Effective operator ($C_i{\mathcal{O}}_i/M^{{\Delta }_i-4}$)

An effective operator is a local interaction built from the retained fields in an effective field theory. Its coefficient records effects of heavier degrees of freedom, and allowed operators respect the relevant symmetries. In four dimensions an operator of mass dimension ${\Delta }_i$ has the displayed coefficient for dimensionless $C_i$ and a heavy mass scale $M$. For example a dimension-six proton-decay operator has a coefficient proportional to $M^{-2}$.