Dimension-eight Operator Basis for Universal Standard Model Effective Field Theory

TL;DR

This paper systematically constructs a complete basis of dimension-eight operators in the Standard Model Effective Field Theory for universal theories, significantly reducing the number of independent coefficients and clarifying their structure.

Contribution

It provides a complete list of independent dimension-eight operators for universal theories, reducing the basis from 44807 to 175 operators, and maps these to fermionic operators using equations of motion.

Findings

Reduced the number of independent SMEFT coefficients at dimension eight from 44807 to 175.

Identified 86 new operators involving higher derivatives of bosonic fields.

Mapped bosonic operators to fermionic operators using equations of motion.

Abstract

We present the basis of dimension-eight operators associated with universal theories. We first derive a complete list of independent dimension-eight operators formed with the Standard Model bosonic fields characteristic of such universal new physics scenarios. Without imposing C or P symmetries the basis contains 175 operators -- that is, the assumption of Universality reduces the number of independent SMEFT coefficients at dimension eight from 44807 to 175. 89 of the 175 universal operators are included in the general dimension-eight operator basis in the literature. The 86 additional operators involve higher derivatives of the Standard Model bosonic fields and can be rotated in favor of operators involving fermions using the Standard Model equations of motion for the bosonic fields. By doing so we obtain the allowed fermionic operators generated in this class of models which we map into the corresponding 86 independent combinations of operators in the dimension-eight basis of Ref. arXiv:2005.00059