[b1_ana] (no subject)

[Elena Long]

So for our measurement of x<~0.6, we might have to worry about these 
effects starting to come into play at the highest point but they should 
have a negligible impact in the three lower points?

Take care,
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 Thu 23 May 2013 09:58:58 AM EDT, Dustin Keller wrote:
> 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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>>