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L0 interpretation of parity violating $A_L$ for Ws

1) definition of sign of $A_L$:
\begin{equation}
A_L=\frac{d\sigma^+ - d\sigma^-}{d\sigma^+ + d\sigma^-}
\end{equation}
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Explore limits at $y=0, x_a=x_b=x$
\begin{equation}
A^{W+}_L=\frac{u(x)\Delta\bar{d}(x) - \bar{d}(x)\Delta u(x)}{2u(x)\bar{d}(x)}; \;\;\;
A^{W-}_L=\frac{d(x)\Delta\bar{u}(x) - \bar{u}(x)\Delta d(x)}{2d(x)\bar{u}(x)}\\
\end{equation}
from this follows:
\begin{equation}
A^{W+}_L=\frac{1}{2}(\frac{\Delta\bar{d}}{\bar{d}}(x) - \frac{\Delta u }{u}(x)); \;\;\; A^{W+}_L<0 \;\; for \;\;\Delta u>0
\end{equation}
and:
\begin{equation}
A^{W-}_L=\frac{1}{2}(\frac{\Delta\bar{u}}{\bar{u}}(x) - \frac{\Delta d }{d}(x)); \;\;\; A^{W-}_L>0 \;\; for \;\;\Delta d<0
\end{equation}