[d2n-analysis-talk] Nachtmann moments, d2 and e06-014?

[Brad Sawatzky]

I was looking into some older notes and was reminded of some questions
I had regarding Nachtmann moments.  See also:
  http://prl.aps.org/abstract/PRL/v105/i10/e101601
  http://arxiv.org/abs/0812.0031

Review of Target Mass Corrections (I'm still working through this paper...)
  http://lanl.arxiv.org/abs/0709.1775

My understanding (which is incomplete) is that the perturbative QCD
moments (ie. moments of g1,2 as well as d2) are evaluated using
expansions of the Cornwall-Norton moments.  The CN moments are the ones
we usually use:  ie gamma^n_1 == Int(x^n * g1(x) * dx)

These evaluations are valid at 'high' Q2.  At lower Q2, target-mass
corrections become important (ie. target recoil corrections).  These
purely kinematical corrections can be removed following the procedure
described in the above links (and associated refs) to allow for
comparison between calculations (made using CN moments) and 'low Q2'
data (?)

Note that the above discussions focus on the RSS data which is
intentionally in the resonance region and is at low'ish Q2 (~ 1.3
GeV^2).

I'm not clear on how/if we apply this procedure to our data.
  - Our Q2's are higher, but not so high that Q^2 >> M^2, so I presume
    target-mass corrections are relevant and need to be addressed?
  - Oscar made a comment to a question of mine from some time back:
     "What one needs to be careful about is to use Nachtmann moments to
      calculate the elastic peak too. The Cornwall-Norton moments way
      overestimate the elastic part."
    I presume this may be relevant for our quasi-elastic tail piece
    contributions?  (Oscar was talking about a hydrogen proton target,
    so his elastic <=> our QE, maybe...)
  - Are the TMC taken into account by the 3He -> neutron correction for
    d2 that Wally gives us?  (I don't think they are, but I'm not sure.)
  - Is CN vs. Nachtmann _only_ relevant when comparing to theory and
    attempting to quantitatively extract higher-twist contributions?

It (naively) looks to me like the Nachtmann expressions are a method to
take actual data at finite Q2 and 'evolve' them (in some sense) to a
kinematic region where they can be compared with theory.  I note that
it only takes out the piece of the Q2 dependence that is associated with
the target mass, so I don't understand why this correction isn't just
made to the d2(Q2) that we get from theory(?) since you can't really get
away from it.  (ie. It is an artifact of a simplified calculation, not
really an experimental correction...)

Zein-Eddine, it would be fantastic if you could weigh in on this and
clarify for me.

-- Brad

-- 
Brad Sawatzky, PhD <brads at jlab.org>  -<>-  Jefferson Lab / Hall C / C111
Ph: 757-269-5947  -<>-  Fax: 757-269-5235  -<>- Pager: brads-page at jlab.org
The most exciting phrase to hear in science, the one that heralds new
  discoveries, is not "Eureka!" but "That's funny..."   -- Isaac Asimov