Irrelevant coupling

In classical power counting in quantum field theory, an irrelevant coupling multiplies a local operator whose mass dimension $\Delta$ exceeds the spacetime dimension $d$. Since the action is dimensionless in natural units, $[g]=d-\Delta <0$. The dimensionless interaction strength scales as

For example, ${\varphi }^6$ in four-dimensional scalar field theory has coefficient $g/{\Lambda }^2$, giving suppression $g(E/\Lambda {)}^2$ at low energy. This explains the usefulness of effective field theory below its cutoff. At an interacting renormalization-group fixed point, relevance is determined by the full scaling dimension, including quantum corrections. ^[ref]

A power-counting nonrenormalizable interaction has a coupling of negative mass dimension, so higher loop orders generally require counterterms of unbounded operator dimension. It is naturally interpreted within an effective field theory below a cutoff.