[Clascomment] OPT-IN: First Exclusive Measurement of Deep Virtual Compton Scattering off 4 He: Toward the 3D tomography of nuclei

[Michel Gar�on]

Sorry if these comments come at the last minute (but still before the deadline). As you’ll see below, I have been looking into some equations (in the draft paper and elsewhere whenever relevant). In the end, I am still a bit confused about some issues. Please bear with me and hopefully you can clarify.

Regards,
Michel.

Issues/concerns:

1) Eqs (1,2) and previous lines: 
-	you define ksi as a function of xB, but the ksi used as a variable in HA (Eqs 1 and 2) is xA/(2_xA) according to Refs [40,41, 38]. Since the discussion of variables rests on Fig.1 which applies to He4, use xA and ksiA right away (even if you are using xB in the figures). 
-	The expressions in Eqs (1,2) are not “complex amplitudes” (l67-68). Moreover these two lines are not compatible with lines 197-198. I would write “We in fact measure a complex Compton form factor (CFF) defined as…”. 

2) Eq. (5) and subsequent lines: 
-	the explicit expressions for the alpha_i are not in [41]. In [38], it is stated on page 34 that the expressions are given in the Appendix A, but they are not there (!). The expressions can be found in the authors’ CLAS analysis note (CAN), which is not public, hence cannot be referenced. Since it takes a few lines of (straightforward but cumbersome) algebra to go from the expressions given in Refs [41, 38] to the alpha_i’s, I would write instead of l199-200:  “The factors alpha_i can be derived from expressions given in Ref. [41]. They are functions of …”. Note that “purely kinematic” should be dropped since there is a form factor dependence.
-	 The form factor FA appears both in A.15 and in A.16 of the CAN. It should not be in the latter. Is this just a typo or did you use A.16 as is in the CFF extraction for this paper ? Please check.
-	Also if you used Ref. [41] to get Eq. (5) and the expression of the alpha_i’s, Im(CFF HA) is not what you write in Eq. (2). It differs by a factor –pi (see e.g.  Eq. (5) of your ref. [42]). And I don’t see that you’ve absorbed this factor –pi in the expression of alpha_0 (5.2 of CAN p. 105).
-	I conjecture that there is a sign error in Eq. B1 of [41]. I don’t see how the replacement in their Eq. 4.21 could lead to a change of sign of S++(1) with respect to the initial kinematical factor. Besides, if you look at the analog expression for the nucleon, Eq. A1 of PRD 82, 074010 (and same in the 2012 BMJ paper), there is no minus sign in S++(1). But then, if S++(1)>0, and the factor –pi should be added, then ALU(90°) will end up being negative (for HA>0 which I assume is true). Confusion on my part ?
-	Independently of the sign issue, I gather from Liuti et al. papers that the theory curves you are plotting are Im(CFF HA) including the pi factor, and not what you write in Eq. (2). So the comparison data from Eq. (5) vs theory would be OK, but not Eq. (2).

3) L185: the form factors do not enter explicitly the DVCS amplitude. They can be obtained as an integral of the GPDs, but that does not justify the sentence.

4) It is stated that the model independent extraction is at leading twist, but this should be reiterated in the two following instances: next to Eq. (5) and in Fig. 6 caption. Otherwise, “model-independent” is too strong (and can be misleading for some readers).

5) Ref. [34] should be replaced by the published paper PRC81 (2010) 035202. Check whether the green points on Fig. 5 changed or not between the conference proceedings and the publication.

Other:

Abstract: I would not use the word “pioneering”. It is not up to us to qualify the measurement in this first publication. Either “first” or nothing. That does not remove any merit to the publication.
L94: remove “previously”.
L97: “dedicated” instead of “specialized”.
L120: “The target cell is…”
L149: “…handbag diagram is expected to be dominant,…”
L184: “the target elastic form factors”
L203: MN was M on L63; but I proposed not to use the nucleon variables there…
L207: distribution
L231: start a new paragraph for systematic uncertainties.
L253: “have larger asymmetries”
Fig.4 inserts too small. In caption: “grey”, “Eq. (5)”.
L262: Ref [43] is qualified as “convolution model” whereas in Fig. 6 caption, it is qualified as “on-shell model”.
L277: it may be better to write “… because alpha_1 is the dominant term in the denominator of Eq. (5)”, since what really matters is alpha_2*Re(CFF HA) << alpha_1, and not alpha_2 << alpha_1.
Fig. 6 inserts too small.