[A1n_d2n] Another physics question -- TMC derivation

[Xiaochao Zheng]

Dear All:

Since my last "call for help" for the Jacobian had a great response rate, I thought perhaps I seek help again from this group, this time for a question that I am stuck with for the past month. (I have already emailed the theorists, but I know there must be similar talent in this group to help me at a level closer to an experimentalist's).

I have been trying to figure out how to derive the target-mass correction (TMC) terms for PVDIS asymmetries. The results were given in
L. T. Brady, A. Accardi, T. J. Hobbs and W. Melnitchouk, Phys. Rev. D 84, 074008 (2011)[Erratum-ibid. D 85, 039902 (2012)], or

https://arxiv.org/pdf/1108.4734.pdf [Eq.(21a) and (21b)]

What I would like to do is to understand how these results were obtained so I can extend it to a new set of asymmetries I am working on.  I have attached a short writeup.  The question is posed on page 4, with pages 1-3 intro to the observables and page 5-7 references.

I am wondering if anyone can help with this? I don't need the exact derivation step by step, but rather instructions for how to do so (and I can deal with the algebra, or find someone to do it).

Thanks in advance!

And if nothing else, I hope this email provides a good weekend read!

Xiaochao
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://mailman.jlab.org/pipermail/a1n_d2n/attachments/20210403/15866db8/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Asym_TMC.pdf
Type: application/pdf
Size: 269565 bytes
Desc: Asym_TMC.pdf
URL: <https://mailman.jlab.org/pipermail/a1n_d2n/attachments/20210403/15866db8/attachment-0001.pdf>