= Vacuum-to-pseudoscalar current selection rule
{title2=$\langle0|V^\mu|P(p)\rangle=0,\quad\langle0|A^\mu|P(p)\rangle\propto p^\mu$}
<Lorentz covariance> allows only a multiple of $p^\mu$ for a vacuum-to-<spin>-zero one-particle current. In its rest frame only the temporal component can remain. A parity-even temporal <vector current> between a parity-even vacuum and parity-odd particle changes sign, forcing that component to vanish. A temporal <axial current> is parity-odd and is allowed. This explains why the <pion decay constant> enters the axial, rather than vector, part of the <weak charged current>.
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