  Precision studies of scattering processes at colliders provide powerful
indirect constraints on new physics. We study the helicity structure of
scattering amplitudes in the SM and in the context of an effective Lagrangian
description of BSM dynamics. Our analysis reveals a novel set of helicity
selection rules according to which, in the majority of 2 to 2 scattering
processes at high energy, the SM and the leading BSM effects do not interfere.
In such situations, the naive expectation that dimension-6 operators represent
the leading BSM contribution is compromised, as corrections from dimension-8
operators can become equally (if not more) important well within the validity
of the effective field theory approach.
