  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 can not be constructed as an expansion in local,
higher-dimensional operators; rather, it 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 $\lambda\sim v/M$. 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.
