= Solution
The operator $(\phi^\dagger+\phi)\bar\psi\psi$ has <mass dimension> $1+3=4$, so $[g]=0$. It is a \b[power-counting renormalizable Yukawa interaction] between a real scalar combination and a <fermion> bilinear. A scalar <vacuum expectation value> contributes to a <Dirac mass term>; its fluctuations couple to the <fermion> pair. This is a schematic scalar–<fermion> theory. In a chiral <gauge theory>, representations must be combined gauge-invariantly, as in the <Standard Model> Higgs–<fermion> interactions. Without additional protecting symmetries, all allowed scalar counterterms must be included as well.
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