# Standard Model Effective Field Theory from On-shell Amplitudes

## TL;DR

This paper introduces a novel on-shell amplitude method to systematically construct and connect amplitude bases with operator bases in the Standard Model Effective Field Theory, especially at dimensions 5 and 6.

## Contribution

It develops a general approach to relate on-shell amplitudes to EFT operators, providing a complete and independent basis for the Standard Model EFT at specific dimensions.

## Key findings

- Constructed amplitude basis for dimension 5 and 6 operators.
- Established one-to-one correspondence between amplitude and operator bases.
- Identified the amplitude basis corresponding to known EFT operators.

## Abstract

We present a general method of constructing unfactorizable on-shell amplitudes (amplitude basis), and build up their one-to-one correspondence to the independent and complete operator basis in effective field theory (EFT). We apply our method to the Standard Model EFT, and identify the amplitude basis in dimension 5 and 6, which correspond to the Weinberg operator and operators in Warsaw basis except for some linear combinations.