Standard Model EFTs via On-Shell Methods

TL;DR

This paper derives the structure of Standard Model Effective Field Theories using on-shell methods, classifying interactions, enforcing algebraic relations, and computing amplitudes and mixing matrices without relying on traditional Lagrangian approaches.

Contribution

It introduces an on-shell framework for classifying SMEFT interactions, providing a new algorithm for amplitude calculations and computing mixing matrices up to dimension 8.

Findings

Classified all SMEFT interactions at lowest order using on-shell methods.

Developed an on-shell algorithm for higher-point amplitude computations.

Calculated the mixing matrix of SMEFT interactions up to dimension 8.

Abstract

We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from a few basic assumptions such as Poincar\'e invariance and locality, we classify all the renormalisable and non-renormalisable interactions at the lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT irrelevant interactions up to mass dimension 8, to linear order in the effective interactions.