= Parity restriction on renormalizable pseudoscalar Yukawa counterterms
{title2=$\mathcal L_{\rm ct}\supset\phi^4,\quad\mathcal L_{\rm ct}\not\supset\phi,\phi^3$}
For an unbroken <parity symmetry in quantum field theory> with $\phi$ a <pseudoscalar>, pure-scalar local <counterterms> of <mass dimension> at most four are even in $\phi$. A four-vertex <fermion loop> requires a quartic <counterterm>, even when the initial <Lagrangian density> shows only a <Yukawa interaction>. The one-point and three-point pure-boson vertices vanish at all orders: their available external <four-momenta> cannot form a parity-odd <Lorentz scalar>.
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