Solution
= Solution
The operator $A^\mu\bar\psi\partial_\mu\psi$ has <mass dimension> $1+3+1=5$, so $[e]=-1$. It is \b[not power-counting renormalizable]. Hermiticity may require a suitable conjugate or a symmetrized derivative, and electromagnetic gauge invariance would require a further consistent completion; neither repair changes its engineering dimension. Such derivative interactions can occur in an <effective field theory>, subject to its symmetries and operator redundancies.