The Rise of SMEFT On-shell Amplitudes

TL;DR

This work develops a framework to express SMEFT in the Warsaw basis through massive on-shell amplitudes, focusing on the electroweak sector without fermions and using an on-shell input scheme based on physical masses.By formulating 3-point massive amplitudes and introducing an 11-dimensional on-shell basis, the authors map SMEFT dimension-6 deformations to on-shell coefficients $\mathcal{G}_i$ and $\mathcal{C}_i$, establishing explicit relations to the Warsaw coefficients and to the SM parameters in the broken phase.The paper demonstrates how 2-to-2 amplitudes can be built from 3-point data via recursion and factorization, with concrete SMEFT examples such as $W\bar{W}\gamma\gamma$ and $W\bar{W}hh$, highlighting when high-energy constraints fix contact terms and when SMEFT provides genuine new structures.Overall, this work lays groundwork for a fully on-shell formulation of massive SMEFT and opens avenues for deeper insights into electroweak symmetry breaking and the interplay between Lagrangian and on-shell EFT descriptions.

Abstract

We present a map between the tree-level Standard Model Effective Theory (SMEFT) in the Warsaw basis and massive on-shell amplitudes. As a first step, we focus on the electroweak sector without fermions. We describe the Feynman rules for a particular choice of input scheme and compare them with the 3-point massive amplitudes in the broken phase. Thereby we fix an on-shell basis which allows us to study scattering amplitudes with recursion relations. We hope to open up new avenues of exploration to a complete formulation of massive EFTs in the on-shell language.