[Sane-analysis] Fits to world A1 and A2

[O. A. Rondon]

Hi,

I have combined SLAC and SANE 2013 spin asymmetries data to parameterize
them as functions of W and Q^2. Bjorken x mixes W and Q dependencies, so
it is a less useful variable in the resonances.

>From inspection of the trends of the data, I have tried simple forms
with uncorrelated W and Q^2 dependencies: A1 and A2 decreasing as 1/W
and log W for both A1 and A2; plain Q^2 for A1; and 1/sqrt(Q^2) to
approximate the twist-3 dependence of A2.

I included only model independent A1 data from SLAC E143 and E155. The
E155 10.5 deg A1 data only ruin the chi squared of the fits, and those
data don't follow the trend of the rest, compare plots on p. 1 (total
errors) and 2 (statistical only) of the report I posted, so I excluded
them from the final fits.

Both sets of data were fitted with total errors, statistical and
systematic added in quadrature. The fit curves to each subset of the
data are more visible individually for A1 (p. 3) than for A2 (p. 5).
Also, note the difference between the 2012 and 2013 SANE A2 (p. 4).
https://userweb.jlab.org/~rondon/analysis/asym/world/A1-A2_fits.pdf

Of course, the 1/W dependence violates unitarity at some W, so the fit
is valid only down to that minimum value, which is somewhere in the
resonances. Similarly, the log W dependence leads to negative A1 below 1
GeV, so there may be need to add some kind of power dependence rather
than plain inverse or log.

We still need to fit A1 and A2 to SANE's data alone, to confirm our
radiative corrections, in particular their systematic errors. Examples
of updated fits to SANE's 2013 data, and a 3-D plot of the 1/W world fit
to A1 can be found here
https://userweb.jlab.org/~rondon/analysis/asym/world/fits_143_155_13.pdf

I have calculated the d2 integral at fixed 3 GeV^2, using the 1/W fits
and NMC parameterization of F1 to calculate g2, with g1 computed using
AAC03 PDFs. The result is d2(3 GeV^2) = 0.0030, which is not too
different from SLAC's published number d2(5 GeV^2) = 0.0025+/-0.0017.

The error on d2 from our fits can be calculated using the fit's
covariance matrix, which is a more accurate estimate than trying to
combine the data's errors, since the covariance matrix includes the
correlations among the fitting parameters, in addition to the errors of
the diagonal terms.

I'll try computing d2(5 GeV^2) and the error on d2 next.

Cheers,

Oscar