[b1_ana] (no subject)

[Dustin Keller]

This is a very good and important question that remains
unanswered.  Historically I think we have assumed that
Azz~b1/F1 is good for x<1 but we also know the cut off
is not sharp.  I think it is not yet understood theoretically
how far in x b1 can be associated with Azz.  If b1 were to
putter-out it would not be so much an issue.

dustin

On Thu, 23 May 2013, Elena Long wrote:

> Good morning,
>
> Just for clarification, what are we considering low x and high x? I'm 
> assuming 0.5 falls in high x, but I was wondering approximately where the cut 
> off is for these effects to start becoming important.
>
> Thank you,
> Ellie
>
> Elena Long, Ph.D.
> Post Doctoral Research Associate
> University of New Hampshire
> elena.long at unh.edu
> ellie at jlab.org
> http://nuclear.unh.edu/~elong
> (603) 862-1962
>
> On Wed 22 May 2013 07:03:12 PM EDT, Dustin Keller wrote:
>> 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
>> 
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