A Green's basis for the bosonic SMEFT to dimension 8

TL;DR

This paper introduces a comprehensive basis of dimension-eight Green's functions for bosonic fields in the Standard Model Effective Field Theory, facilitating higher-order renormalization and matching with ultraviolet models.

Contribution

It provides a new, independent basis of 86 dimension-eight operators in momentum space, proven without algebraic identities, and demonstrates practical applications in matching and integrating out heavy fields.

Findings

Implemented basis in matchmakereft for scalar integrations

Calculated dimension-eight Wilson coefficients for heavy scalars

Simplified redundant Lagrangians using the new basis

Abstract

We present a basis of dimension-eight Green's functions involving Standard Model (SM) bosonic fields, consisting of 86 new operators. Rather than using algebraic identities and integration by parts, we prove the independence of these interactions in momentum space, including a discussion on evanescent bosonic operators. Our results pave the way for renormalising the SM effective field theory (SMEFT), as well as for performing matching of ultraviolet models onto the SMEFT, to higher order. To demonstrate the potential of our construction, we have implemented our basis in matchmakereft and used it to integrate out a heavy singlet scalar and a heavy quadruplet scalar up to one loop. We provide the corresponding dimension-eight Wilson coefficients. Likewise, we show how our results can be easily used to simplify cumbersome redundant Lagrangians arising, for example, from integrating out heavy fields using the path-integral approach to matching.