Vacuum energy in the effective field theory of general relativity II: Inclusion of fermions and a comment on the QCD contribution

TL;DR

This paper extends previous two-loop effective field theory analysis of vacuum energy in general relativity to include fermions, showing the graviton remains massless and discussing QCD contributions and chiral symmetry.

Contribution

It introduces a two-loop analysis with fermions in the effective field theory of gravity, confirming the masslessness of the graviton and addressing QCD vacuum energy issues.

Findings

Graviton remains massless at two-loop order with fermions.

QCD vacuum energy contributions require fine-tuning.

Chiral symmetry is compatible with flat Minkowski background.

Abstract

Recently in the framework of a two-loop order calculation for an effective field theory of scalar and vector fields interacting with the metric field we have shown that for the cosmological constant term which is fixed by the condition of vanishing vacuum energy the graviton remains massless and there exists a self-consistent effective field theory of general relativity defined on a flat Minkowski background. In the current paper we extend the two-loop analysis for an effective field theory of fermions interacting with the gravitational field and obtain an analogous result. We also address the issues of fine tuning of the strong interaction contribution to the vacuum energy and the compatibility of chiral symmetry in the light quark sector with the consistency of the effective field theory of general relativity in a flat Minkowski background.