Past exam of the gauge field theory course of the University of Cambridge / 2013 / Paper 1 / 3 / c / Solution

The operator ${\varphi }^{†}\varphi \bar{\psi }\psi$ has mass dimension $2+3=5$, giving $[g]=-1$. It is not power-counting renormalizable as a fundamental interaction treated to arbitrary energy. It is a perfectly usable dimension-five effective operator below its suppression scale. Successive orders in that effective field theory require a derivative and operator expansion rather than one finite set of parameters valid at every order.