Bases of massless EFTs via momentum twistors

TL;DR

The paper develops an algebraic, amplitude-based method to construct a basis of massless EFT contact terms directly at the level of 4-point amplitudes by employing momentum twistors. It reexpresses local contact terms as rational functions of Lorentz-invariant spinor contractions and introduces a compact master formula indexed by two integers (n,k) that fixes the EFT order via the canonical dimension D = 2n + 4 − ∑_i h_i and enumerates a finite set of basis elements for each helicity configuration. Through explicit 4-point examples—scalars, scalar-spin, and Euler–Heisenberg photons—the work demonstrates how the basis reproduces known EFT operators (e.g., up to dimension-8) and clarifies parity relations and locality constraints. The approach is simpler for higher-spin cases, directly complements Hilbert-series counting, and provides a pathway toward higher-point amplitudes, while remaining limited to massless 4D theories and not manifestly parity-invariant in its foundational form. Overall, this momentum-twistor framework offers a practical, on-shell toolkit for systematically enumerating EFT contact structures in massless theories.

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.