 Solution

The operator $({\varphi }^{†}+\varphi )\bar{\psi }\psi$ has mass dimension $1+3=4$, so $[g]=0$. It is a 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.