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Between spin-zero pseudoscalars, Lorentz covariance decomposes a vector current matrix element into $(p+k{)}^{\mu }{f}_{+}(q^2)+(p-k{)}^{\mu }{f}_{-}(q^2)$, with $q=p-k$. Strong interaction parity symmetry in quantum field theory makes the corresponding axial current matrix element vanish.

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.