[b1_ana] (no subject)

[Dustin Keller]

The Hoodbhoy, Jaffe and Manohar paper does express the final relationship 
to observables using the beam orientation, and there are several 
proceeding steps that get us to that point that are not covered.
Its important to be critical of what we are actually measuring in terms of 
asymmetry and its definition.

What we will be measuring is Azz or in Jaffes script ~b1/F1.  As an 
observable Azz seems to have a very generalized definition that does no 
change at various x regions but of course does have orientation 
dependence.  Assuming this is true allows us to bridge to the Arenhovel 
formalism.  Naturally for low x Jaffes relation is valid for a target 
helicity pointing along the electron beam.  In the Arenhovel formalism 
this is only an approximation, but a good one.  This approximation likely 
lives in the ratio b1/F1.  Because our last kinematic points may not be 
strictly thought of as low x its probably a little more accurate to use 
the corrections afforded to us by the Arenhovel formalism.  This would 
include a small correction to Azz from the Wigner rotation and possible a 
small correction from the vector target-only asymmetry.  By making these 
corrections for the higher x points the accuracy to Azz and b1/F1 is 
slightly increased.  This line of thinking would not be valid for the 
sigma_para - sigma_perp case in which you are acquiring b1 directly.  But 
being we are measuring Azz we are not strictly using Jaffe for anything. 
To clarify, I can't think of any reason that for low x that one could not 
use the language Jaffe uses to describe the cross section in relationship 
to b1 and F1.

The corrections to Azz come into play for higher x where 
pointing along the q-vector can lead to a measurable difference.  So it 
maybe best to consider a response to any inquires from the PAC about this
with some flexibility around q-vector orientation.  As it is the correction
to Azz is a multiplicative factor of ~0.9 and the target-only vector 
asymmetry is near negligible.

dustin