[Sane-analysis] Update Re: Calculating d2

[O. A. Rondon]

I have posted an update to the draft on calculating d2. On fig. 5, shows
the difference between using the perturbative form of g1 calculated
directly from DSSV PDF's and the form including TMC's.
https://userweb.jlab.org/~rondon/analysis/asym/world/A2p-v5a.pdf

As it's discussed in detail in this recent review of TMC's, the TMC
corrected versions of structure functions are needed to compare to (or
use instead of) experimental data
http://dx.doi.org/10.1088/0954-3899/35/5/053101

At some point we should also use more up to date PDF's, like the recent
LSS one suggested by Peter Bosted or the JAM ones.

When writing the draft, I found a bug that affected my calculations of
d2 that I shared in January (I was using 1/Q^2 instead of 1/sqrt(Q^2) to
compute A2 using the fit). I've posted an updated version
https://userweb.jlab.org/~rondon/analysis/asym/world/d2-ok.pdf

A file comparing the old and new versions is also available
https://userweb.jlab.org/~rondon/analysis/asym/world/d2-2.pdf

It can be seen that d2(Q^2 <~ 4) < 0 for most cases. While this is a bit
unexpected, d2p < 0 is predicted by three QCD sum rules calculations,
see slide 31 at the link below
http://galileo.phys.virginia.edu/~or/diffraction2014/diff2014h6c.pdf

Last week we talked with Whit about improving the fit's agreement with
the data at low W, which is dominated by SANE. We considered adding some
extra terms, like Breit-Wigner resonant shapes, with fixed invariant
masses and widths, to improve the fit convergence, which becomes poor
when many parameters are allowed to float, like it's seen on slide 4 of
my early report on fitting A1 data
https://userweb.jlab.org/~rondon/analysis/asym/Q2/A1dis.pdf

We can try this approach using the resonance parameters from our HMS
SANE data at 1.8 GeV^2, fitted by Hoyoung, and the RSS fit ones, which
are very similar.

I have an appointment tomorrow that may keep me from joining the meeting
at 3:30. The meeting could either start on time and I'll join when I
can, or we can move it to 4:00, whichever is best for others.

Cheers,

Oscar


O. A. Rondon wrote:
> I've added a plot to the draft d2 note, showing the individual terms
> contributing to the d2 integrand
> 
> https://userweb.jlab.org/~rondon/analysis/asym/world/A2p-v5.pdf
> 
> Fig. 6 shows that the observed Q^2 dependence of d2 comes from the
> 1/sqrt(Q^2) term in the fit, which dominates at smaller Q^2 and makes
> the full integrand 3gT - g1 negative over a wide enough range of x so
> even the x^2 weight is not enough to compensate for it. The Q^2
> dependence of g1 is minimal.
> 
> This is consistent with the weaker dependence of the data on Q^2 than on
> W, shown on the plots I shared last time.
> 
> Cheers,
> 
> Oscar
> 
> 
> O. A. Rondon wrote:
>> I have updated the draft about the d2 method. New version here:
>> https://userweb.jlab.org/~rondon/analysis/asym/world/A2p-v4.pdf
>>
>> Mark's question about fit choice led me to spot a typo on the
>> 1/sqrt(Q^2) b1 parameter shown for the 1/W fit. The parameter is b1 =
>> -0.0423, not +0.432, which makes lots more sense.
>>
>> Also, I have posted some illustrative plots of the 1/W fit, vs W and vs
>> Q^2. In each case the fit is calculated at the data's W, Q^2 for each
>> subset (SANE 4.7, 5.9, etc.), and at constant values of the variable not
>>  used as abscissa.
>> https://userweb.jlab.org/~rondon/analysis/asym/world/A2_data-fits.pdf
>>
>> It can be seen that the W dependence dominates, as expected, from the
>> larger a1 factor in front of 1/W versus the b1 factor in front of 1/Q,
>> for comparable W and Q^2 ranges. I think this may answer in part
>> Mark's request about what data contribute at each Q^2.
>>
>> I have also posted the spreadsheets I use to get the numbers and make
>> the plots. They are a bit big, but the main contents related to d2 is in
>> the tabs that open when the files are first loaded. Look for the latest
>> OpenOffice *.ods files in the same folder as the d2 draft
>> https://userweb.jlab.org/~rondon/analysis/asym/world/
>>
>> I think it was clear in the end, but when I mentioned during the meeting
>> that the g1 twist expansion only involves even twist, I meant that the
>> OPE expansion of g1 involves only twist-2 matrix elements of even spin
>> (a0, a2, etc.) but only a0 is dynamic twist. The rest are TMC's. The
>> same goes for g2 and the higher spin d_i's.
>>
>> Cheers,
>>
>> Oscar
>>
>>
>>
>>
>>
>>
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