[Clascomment] OPT-IN:Longitudinal target-spin asymmetries for deeply virtual Compton scattering

[Silvia Niccolai]

Dear Michel,
thanks for your comments. Here are our replies to some of your points:

On Tue, 7 Oct 2014, Michel Garçon wrote:

> - In the abstract and in some instances in the text, the TSA are qualified as a
> signature of the DVCS/BH interference. Strictly speaking, any process 
> which conserves helicity will, when interfering with BH, generate a 
> sin(phi) spin asymmetry. In addition, DVCS2 can also generate a sin(phi) 
> term at leading twist: see BMJ, arXiv:1212.6674, eqs 41 and 49. What is 
> true is that within all GPD models, BSA and TSA arise mostly from 
> DVCS/BH interference. So instead of "which are a signature
> of the interference...", something like "which are expected to arise 
> mostly from the interference".

First of all, we don't mention sin(phi) in the abstract. We only say that 
the asymmetry is a signature of the DVCS/BH interference. And this is 
basically the same wording of all the previous CLAS DVCS papers (Stepan, 
FX's and Shifeng), which were (especially FX's) at around our same 
kinematics.
Here are the words from FX's abstract:
"These asymmetries result from the interference of the Bethe-Heitler 
process and of deeply virtual Compton scattering."
Here is Shifeng's abstract:
"A significant azimuthal angular dependence was observed, resulting from 
the interference of the deeply virtual Compton scattering and 
Bethe-Heitler processes."
I don't see why only in our case we should "soften" this statement, 
with words like the ones you suggest, when we are in the same kinematics 
as our predecessors. 
Besides, are you sure that the sin(phi) coming from the DVCS term appears 
at leading-twist? In the BMK paper I usually refer to when I want to 
understand this stuff (Nucl.Phys. B629 (2002) 323-392, ref [6]) the 
sin(phi) DVCS term (eq. 26, and eq. 47) is said to be a twist-three term. 
In has a "K" coefficient, which is suppressed at leading twist. This is also said in 
words esplicitly at page 10 and at page 14.
Have things changed from that BMK to the BMJ you refer to? It is a bit 
more difficult for me to understand this new paper as I haven't read it 
yet, and it seems a bit out of our scope, as it refers to VCS and not 
DVCS. However, at page 8 of BMJ they lists the changes compared to the 
previous paper, but nothing seems as drastic as "the sin(phi)_DVCS term 
passed from being higher twist to leading twist". Please elucidate.

However, from yours and other's comments we realize that we have been 
probably too drastic in not mentioning at all the leading-twist 
approximation in the abstract (this was done to follow our Ad Hoc 
committee's request not to be too technical in the abstract, and "twist" 
is an obscure concept), so we now include this 
modification in the abstract:
"In the framework of Generalized Parton Distributions (GPDs), at leading 
twist, the $t$ dependence of these asymmetries provides insight on the 
spatial distribution of the axial charge of the proton, which appears to 
be focused in its center."

> - Abstract last line: chiral-even GPDs.

OK.

> _ line 47: Q2 = -(e-e')2

OK.

> - line 56: remove "exactly", which is antinomic with perturbative (in a
perturbative expansion, there is always a truncation).

OK.

> - line 67-68: "The BH process has a larger contribution to the cross section
than DVCS in most of the phase space, but ..."

This sentence has already been modified, following another collaborator's 
comment, as follows: "At the cross-section level BH is typically larger 
than DVCS..."

> - line 76: statement is not correct (see first comment).

I am not convinced, I think this is true at leading twist, and the 
sentence specifies this.

> - line 78: the Compton form factors were introduced earlier, e.g. in ref[6].
> The alternate definition in Ref [8] leads to ambiguities, like in line 
> 101-102: there you mean the four ImF (in Ref[8] definition), which are 
> not imaginary !!
> The 4 CFFs in [6] are imaginary, the 8 in [8] are real. I would strongly 
> urge that we use the definition of [6], and then we can talk 
> unambiguously of their
> real and imaginary parts.

The word imaginary (which appeared only in one place) has been removed, 
we are using now "the four ImF" as you said. In ref. [6] I don't find a 
definition of the CFFs that can be as compact and simple as the one I 
report here. Now the paper doesn't contain mention of any real or 
imaginary part.

> - line 80: "a "generic" GPD" -> "any of the four GPDs"

OK.

> - line 82-83: more precise to say "quark-helicity (in)dependent" than "spin (in)dependent".

OK.

> - line 94: subscript in a1.

OK.

> - line 98: should not there be a Q2 dependence as well ?

Yes, you are right, corrected.

> - line 110: see first comment

See reply.

> - line 118: can safely remove "DVCS/BH" here.

OK.

> - line 157-158: latex for degrees: $^{\circ}$.

OK.

> - line 171 and 203: replace DVCS by e'p'gamma

OK.

> - line 217 (optional): strictly speaking, it would be better to state that this
(small!) correction is model-dependent.

We have removed a sentence describing it following the advice of our Ad 
Hoc committee. In the long paper that we are about to also publish (half 
way through Ad Hoc review) we'll include a table with the bin-by-bin 
values of the correction. You'll see that it is so small that it is not 
worth to spend too many words - and words that can scare, such as 
"model-dependent" - for it.

> - line 234: 15% instead of 14.8. (hard to calim such a precision on the systematic uncertainty!)

OK.

> - line 241: see first comment

Added "at leading twist" in the sentence.

> - line 264-265: the statement that TSA is mostly sensitive to H_tilde may not be correct.
> The main (and comparable) contributions to TSA come from both H and 
> H_tilde. You could illustrate this by plotting in fig.3 either H only or 
> H_tilde only contributions (not necessarily for the paper, but to verify 
> my statement). I think this must be made clear in the paper. BSA is 
> mostly sensitive to H, while TSA has an added sensitivity to H_tilde.
> Then this will temper the conclusions about the t-slope uniquely 
> attributed to H_tilde.

If we don't make assumptions on the relative size of H and Htilde, and 
look only at the coefficients in front of the various CFFs, you'll agree 
with us that Htilde dominates the TSA at our kinematics. In your
follow-up email you compute the ratio of the two pieces of the TSA (the H 
and Htilde ones), using also approximate values for H and Htilde and 
obtain a ratio of almost 1. In our original eg1-dvcs proposal using 
similar arguments we had arrived at the expression TSA ~ Htilde + 1/2 H.

Let me say that here your extrapolating the t=0 case (for which, 
if I follow correctly your calculations, Htilde/H ~ 1/8) to all t, is not 
necessarily correct in my opinion.

You can judge this by looking at the attached plot.

It shows the CFFs ImH (black) and ImHtilde (red) that we extracted using 
our TSA, BSA and DSA from this experiment and Michel's fitting code. As 
you can see, apart from the lowest t bin, where there is about a factor of 
2 between the two CFFs, the difference is not that strong for higher t 
values, due to the sharp difference in t-slope (which is what we 
discuss in our paper) between the two CFFs. So, If we assume a different 
relative ratio (such as 2, as we did for the proposal, if not less) 
between Htilde and H, our statements of the TSA being mostly sensitive to 
Htilde don't seem unreasonable to me.

Still looking at our CFF plot, I would also say that also the relative 
error bars of ImH and ImHtilde show that our data are particularly 
sensitive to Htilde, as it has smaller error bars - and in 
this fitting method the size of the error bars somehow reflects the 
sensitivity of each parameter to the combination of observables adopted.

Finally, reasoning in another way, the t slopes of the BSA and the TSA are 
very different. If the BSA is all due to ImH, and the TSA is a mixture of 
H and Htilde, the difference in slope to me is to be attributed to Htilde.

So, I don't see the need to soften our statements, which are not, anyway, 
very strong ones: in the abstract we say "...provides insight on the 
spatial distribution of the axial charge...". In the conclusions we say 
"the t slope of the asymmetry,..., suggests,...". Our wording is cautious 
enough.

> - Fig 4 caption: HERMES uses a moment (which I do not like because of
the denominator); it should be stated at the end of the first sentence
that it is not exactly the same quantity which is plotted: after "sin(phi)
amplitude of AUL", add in paranthesis "(alpha, or AUL(90°), or sin(phi)
  moment of AUL depending on the publication, all definitions giving the
same results within the present uncertainties)".

We are aware of the analysis method adopted by HERMES and Shifeng (and we 
don't like it either). In the text we specify that to make the comparison 
with the world data we have changed our fitting function, removed the 
denominator and added the sin(2phi) term. So we are comparing the 
sin(phi) term obtained using the same function.

> - line 332: arising mostly from

...

> - line 347-349: the statement is too strong, first because not only H_tilde
> contributes to TSA, second because GPD models at leading twist are not 
> expected to be valid when t/Q2 is not small.

Sentence on higher-twists is added in the conclusions: "Thanks to their 
vast $t$ coverage, our results can also provide a starting point to 
understand higher-twist effects." This emphasizes the positive of our 
data.

> - ref [6]: consider adding (within the same reference): BMJ, arXiv:1212.6674
> (I do not know why it is not published...); BMK did not give the 
> formulae for TSA.

I need to need this paper first and understand if it really applies to our 
case, given that it is for quasi-real Compton scattering.

> - ref[17]: add in the same reference which parameterization of the FF is used.

OK.

> - ref[20]: I believe it is published in EPJC 53, 349 (2008). Please check it is the same.

It is a bit different but actually seems better. Thanks for finding it!

> That's all!

We hope the new version that we'll release once the review period is over 
will satisfy you.

Thank you again and best regards,
Silvia

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