When a new heavy particle is discovered at the LHC or at a future high-energy collider, it will be interesting to study its decays into Standard Model particles using an effective field-theory framework. We point out that the proper effective theory must be based on non-local operators defined in soft-collinear effective theory (SCET). For the interesting case where the new resonance is a gauge-singlet spin-0 boson, which is the first member of a new sector governed by a mass scale M , we show how a consistent scale separation between M and the electroweak scale v is achieved up to next-to-next-to-leading order in the expansion parameter λ ∼ v/M . The Wilson coefficients in the effective Lagrangian depend in a non-trivial way on the mass of the new resonance and the masses of yet undiscovered heavy particles. Large logarithms of the ratio M/v can be systematically resummed using the renormalization group. We develop a SCET toolbox, with which it is straightforward to construct the relevant effective Lagrangians for new heavy particles with other charges and spin.