= Chiral scalar-doublet Yukawa model
{title2=$\mathcal L_Y=-g\bar\psi(\phi_1+i\gamma_5\phi_2)\psi$}
The combined transformation $\psi\mapsto e^{-i\alpha\gamma_5/2}\psi$ and $(\phi_1+i\phi_2)\mapsto e^{i\alpha}(\phi_1+i\phi_2)$ preserves this interaction. The <Dirac adjoint> transforms with the same axial exponential as $\psi$. For potential $-\mu^2r^2/2+\lambda r^4/4$, $v=\mu/\sqrt\lambda$ gives a radial scalar of squared <mass> $2\lambda v^2$, a massless <Goldstone boson> and <fermion> physical <mass> $|g|v$. Cubic scalar vertices appear after the shift: $hhh$ has factor $-6i\lambda v$ and $h\pi\pi$ has factor $-2i\lambda v$.
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