= Angular asymmetry of a chiral charged-current interaction
{title2=$A(\theta)$}
For the massless common vector-axial coupling at both vertices in <weak charged-current quark scattering>, subtracting opposite directions gives
$$
\boxed{A(\theta)=\frac{8P^2Q^2}{(P^2+Q^2)^2}\frac{\cos\theta}{1+\cos^2\theta}.}
$$
It is undefined for $P=Q=0$. Overall rate normalization cancels. Pure vector or axial interactions have zero asymmetry, while $P=\pm Q$ gives its maximal coefficient. The inequality $4P^2Q^2\leq(P^2+Q^2)^2$ implies $|A|\leq1$. This unpolarized observable does not distinguish purely left- from purely right-handed couplings applied at both vertices.
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