One-loop Effective Action up to Dimension Eight: Integrating out Heavy Fermion(s)

TL;DR

This paper derives a universal one-loop effective action up to dimension eight for heavy fermions using the Heat-Kernel method, applicable to generic theories and capturing CP-violating effects.

Contribution

It introduces a method to compute the fermionic effective action up to dimension eight, applicable to generic UV theories without specific model assumptions.

Findings

Provides explicit Heat-Kernel coefficients for fermionic operators.

Captures CP-violating and conserving effects in the effective action.

Applicable to a wide class of theories with heavy fermions.

Abstract

We present the universal one-loop effective action up to dimension eight after integrating out heavy fermion(s) using the Heat-Kernel method. We have discussed how the Dirac operator being a weak elliptic operator, the fermionic operator still can be written in the form of a strong elliptic one such that the Heat-Kernel coefficients can be used to compute the fermionic effective action. This action captures the footprint of both the CP conserving as well as violating UV interactions. As it does not rely on the specific forms of either UV or low energy theories, can be applicable for a very generic action. Our result encapsulates the effects of heavy fermion loops only.