  I present a novel method of deriving a basis of contact terms in massless
effective field theories (EFTs). It relies on the parametrization of $N$-body
kinematics via the so-called momentum twistors. A basis is constructed directly
at the amplitude level, without using fields or Lagrangians. The method
consists in recasting any local contact term as a sum of rational functions
built from Lorentz-invariant contractions of momentum twistors. The end result
is equivalent to constructing a basis of higher-dimensional operators in an EFT
Lagrangian, however it is considerably simpler, especially for theories with
higher-spin particles. The method is applied to contact terms in 4-point
amplitudes. I provide a compact algebraic formula for basis elements for any
helicity configuration of the external particles, and I illustrate its usage
with several physically relevant examples.
