Amplitude bases in generic EFTs

Abstract

We present for the first time an efficient algorithm to find a basis of kinematically independent structures built of (massless and massive) spinor helicity variables in four dimensions. This method provides a classification of independent contact terms for the scattering amplitudes with generic masses, spins and multiplicity, in any effective field theory (EFT). These contact terms are in one-to-one correspondence with a complete set of irrelevant operators in the EFT. As basic applications of our method, we classify the $D^{2n}{F}^4$ contact terms in SU$(N)$ Yang-Mills theory for $n\le 8$, dimension-six operators involving five $W^{\pm }$, $Z$ and $\gamma$ vector bosons, and spin-tidal effective interactions for spin-1 massive particles in gravitational theories.

arXiv comment20+8 pages. v3: Sections 2 and 3 expanded

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• An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes
• Constructing on-shell operator basis for all masses and spins
• Constructing Generic Effective Field Theory for All Masses and Spins
• Primary Observables for Indirect Searches at Colliders
• The New Formulation of Higgs Effective Field Theory
• On-shell Supersymmetry and higher-spin amplitudes