Date: Mon, 09 Apr 2007 19:54:50 -0400
From: "O. A. Rondon" <or@virginia.edu>
To: Karl Slifer <slifer@jlab.org>
Subject: Re: RSS moments


I also think that in scenarios III and IV there are two issues:

- the pdf's g1's disagree with data for x<x0, see your table in sec.
1.1.3, compared to the BT or OR integrals. This means that using g1(pdf)
overestimates the integrand of eq. (9). Perhaps a more "fair" approach
would be to normalize the pdf-based integrals by scaling them by the
ratio Int_0^x0(BT or OR)/Int_0^x0(pdf).

- extrapolating the data based DIS fits into x>x0 has the problem that
the fits aren't pure DIS since there are significant tails of resonances
extending down below x<x0. So I am not sure using the BT or OR fits we
would be integrating DIS g1 in eq. (9).

My suggestion is that we get an average of scenario I plus four values
of scenario III for g1(pdfs) only, previously normalized to the data
based integrals as indicated above. I say four values because I think
AAC-2 and GRSV-2 are independent from their NNN-1 versions, judging from
your table in sec. 1.1.3.

I then get <Int_0^x0> = 0.0242+/-0.0017, or 6.9% relative. I am taking
the std. dev of the sample (root of variance divided by the d.o.f. 4 = 5
data values - one parameter (mean)), rather than the parent std. dev.,
which is a bit better, 0.015. It seems you are taking the parent std.
dev. for your result 0.0236+/-0.054, rather than the sample's 0.061, but
since we get both the avg. and dev. from the same set of numbers we need
to reduce the d.o.f. by one.

A final option would be not to scale the scenario III pdf integrals, but
still exclude from it the data based DIS fit integrals.

For the RSS results on fig. 3, there are no numbers in the draft
(central values or errors).

An unrelated comment: please remember to give Zein-Eddine some materials
for his summary talk.

Cheers,

Oscar