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

[Silvia Niccolai]

Hello Stepan,
thank you a lot for your comments. Here are our replies to some of the 
points you raise:

> abstract - phrase "..., which are a signature of the interference of the deeply virtual Compton
> scattering and the Bethe-Heitler processes, ..." strictly speaking this is not true, in DVCS amplitude there is a term
> $s^{DVCS}_{1,LP}$ that can generate sin(\phi) modulation.

Looking at Belitsky's paper, the s^{DVCS}_{1,LP} term you mention is 
the one coming from the DVCS^2 contribution.
This term appears with a K (~t/Q2(1-xB)...) coefficient, which means that 
this should be suppressed at leading twist. In the Belitsky paper, the 
s^{DVCS}_{1,LP} term is indeed said to appear only from twist three.
We think that for the abstract limiting ourselves to discuss the main 
sin(phi) component, which is the one due to the interference term, is 
appropriate. Otherwise, how else would you propose to phrase it?

> line 27 - remove "and" after coma, nucleons are hadrons

Yes, and in fact we say "nucleons in particular".

> line 31 - it use to be called Deep Inelastic Scattering (DIS), not deeply inelastic scattering

OK. Changed.

> line 38 - sentence make no sense, should be revised. What it means "... considering only quark GPDs ..., there are four different GPDs ...

It means neglecting gluon GPDs. Usually the typical sentence 
is "considering only the quark sector". We changed it this way to make it 
more understandable for a general audience, following a request of our Ad 
Hoc committee. Is it really not clear? Why do you say it makes no sense?

> line 49 - if word "small" is used, then it should be "-t" not "t"

OK, corrected.

> line 59 - better to say "The definitions of the kinematic variables are in ..."

OK, corrected.

> line 67 - why BH is more important, what means more important, more important for what? Looks like improper use of word, instead of "important" may be better to say "larger" or "significant"

OK, corrected.

> line 115 - I do not see where parentheses were open to close it after "...[11])", ")" must be removed.

OK, corrected, thanks for noticing.

> line 124 - GPDs do not depend on \phi, and \phi dependence of asymmetries have been studied in previous measurements, so change the line to "...its Q$^2$, $x_B$, and t ...". Here no need to have "-t".

Yes, but we refer to the \phi dependence of the asymmetry, not of the 
GPDs. We want to point out the difference of our data compared to previous 
ones: only with our data we have 4-D bins, and we can study \phi 
distributions as a function of the other 3 variables simultaneously. This 
was not done by any of the two previous experiments (HERMES and Shifeng).

> line 130 - no need for minus sign in front to of "t", you are not quoting a value
OK.

> line 152 - at the trigger level CLAS cannot discriminate between negatively and positively charged pions, so remove word "negative" in front of "pion"

Actually, here we are no longer at the trigger level, we are referring to 
the offline PID cuts on the EC energy deposition, which are done on 
negative tracks (based upon the DC information). So we think it is correct 
to leave the word "negative" in front of pions.

> line 154 - better to say "...three regions of drift chambers ...". Each region has many layers, total of 34

Yes, you are right, changed.

> line 183 - there is an additional space between the word "target" and coma

OK, fixed, thanks.

> line 235 - it should be " the total systematic uncertainty was ..."

OK, fixed.

> line 256 and Fig. 4 - I am not sure there is an "approved" convention on how count panels on a figure, but it might be better to explicitly define which panels, instead of saying first five panels, or panels 1-5.

In this case, hopefully being so different the "first five" panels from 
the other, I'd hope the notation is acceptable. If you don't mind, I'd 
wait to see what the PRL editors suggests, because every added word makes 
the paper longer... :-O

> line 266, line 340 - discussions of t-slope and axial charge, while it clearly there will be
connection between t-slope, spatial position towards center and the axial charge, it is not clear
to me how large t/Q2 plays here for the presented simplistic model at leading twist/leading order.
Paragraph on page 1, line 45, clearly states that this process is valid for t/Q2 << 1, is not it.
Some explanations are needed in addition to the axial charge distribution.

Yes, it is true that we are being a bit "general" here (but being it a 
PRL, we have to), and not going very deeply into discussions that go 
beyond the leading-twist approximation.
Let me first say that the data we select have the cut -t<Q2, so no events 
have t greater than Q2. If you look at Fig. 4, you'll see that our worse 
t/Q2 ratio is for the last point of bin 1, and it is ~0.65. Where exactly 
is the limit between leading-twist and twist-3 in terms of t/Q2 is not 
fully clear to me. According to Dieter Muller this limit is -t<Q2/4 (and 
you see it in the blue curves in this same figure). According to others, 
Dieter is too "strict". So, you say that it is not clear to you how large 
t/Q2 plays a role here, well, it is not clear to me either...
Our data have low precision in the low-Q2/high-t bins, so unfortunately 
they don't allow us a very refined analysis extracting the various 
sin(nphi) terms, to look for higher-twist effects. In our long paper, 
which is under Ad Hoc review at the moment, we also include the 
beam-spin and double-spin asymmetries, and this allow us to constrain the 
denominator cos(phi) term, and to make a little exploratory study adding a
sin(2phi) term to the numerator of our fitting function, but even so 
the precision of our data doesn't allow us to say anything conclusive or 
strong enough as far as where the leading-twist ceases to be a valid 
approximation. So we can't really say much about this, in this paper.
As far as our statement on the t-slope of the asymmetry being flatter than 
that of the BSA, I don't think this would be modified if we went beyond 
the leading-twist approximation. What would change would be what 
combination of GPDs would be involved in this observable (non-linear 
combinations of GPDs would come into play). But I would dare say that the 
higher-twist corrections wouldn't be so important to change the fact that 
Htilde is the "dominant" GPD in the TSA.
Bottom line, the issue of the 
higher-twist effects is quite complicate, and I am not sure this paper, 
and these data, are going to bring much light into it.
If you have any suggestions on how to address this aspect that you raised, 
please let us know.

Thank you very much and best regards,
Silvia


> Thanks, Stepan
>