Quark axial-vector current in nucleion

[Andrea M.]

In almost all direct detection articles (see for example Jungman, G., Kamionkowski, M. & Griest, K., 1996. Supersymmetric dark matter) I found the following parametrization for the matrix element of the quark axial-vector coupling:
$$
\langle n|\bar q\gamma_\mu\gamma_5q|n\rangle=2s_\mu^{(n)}\Delta q^{(n)}
$$
where $\Delta q$ is the fraction of the nucleon spin carried by quark $q$ and $s_\mu^{(n)}$ is the spin of the nucleon $n$. Even if this make sense i would like to have a reference where find a derivation or a justification of this fact.

 

[fzero]

There's a useful discussion in Jaffe and Manohar, particularly section VI. A scanned pdf file from KEK is available at the link.

 

[Andrea M.]

Thank you, I'll check it out!