Integrating Out New Fermions at One Loop

TL;DR

This paper develops a streamlined, transparent method for deriving the one-loop effective action when integrating out heavy fermions, including chiral interactions, using functional determinants, with applications to toy and cosmological models.

Contribution

It introduces a simplified, algorithmic approach to compute the fermionic one-loop effective action that handles chiral interactions directly, improving upon previous methods.

Findings

Simplified computation of fermionic one-loop effective actions.

Method accounts for chiral interaction terms easily.

Applied to toy and cosmological phase transition models.

Abstract

We present the fermionic universal one--loop effective action obtained by integrating out heavy vector--like fermions at one loop using functional techniques. Even though previous approaches are able to handle integrating out heavy fermions with non--chiral interactions, i.e. vanishing $\gamma^5$ interaction terms, the computations proceed in a tedious manner that obscures a physical interpretation. We show how directly tackling the fermionic functional determinant not only allows for a much simpler and transparent computation, but is also able to account for chiral interaction terms in a simple, algorithmic way. Finally, we apply the obtained results to integrate out at one loop the vector--like fermions appearing in a toy model and in a fermionic model that exhibits strong cosmological phase transitions.