The geometric SMEFT

TL;DR

The paper introduces the geometric SMEFT (geoSMEFT), a novel approach leveraging field space geometry to simplify high-order calculations and achieve a complete characterization of amplitude perturbations in the Standard Model Effective Field Theory.

Contribution

It presents the geoSMEFT framework, enabling easier high-order computations and a comprehensive description of amplitude perturbations in SMEFT using geometric methods.

Findings

Complete $ ext{O}(1/ ext{Lambda}^4)$ results obtained with geoSMEFT.

Demonstrated the use of geoSMEFT in practical examples.

Simplified high-order calculations in SMEFT using geometric invariants.

Abstract

Effective field theories, like the Standard Model Effective Field Theory (SMEFT), are defined by a chosen field content and a set of symmetries, up to a cut off scale $\Lambda$. Usually, in order to perform calculations, gauge independent field re-definitions consistent with the symmetries of the theory are then used to redefine the fields. This procedure results in a fixed (non-redundant) operator basis, that is not itself field re-definition invariant. Recently, an alternative approach of identifying and calculating with field space geometry has been developed. Field redefinition invariants, characterising field space geometry, appear in observables in amplitude perturbations, and have an expansion in terms of local operators. In the case of the SMEFT, calculating via the geometric approach is known as the geoSMEFT. This approach makes it much easier to calculate at high orders in $1/\Lambda$ in the SMEFT, and can directly result in a complete characterisation of an amplitude perturbation in the $1/\Lambda$ expansion. Using the geoSMEFT, several consistent and complete $\mathcal{O}(1/\Lambda^4)$ results are now known. We define the geoSMEFT and demonstrate its use in some examples.