Mass gap without vacuum energy

TL;DR

This paper explores how certain nonlocal deformations in massless theories can generate a mass gap without affecting vacuum energy, with implications for gauge theories and Gribov copies.

Contribution

It introduces a renormalization scheme that maintains ultraviolet softness, leading to vanishing low-dimensional renormalized quantities like mass and cosmological constant.

Findings

Normal mass terms vanish after renormalization.

Cosmological constant remains unaffected by the deformation.

Soft nonlocal effects influence gauge theories and Gribov copies.

Abstract

We consider soft nonlocal deformations of massless theories that introduce a mass gap. By use of a renormalization scheme that preserves the ultraviolet softness of the deformation, renormalized quantities of low mass dimension, such as normal mass terms, vanish via finite counterterms. The same applies to the renormalized cosmological constant. We connect this discussion to gauge theories, since they are also subject to a soft nonlocal deformation due to the effects of Gribov copies. These effects are softer than usually portrayed.