OPT-IN:A multidimensional study of the structure function ratio σLT′/σ0 from hard exclusive π+ electro-production off protons in the GPD regime

[Daniel Carman]

Dear Stefan et al.,

I have red through your paper draft on the sigLT' analysis of CLAS12 RG-A data and pass along
my comments below. If you have any questions, let me know. Best of luck with the submission
and review process at the journal.

Regards,
Daniel
---------------------------------------------------------------------------
General:
 - You are not consistent with your usage of "electroproduction" vs. "electro-production" in the
   paper. I prefer the former usage. Use the same form throughout.
 - You are not consistent with your usage of "beam spin asymmetry" vs. "beam-spin asymmetry" in
   the paper. Use the same form throughout.
 - You are not consistent with your usage of "subprocess" vs. "sub-process" in the paper. Use
   the same form throughout.
 - You are not consistent with your usage of "unpolarized" vs. "un-polarized" in the paper. Use
   the same form throughout.
 - You are not consistent with your usage of comments in lists. You mix randomly usage of
   "A, B, and C" with "A, B and C". Be consistent throughout the paper.
 - You reference supplementary material, but it was not provided for review. Please send me a
   draft so that I can give feedback.
   
Page 1:
 - Abstract:
   - Line 2. Use "The study was done based ...".
   - Line 3. Use "liquid-hydrogen".
   - Line 7. Use "Generalized Parton Distributions".
   - Line 9. Use "It was found that the ...".
 - Line 18. Use "... parts [4,5] has been proven".
 - Line 29. Use "... 27,37] have shown that the ...".
 - Line 42. Use "For example, the first ...".

Page 2:
 - Line 54. Use "... and $\sigma_T$, which contribute to ...".
 - Line 55. Use "... sigma_L$, correspond to coupling to longitudinal ...".
 - Line 57. Use "... virtual photons. $\sigma_{LT}$, ...".
 - Line 62. Use "$\sigma_{LT'}$ can be expressed ...".
 - Line 63. "sub-process amplitudes". What do you mean by this term? It should be introduced here instead
    of much later in the paper (line 269).
 - Line 65. Use "For the $\pi^+$ channel, the imaginary ...".
 - Line 72. Use "... fundamental observables like the ... ($u$) and down ($d$) quarks ...".
 - Lines 83, 87, 88. Use "$t$-channel".
 - Line 90. Use "$t$-dependent".
 - Line 91. Use "... introduced in Ref. [34].".
 - Line 92. Use "elastic $\pi - N$".
 - Line 93. Use "$\rho - N$".
 - Line 94. Use "non-zero"
 - Line 96. Use "... provides a unified ... real photon point, as well as ...".
 - Line 107. Use "... ({\it i.e.} Ref. [43])".
 - Line 108. Use "... and $\phi$, while the ...".
 - Line 112. Use "... energies that were available ...".
 - Line 114. Use "higher-twist".
 - Line 115. Use "... with fine binning is needed ...".
 - Line 128. Use "... 40-55~nA, impinging ...".
 - Line 130. Do not need Ref. [44] as it was already given on line 124.
 - Line 153. Use "signal-to-background".
 - Line 155. Use "... t_{min} +1$~GeV$^2$, making a ...".

Page 3:
 - Fig. 2. Poor quality, grainy plots. Please remake.
 - Fig. 2 caption:
  - Line 3. Use "The raw distributions (upper histogram in each plot) were fit with a ...".
 - Line 160. Use "... background) was fit with a Gaussian ...".
 - Line 161. Use "third-order".
 - Line 170. Use "... see Fig. 2), and was used to estimate ...".
 - Line 179. Use "The BSA was determined ...".
 - Eq.(3). End the equation with a comma for proper punctuation.
 - Line 184. Use "$P_e$ was measured ...".
 - Line 185. Use "... of CLAS12 to be 86.3\%$\pm$2.6\%.".
 - Line 189. Use "... their uncertainty were then given ...".
 - Line 192. Use "... asymmetry was calculated based on standard error propagation.".
 - Line 197. Use "(see Eq.(1))".
 - Line 202. Use "Even in the highest $Q^2$ bin shown, a precise ...".
 - Line 203. Use "As expected, the ...".
 - Line 205. Use "... terms in Eq.(1) on $\sigma_{LT'}/\sigma_0$ was studied ...".
 - Line 207. Use "... to be on average ...".
 - Line 208. Use "... and, therefore, much smaller than ...".
 - Line 209. Use "... uncertainty, and was considered as a ...".
 - Line 214. Use "... two methods, which was on average 4.9\%, was considered as a systematic ...".
 - Line 222. Use "... by comparing the injected and ...".

Page 4:
 - Fig. 4 caption:
  - Line 1. Use "... of $\phi$ for representative $-t$ bins ...".
 - Line 223. Use "2.6\%".
 - Line 224. Use "... (3.0\%) were studied based on ...".
 - Line 228. Use "... definitions, were investigated ...".
 - Line 232. Use "On average it was found to be on the order ...".
 - Line 245. Use "... 8 and 9, which cover a ...".
 - Line 246. Use "... bins, clearly shows the ...".
 - Line 251. Use "... shape that can be explained ...".
 - Line 252. Use "The non-$\phi$-dependent cross ...".
 - Line 268. Use "$\sigma_{LT'}$ can be ...".
 - Line 273. You have two sets of closing parentheses about "eff". Use the proper set before eff.
 - Line 274. Use "{\it i.e.}".
 - Line 280. Use "... in Fig. 5, which shows ...".
 - Line 288. Use "cannot".
 - Line 292. Use "... ratio $\sigma_L$ and $\sigma_T$ can ...".
 - Eq.(8). End the equation with a period for proper punctuation.

Page 5:
 - Fig. 5 caption:
  - Line 3. Use "The blue band shows the ...".
 - Line 296. Use "... by $H_T$, while the ...".
 - Line 305. Use "... given in Eq.(9),".
 - Eq.(9). End with a period for proper punctuation.

Page 6:
 - Line 315. Use "Based on Eq.(9) ...".
 - Line 319. Use "... overall factor of 1.5 (brown dashed line) and by a factor of 2.0 ...".
 - Line 321. Use "... to such a variation ...".
 - Line 324. Use "... results is observed.".
 - Line 326. Use "... is concerned, but the consequences ...".
 - Line 335. Use "... existing data, {\it e.g.} Refs. [8,12,13,15,20), as well as the aforementioned HERMES ...".
 - Line 343. Use "... $H_T$, it will become ... to extract the tensor charge of the proton, which is ...".
 - Line 345. Use "... so far only poorly constrained.".
 - Line 346. Use "The JML model, which turns ...".
 - Line 348. Use "$Q^2$".
 - Line 348. Here and on line 366, you change notation from $W$ to $\sqrt{s}$, why? I recommend you use $W$ given
   how you have introduced your notation.
 - Line 348. Use "4~GeV". The tilde keeps the units with their values when setting up line breaks.
 - Line 354. Use "... short by a factor of two on average to reproduce the experimental values.".
 - Line 359. Use "For instance, only ...".
 - Line 365. Use "... transverse amplitude, which also misses ...".
 - Line 366. Use "... the experimental value by a factor ...".
 - Line 371. Use "... showed that, especially, the magnitude ...".
 - Line 374. Use "... fit for the dominant GPD $H_T$ ...".
 - Line 377. Use "Regge-based".
 - Line 378. Use "... underestimates $\sigma_{LT'}/\sigma_0$ ...".
 - Line 380. Use "... low $Q^2$, the Regge ...".
 - Line 382. Use "GPD-based".

References:
 - Put your citations in the order cited in the text.
 - Use "{\it et al.}" in the references.
 - For published papers, do not include the arXiv number.
 - [3] and [4] have spurious numbers "7." and "8." before the authors names.
 - [4]. Use "A.C. Irwing and R.P. Worden.
 - [5] and [6]. Put the collaboration name after the lead authors.
 - [35]. Use "{\it CLAS Collaboration}".
 - [36]. Use "{\it HERMES Collaboration}".
 - [43] and [44]. Use "{\it CLAS Collaboration}".
 - [45]. Use "M. Morhac {\it et al.}, ...".