Integrating out heavy scalars with modified EOMs: matching computation of dimension-eight SMEFT coefficients

TL;DR

This paper develops an automated method for calculating dimension-eight SMEFT coefficients when integrating out heavy scalars, improving the precision of EFT matching for new physics searches at colliders.

Contribution

It introduces a systematic algorithm for matching dimension-eight operators in SMEFT with proper equations of motion, applicable to generic scalar extensions of the Standard Model.

Findings

Provides a step-by-step procedure for non-redundant basis Wilson coefficients.

Applies the formalism to various scalar extensions, including tree-level and loop effects.

Highlights the importance of dimension-eight operators in Higgs and electroweak phenomenology.

Abstract

The shift in focus towards searches for physics beyond the Standard Model (SM) employing model-independent Effective Field Theory (EFT) methods necessitates a rigorous approach to matching to guarantee the validity of the obtained results and constraints. The limits on the leading dimension-six EFT effects can be rather inaccurate for LHC searches that suffer from large uncertainties while exploring an extensive energy range. Similarly, precise measurements can, in principle, test the subleading effects of the operator expansion. In this work, we present an algorithmic approach to automatise matching computations for dimension-eight operators for generic scalar extensions with proper implementation of equations of motion. We devise a step-by-step procedure to obtain the dimension-eight Wilson coefficients (WCs) in a non-redundant basis to arrive at complete matching results. We apply this formalism to a range of scalar extensions of the SM and provide tree-level and loop-suppressed results. Finally, we discuss the relevance of the dimension-eight operators for a range of phenomenological analyses, particularly focusing on Higgs and electroweak physics.