Allomorphic corrections to semileptonic processes

The notion of allomorphic corrections to $S$-matrix elements for semileptonic processes, which by definition are absent in the lowest nontrivial order of perturbation theory, is introduced and analyzed. The complete fourth-order allomorphic corrections to the leptonic weak currents are calculated in an arbitrary gauge model of weak and electromagnetic interactions, treating the strong interactions (assumed mediated purely by gauge vector gluons) to all orders. These results are used to analyze the induced leptonic pseudoscalar current in charged-pion decay, and it is shown that weak restrictions on particle masses suffice to preserve the $V-A$ structure at the leptonic vertex to $O\left(\alpha G_F\right)$. A preliminary discussion of the allomorphic corrections to hadronic weak currents is presented in the context of neutral-kaon decay ($K^0\to {\mu }^{-}{\mu }^{+}$). It is shown that in theories in which the kaon field dimensionality is two or less, the usual suppression mechanisms involving charmed quarks probably do not suffice to remove induced neutral, strangeness-changing currents in $O\left(\alpha G_F\right)$.