Bases of massless EFTs via momentum twistors

Abstract

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.