[Sane-analysis] Calculating d2

[O. A. Rondon]

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
> 
> 
> 
> 
> 
>