[Sane-analysis] d2 update

[O. A. Rondon]

Hi,

Here are updated preliminary Cornwall-Norton results for d2 (integrated
numerically from 0 to 1). I found some bugs in my previous calculation,
so the earlier result d2(3 GeV^2) mentioned in my email about fits to A1
and A2 (at bottom) is wrong.

I've posted a file showing d2 for three values of Q^2, calculated with
g2 from the fit to A2(1/W) and the NMC parameterization of F1, and with
two versions of g1: using AAC 2003, and using the fit to A1(1/W) with
the NMC F1.

Both results for d2(5 GeV^2) agree with SLAC's published combined result
(E143/155/155x) within less than a sigma of the error. But d2 < 0 for
Q^2 < ~ 4 GeV^2 with either version of g1. Since the result is more
negative for AAC g1, it's clear that the unexpected result is not due to
g2, but to the small magnitude of g1(x>0.3), especially for the AAC's
one (p. 2, top panels)

Although we need to check these results using g1 from other PDF's, this
may be an indication that d2 does have an unexpected Q^2 dependence,
which, until now, was based on just the SLAC result at a single Q^2
point. Of course, the negative result is consistent with the truncated
d2(0.3<x<0.8) calculated from only SANE's data.

The choice of F1 to get g2 from A2 is also important, since the
existing NMC and SLAC parameterizations of F2, plus R1990/1998, only
cover the DIS range W> sqrt(3) GeV, and the F1F209 parameterization
which works in the resonances, fails badly at low x (p. 2, bottom plot)

The file with the d2 results is here:
https://userweb.jlab.org/~rondon/analysis/asym/world/d2.pdf

The d2 results from SANE's measured g1 and g2 (with F1 from F1F209) (p.
7), and other interesting plots, including g2(world) (p. 3), are here :
https://userweb.jlab.org/~rondon/analysis/asym/world/A180_Aperp-q2-x_d2-xmin.pdf

Cheers,

Oscar

O. A. Rondon wrote:
> 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
> 
> 
> 
> 
>