[Sane-analysis] Reminder of Sane meeting at 4:30pm Thurs Oct 6th in L210A

[Oscar Rondon]

Hi Whit,

Thinking of the comment at the end of your email, it looks to me that it
would be best not to use LSS or other PDF's that are corrected for
Higher Twists, but rather ACC or similar. I'm not sure if DSSV is HT
corrected. I think that there may be another LSS version without HT
corrections, too.

However, even for AAC, etc., since the PDF's have been extracted from
data at high Q^2, but Bjorken x not close to 1, we still need to add
target mass effects to use them at our low Q^2 and high x region.

All Nachtmann moments use measured g1 and g2 to get twist-2 a_n and
twist-3 d_n matrix elements of any spin n=0,2,4,.. (n=2,4,.. for d_n).
This is how they isolate the lowest-spin dynamic HT's while correcting
for the target mass at any Q^2 or x.

On the other hand, the first C-N moment of g1, Gamma_1, mixes twists and
spins. Some call all the terms in this mixture "target mass", because of
the M^2/Q^2 coefficient in the expansion, but that's not correct. Only
the terms of higher spin for the same twist, e.g. the kinematic HT
elements a_n>0, d_n>2, f_n>2, are "target mass".

What is true is that all HT's, dynamic and kinematic, are suppressed by
(M^n/Q^n), n=2,4,.. That's why transverse polarized scattering AT HIGH x
is so important, because it gets to HT d2 without having to fit some
type of Q^2 dependent twist expansion.

This works even with C-N moments because the next (3rd) moment after
Gamma_1 only involves the twist-2 a_2 (the first term after a_0 in the
twist-2 spin expansion, i.e. a twist-2 target mass term). The x^2 weight
in the g1 integral gets rid of d's and f's, and of f's in the g2 one,
that's why there is a C-N form of d_2 (without f's admixture). The
problem is that the higher spins n>2 still contribute to d_2 from C-N
moments, which is where Nachtmanns come in.

You probably have it already, but this paper has a good derivation of
the C-N moments, especially the discussion of the next term in the
expansion of the T_\mu,\nu Compton amplitude, after eq. (34)

http://dx.doi.org/10.1016/0370-2693(94)91244-0

Since we don't have enough SANE g1 data, combining our measured A2 that
dominates the world data at low x, with world g1 as obtained from PDF's
not corrected for HT's seems to me the best way to get d2, with the
added advantage that the A2 contribution is enhanced by a factor of 3
over that of g1.

Finally, about the f_n, I should mention that I asked several theorists,
by email and in person, about moment equations for twist 4 f_n, like
those for a's and d's, and I never got an answer, other than (I think)
they would be enormously complicated to derive, because of all the
correlations (qqgg, qqqq, ... ?).

Cheers,

Oscar


Whitney R. Armstrong wrote:
> I think things are clearing up for me now. If A2 fit is going to be used
> all TMCs and higher twist effects need to be added back into g1
> calculated from models.
>