that the paper be as well written as possible.

Regards,
Daniel

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General:
 - You are not consistent with your virtual photon notation. Sometimes you use $\gamma_v$ and
   sometimes $\gamma^*$. Please review throughout (including in Figure labels/keys).
 - Figure caption style. You had a style issue in the previous draft where the captions line were
   all different lengths (instead of evening fitting the column width). This has largely been fixed,
   but there are still several figure captions with this issue, Figs. 4, 6, 7, 9, 12, 13, 15.
 - Figure axis labels and values. Many of your figures have labels that are too small and need to
   be enlarged. I note Figs. 8, 9 11, 12, 13, 15, 16, 19.

Page 1:
 - Line 25. Use "These studies have provided ...".
 - Line 35. Use "... from the experimental results ...".
 - Line 62. Use "... of the $\gamma_vpN^*$ electrocouplings ...".
 - Line 65. Use "Coupled-channel approaches ...".
 - Line 66. Use "... extraction of the $\gamma_vpN^$ ...".
 - Line 68. Use "Recently, the $\pi N$ and $\eta p$ ...".

Page 2:
 - Line 96. Use "... results on the $\gamma_vnN^*$ ...".
 - Line 100. Use "... that underline $N^*$ ...".
 - Line 102. Use "Analyses of the $\gamma_vpN^*$ ...".
 - Line 114. Use "... modest over the entire $Q^2$ ...".
 - Line 135. Use "... validate credible insight ...".
 - Line 142. Use "... final state pion ...".
 - Eq.(1). You do not define $p_s$ in this equation until the next section. I suggest for Line 156,
   "where $p_s$ is the spectator proton in the deuteron. This process has been measured with ...".
 - Line 160. Use "... analysis procedures ...".
 - Line 161. Use "... are described in Sections II-VI".
 - Line 168. Use "... to investigate pion electroproduction ...".
 - Line 174. Use "(see Section IX)".
 - Line 178. Use "... the final state interactions ...".
 - Line 181. Use "In the process of Eq. (1) ...".

Page 3:
 - Line 216. Use "However, it is better to choose the invariant mass as $W_f = p^\nu + (\pi^-)^nu$,
    which is well defined and measured directly from the $p$ and $\pi^$, rather than as
    $W_i = q^\nu + n^\nu$, which is affected by the off-shell effects of the target nucleon, to
    present the final cross section.".
 - Line 223. Use "... rest mass of the free neutron.".
 - Fig. 1 caption:
   - Line 2. Use "... + p + p_s$ process: ...".
   - Line 3. Use "... (c) are the two main ...".
 - Line 249. Use "(deuteron rest frame)".
 - Line 252. Use "... and the four-momentum transfer $Q^2$ ...".
 - Lines 257-266. Your axis notation with subscripts "nrest", "CM", and "c.m." are unnecessarily
   confusing. Furthermore to make things more awkward, you use a different notation in Fig. 2. Please
   revisit this to be consistent and clear (and as simple and straightforward as possible).
 - Line 263. Use "... then set $\hat{z} ...".
 - Line 266. Use "... as $\cos \theta ... are also ultimately calculated ...".

Page 4:
 - Line 275. You say "identical set of detectors", but your Fig. 3 shows that this is not true. The
   large-angle calorimeters are the exception and they are not even mentioned anywhere. Perhaps a
   remark is needed that they are not considered in this analysis.
 - Line 289. Use "(see Fig. 4)".
 - Line 291. Use "... normal-conducting magnet to keep low-momentum electrons ...".
 - Line 292. Use "M{\o}ller".
 - Line 293. Use "... chambers).". (Drop "for the main CLAS torus magnets").
 - Line 298. Use "... windows (see Fig. 4).".
 - Fig. 3 caption:
   - Lines 2, 5, 6. Use "beamline".
   - Line 3. "The tracks shown correspond, ...".
 - Line 310. Use "... electron candidates ...".
 - Line 311. Use "... (inbending toward the beamline in the ...".

Page 5:
 - Line 315. Use "... output from the summing electronics gave rise to amplitude ...".
 - Line 317. Use "According to Ref. [51], the ...".
 - Fig. 6 caption:
   - Line 2. Use "... in sector 2, ...".
 - Line 321. Use "The torus magnetic field bent the electrons ...".
 - Line 346. Use ".. red curves in Fig. 7) defined as".
 - Line 349. Use "... or right photomultiplier tube (PMT) in ...".
 - Fig. 7 caption:
   - Line 1. Use "... distributions of the left ...".
   - Line 2. Use "... in the tenth CC ...".
 - Line 352. Use "The EC was used for ...".
 - Line 360. Use "... deposited energy $E_{total}$ for showering ...".
 - Line 361. Use "... proportional to their momentum, resulting in ...".

Page 6:
 - Line 363. Use "... for electrons in the EC is ....".
 - Fig. 8 caption:
   - Line 1. Use "$E_{total}/p$ versus ...".
   - y-axis. Label is inconsistent with the text.
 - Line 383. Use "... from the SC, $l_e^{SC}$ is the electron path length from the vertex to the SC
   hit, and $c$ is ...".
 - Line 391. Use "... low gain PMTs were ...".
 - Fig. 9 caption:
   - Line 1. Use "... versus $p$ distribution. (b) Proton $\Delta T$ ... for sector 1 are shown on
     each plot.".
 - Line 406. Use "... beam energy of 2.039~GeV, ...".

Page 7:
 - Line 429. Use "... mass squared for all ...".
 - Fig. 10 caption:
   - Line 7. Use "... $\sim$0.88~GeV$^2$.".
 - Line 434. Use "... to select the maximal ...".
 - Line 449. Use "... described in Ref. [54]. For protons, which were outbending (bending away from
   the beamline), momentum-independent ...".
 - Fig. 11 caption:
   - Line 4. Use "... distributions for the selected $\theta_e$ ...".
   - Comment. The vertical shaded band in the top picture is not explained in the caption.
 - Line 461. Use "... versus $p$ distributions for the particles in each sector, ...".
 - Line 464. Use "... for $\pi^-$, which was applied ...".

Page 8:
 - Fig. 12. The plots are different sizes (they should match) and the top labels need spaces between
   the momentum value and the GeV unit.
 - Fig. 12 caption:
   - Line 1. Use "... for $\pi^-$s (a) and protons (b) ...".
 - Line 468. Use "The "spectator" proton missing ...".
 - Fig. 13 caption:
   - Line 1. Use "... of $\pi^-$s in sector 2 ...".
 - Fig. 16 is referenced in the text before Fig. 15. Switch the order of the figures.

Page 9:
 - Fig. 15 caption:
   - Line 2. Use "... between the simulation thrown and reconstructed momenta.".
 - Line 493. Use "... perfectly. No meaningful difference ...".
 - Line 496. Use "... up to $\vert \vec{p}_s \vert = 200$~MeV ...".
 - Line 501. Use "... between the spectator proton ...".
 - Line 502. I do not understand the remark "corresponding to an energy transfer larger than 50 keV".
   Can you say a bit more to make your statement clear.
 - Line 508. Use "50~keV".
 - Eq.(18) last line. Use "(in~Fig.~17),"

Page 10:
 - Fig. 17 caption:
   - Line 1. Use "... momentum distribution of the "spectator" proton $\vert \vec{p}_s \vert$ of ...".
   - Line 2. Use "... black histogram) and simulation ...".
   - Line 3. Use "... blue histogram) where the ...".
 - Line 545. Use "... initial state neutron ...".
 - Lines 545 and 549. The statements "The initial neutron mass was set to the neutron rest mass." and
   "and its mass set to the proton rest mass". Are these not trivial statements? What else would you
   set the mass of the neutron and proton to be?
 - Fig. 18 caption:
   - Line 1. Remove "(Color online)".
 - Line 564. Use "To mitigate this problem, various ...".
 - Line 571. Use "Bin-centering corrections".

Page 11:
 - Line 587. Use "Acceptance-correction factors ...".
 - Line 597. Use "... passing all of the analysis ...".
 - Line 604. Your four-vector notation here has changed from what you introduced earlier. Please review
   and be consistent.
 - Line 607. Use "The same number of ...".
 - Line 608. Use "... effects were generated by the ...".
 - Line 617. Use "Finally, $RC$ was ...".
 - Line 633. Missing the closing parenthesis on the parenthetical.
 - Line 644. Use "... in Table III".

Page 12:
 - Table III.
   - What is the meaning of the entry labeled "Boosts"? What is the source of the systematic uncertainty?
   - What is the meaning of the entry labeled "Potential"? How did you estimate the systematic uncertainty?
   - Please add a single horizontal line before the "Total" line to set it off.
 - Line 648. Use "in the CLAS Physics Database [ref]". (As this is the first mention, you need the ref. here.)
 - Line 650. Use "... systematic uncertainty is the yield normalization.".
 - Line 655. Use "... we also cross-checked against ...".
 - Line 658. Use "We found that the ...".
 - Eq.(24). Note here and elsewhere your differential notation is not consistent. You have d^2 on the LHS
   and d^4 on the next cross section. In reality you should use "\frac{d^2}{d\Omega}", the notation
   "\frac{d\sigma}{d\Omega}" is a shorthand notation. Please review your  notation to avoid inconsistencies.
 - Eq.(24). There is a spurious minus sign on your "d^4\sigma$ term on the "d\Omega" subscript.
 - Line 674. Use "... the bin-centering correction ...".
 - Line 680. Use "... liquid-deuterium, $l_T$ is the ...".
 - Line 686. You different cross section terms are a bit confusing. How about using "... is the cross section
   $\frac{d\sigma^{ex}}{d\Omega_\pi^{c.m.}}$ calculated after ..."?

Page 13:
 - Line 696. Use "... to Eq.(23) by".
 - Line 714. Use "... with increasing $\vert \vec{p}_s \vert$".
 - Line 722. Use "... process defined by".
 - Line 725. Your four-vector notation here is different that what you introduced earlier. Please review and
   be consistent with your notation.
 - Line 751. Use "... are represented by the ...".
 - Line 769. Use "... simulation are smaller than ...".
 - Line 785. Use "... from the measurements reported here demonstrates ...". (Drop "and shown in Figs. 23-25".)

Page 14:
 - Fig. 20, 21, 22:
   - On your W labels, add a space between the value and the GeV unit.
   - I do not see the value added by including Figs. 21 and 22. The value is pretty much flat at 0.8. Too
     many figures included in the paper of a trivial nature (or easily explainable in words) will ultimately
     detract from your main physics results.
 - Line 797. Use "... one-photon-exchange approximation ...".
 - Line 798. Use ".. the $\phi_\pi^{c.m.}$ angular distributions ...".
 - Eq.(31). In the last two lines use "\sin" to keep the sine in roman font.

Page 15:
 - Line 843. Use "(see Fig. 26)".
 - Line 854. Use "Here, the $\pi N$ ...".
 - Line 869. Use "At $\cos \theta_\pi^{c.m.} < 0.5$, the ...".

Page 16:
 - Fig. 22 caption:
   - Inconsistent spacing about the inequality symbols.
 - Line 875. In referring to Fig. 27 you state that there should be agreement between the pi-n and pi+p
   results. You explicitly point out the good agreement for cos \theta < 0.5. However, you say nothing about
   the range cos \theta > 0.5 where the results are very different. You need to say something here about
   what is going on. (There is an elephant in the room that cannot be ignored.)
 - Line 882. Use ".. can be written as".
 - Line 887. Use "$l$ is the orbital angular momentum of the ...".
 - Eq.(35), (36), (37): These equations should be removed. They are just a trivial re-expression of
   Eqs(32)-(34).

Page 17:
 - Fig. 23, 24, 25 caption:
   - Line 1. Steradians are abbreviated as "sr" not "Sr".
 - Line 914. Use "... model [56] by ...".
 - Line 922. Use "... sensitivity of $A_0 ...".
 - Line 927. Use "by the measurements.".

Page 18:
 - Figs. 24 and 25 caption:
   - Line 5. Use "... world data [44-46].".
 - Line 951. Use "... dependence of the $\sigma_{LT}$ ...".

Page 19:
 - Fig. 25. Why is the range of cos \theta shown here not the same as for Figs. 23 and 24? Perhaps you
   should make a note in the caption.
 - Line 974. Use "dataset".
 - Line 981. Use "... electroproduction are about ...".
 - Line 985. Use "... assuming the one-photon-exchange ...".
 - Line 991. Use "... further support the reliable extraction ...".
 - Line 1013. "... by running further exclusive deuterium target experiments ...". Those experiments have
   already by run (RG-B, RG-M). I recommend you review your statement. The data, as they say, is already in
   the can.

Page 20:
 - Fig. 26 caption:
   - Line 7. Use "... MAID2007 [56] (blue line) models."
   - Line 9. The final sentence should end with a period.
 - Line 1026. Use "... Department of the University".
 - Line 1027. Use "... (USC), Jefferson ...".
 - Line 1028. Use "... (JSA), the National ... of Korea, and the ...".
 - Eq.(A3). Use "\sin".
 - Line 1038. Use "... beam energy, and ...".
 - Line 1040. Use "... $\Omega_\pi^{c.m.}$ corresponds ...".
 - Line 1041. Use "... outgoing $\pi^-$, and ...".
 - Line 1043. Use "\sin".
 - Eq.(A5). Use "\tan".
 - Eq.(A6). Use "\tan".
 - Eq.(A7). End with a period for proper punctuation.

Page 21:
 - Fig. 27 caption:
   - Line 3. Use "... available CLAS $\pi^+n$ electroproduction cross section results (magenta points).".
   - Line 5. End the last sentence with a period for proper punctuation.
 - Ref.[8]. This is not a CLAS Collaboration paper.

Page 22:
 - Fig. 28 caption:
   - Line 6. Use "... (black dashed lines) and ... (black solid lines).".

Page 26:
 - Ref.[68]. First author should be "A.N. Hiller Blin".