Standard Model Effective Field Theory: Integrating out Vector-Like Fermions

TL;DR

This paper develops a detailed analytical method to match vector-like fermion models to the Standard Model effective field theory, providing numerical constraints on new fermion generations.

Contribution

It introduces a covariant derivative expansion approach for fermionic models, addressing gamma matrix complications and enumerating all relevant operator contributions.

Findings

Analytical formulas for dimension-6 operator matching.

Numerical constraints on vector-like quarks and leptons.

Detailed study of gamma matrix effects in fermionic expansions.

Abstract

We apply the covariant derivative expansion of the Coleman-Weinberg potential to vector-like fermion models, matching the UV theory to the relevant dimension-6 operators in the standard model effective field theory. The $\gamma$ matrix induced complication in the fermionic covariant derivative expansion is studied in detail, and all the contributing combinations are enumerated. From this analytical result we also provide numerical constraints for a generation of vector-like quarks and vector-like leptons.