[Sane-analysis] Reminder of Sane meeting at 4:30pm Thurs Oct 6th in L210A

[Oscar Rondon]

Hi Whit,

I think it's just eq. (114), where I believe the sum over quark flavors
is put inside the integrals, so the perturbative g1 from PDF's is taken
to be

g1_pert = Sum_q [(g_A^q)^2 + (g_V^q)^2]/4 F^q(xi)

where the individual F^q must be the polarized Delta_u, Delta_d, etc.,
PDF's. The Sum_q step is done in the DSSV, AAC03E, etc., subroutines
that produce g1_pert. Then, TM_SUBC outputs the left hand side of eq.(114).

I am not sure about the differences in g2WW from the two forms of g1. I
think that since the claim is that g2WW is insensitive to the TMC's, the
problem may be with the different ranges of integration for g1(x) vs
g1_TMC(xi), since xi(x=1) < 1 for M^2/Q^2 .ne. 0, so one may need to
integrate to xi = 1, although on p. 453, B and T talk about setting
g1_perturbative to zero for xi > 1.

Another problem with g2WW is that the unmeasured region x < x_min
becomes more important, since the integral part of it depends on 1/x
unlike the x^2 factor of the d2 moments. In any case, I don't use g2WW
to get d2. My suggestion would be to not deal with g2WW for d2, although
we may need it for Gamma_2 and the B-C sum rule.

Cheers,

Oscar




Whitney R. Armstrong wrote:
> Hi Oscar,
> 
> Thanks for providing these important plots.
> 
> I have no idea what formula is being implemented in
> https://userweb.jlab.org/~rondon/analysis/asym/world/tme/TM_SUBC.F
> There is all sorts of fortran obfuscating things. Can you provide me a
> formula or reference here? I am assuming it is the Mellin inverted
> higher-spin matrix element a_3 part (where a_1 is the lowest spin
> twist-2 matrix element), but I cannot find g1(x) written explicitly with
> this TMC.
> One thing is rather confusing here. The TMC to g1 from Blumlein  and
> Tkabladze involves purely the purely twist-3 contribution to g2(tau=3).
> This is equation 158 in their paper
> (http://inspirehep.net/record/481386). But in their previous section on
> twist-2 relations, they have g2_WW but don't have the explicit twist
> labels g1(tau=2).
> I am guessing they do this because "the WW relation holds in the
> presence of target mass corrections". Meaning either g1(tau=2; M=0) or
> g1(tau=2; M=Mp) can be used. However, if the g1(tau=3; M=Mp) TMC is
> applied too, the WW relation does not hold (I think).
> Anyway, with the twist-2 TMC the increase of g1 at large x is similar to
> the expected increase from the genuine twist-3 TMC as well.  For example
> the latest jam result: https://www.jlab.org/theory/jam/gallery/LTHT.jpg
> 
> Looking at your spreadsheet, is the difference in g2WW with and without
> TMCs added to g1 (AAC) due to finite bins in the integration?
> I think things are clearing up for me now. If A2 fit is going to be used
> all TMCs and higher twist effects need to be added back into g1
> calculated from models.
> 
> Cheers,
> Whit
> 
> 
> 
> 
> On Sat, Oct 08, 2016 at 06:35:35PM -0400, Oscar Rondon wrote:
>> Hi,
>>
>> Following up on the discussion at the analysis meeting about the need to
>> apply target mass effects (TME) to the pertubative form of the g1p SSF
>> calculated from PDF's (e.g. as in Fig. 5 of the tech. note on getting
>> d2,) I've posted the FORTRAN code I've used to apply TME's at
>> https://userweb.jlab.org/~rondon/analysis/asym/world/tme/
>>
>> (The d2 tech note is here
>> https://userweb.jlab.org/~rondon/analysis/asym/world/A2p-v5b3.pdf )
>>
>> Basically, it's an implementation by Peter Bosted of the TMC analysis of
>> Blumlein and Tkabladze, ref. [27] of the RSS g1p paper, with the DSSV
>> and AAC03 PDF's called as subroutines, but any other set of PDF's could
>> be used, too. The program outputs the perturbative g1p and and the g1p
>> with TME, at constant Q^2 as a function of Bjorken x and Nachtmann xi.
>>
>> Examples of the output are shown in the file aac1-stat_pdf.eps in the
>> folder. The plot shows g1p computed with the statistical PDF of
>> Bourrely, Soffer and Bucella, and the AAC03 version, with and without
>> TME. These curves are basically the same ones plotted in Fig. 3 of the
>> RSS g1p paper.
>>
>> Examples of g1p with TME relevant to SANE can be found in tab "aac_2" of
>> the OpenOffice spreadsheet aac_q2-2.ods in the same folder. The
>> calculation of d2 from World + SANE A2 data is found in tab "g2bar"
>> including some of the plots shown in the d2 tech note.
>>
>> On a related subject, the advantage of using the fits' full covariance
>> matrix to estimate the errors of the moments calculated from the fit is
>> illustrated on the plots shown in the following file, which compares the
>> uncertainties for C-N or Nachtmann d2 (or M23) calculated with just the
>> matrix's diagonal elements only (p. 1) and with the full correlations
>> (p. 2)
>> https://userweb.jlab.org/~rondon/analysis/asym/world/d2-WA-fits.pdf
>>
>> The moments for these plots that I posted in June 2015 were calculated
>> with the then current version of Whit's A2 with E' > 1.3 GeV. The
>> results for E' > 1.0 are on p. 3.
>>
>> Cheers,
>>
>> Oscar
>>
>>
>>
>>
>>
>>
>> Mark Jones wrote:
>>> Reminder of Sane meeting at 4:30pm Thurs Oct 4th  in L210A
>>>
>>>
>>> Cheers,
>>>        Mark
>>>
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>>
>>
>>
>>
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