[Sane-analysis] d2 update: Nachtmann moments

[O. A. Rondon]

Here is d2 calculated using both C-N and Natchmann moments. The top plot
on p. 3 shows d2 calculated as before using AAC 2003 g1 and g1 from my
A1, A2(W, Q^2) fits to SANE and SLAC data, but computing the M_2^3
Nachtmann moment, instead of the C-N one (The C-N results are on p. 1,
with updated labels).

The difference between d2 for the two input g1's is smaller for
Nachtmann than for C-N (about 1/2). At 5 GeV^2, the agreement with the
published C-N SLAC average also improves.
https://userweb.jlab.org/~rondon/analysis/asym/world/d2.pdf

The expression for the M_2^n=3 moment is taken from eq. 3 of the RSS PRL
on twist-3,
http://prl.aps.org/abstract/PRL/v105/i10/e101601

Since the OPE moments are based on measured SSF's, target mass effects
(as opposed to Target Mass corrections) were applied to the g1 SSF from
the (asymptotic) AAC PDF's, to make it approximate the experimental
values, in order to combine it with the g2 SSF from the A1, A2 fits to
data. (The NMC F1 used to get the SSF's from the SA's is a
parameterization of experimental data, so it does not need target mass
effects; this should be kept in mind if F1 from PDF's is used at some
point). The bottom plot on p. 3 shows d2 for AAC g1 with and without
target mass effects. It's a  small but not totally negligible difference
(~20% at 5 GeV^2).

Cheers,

Oscar