Mass Gap in Infinite Derivative Non-local Higgs: Dyson-Schwinger Approach

TL;DR

This paper uses Dyson-Schwinger equations to analyze non-perturbative effects in non-local Higgs theories, revealing a mass gap in the spectrum influenced by non-locality and self-interactions, with implications for particle physics and cosmology.

Contribution

It extends Dyson-Schwinger formalism to non-local Higgs theories, providing a method to predict the non-perturbative spectrum and mass gap in these models.

Findings

Mass gap arises from non-local self-interactions.

Mass gap diminishes in the UV, approaching conformal behavior.

Method allows non-perturbative spectrum prediction in non-local QFTs.

Abstract

We investigate the non-perturbative degrees of freedom in the class of non-local Higgs theories that have been proposed as an ultraviolet completion 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by string field theory. At the perturbative level, the degrees of freedom of non-local Higgs are the same of the local theory. We prove that, at the non-perturbative level, the physical spectrum of the Higgs mass is actually corrected from the "infinite number of derivatives" present in the action. The technique we use permits to derive the set of Dyson-Schwinger equations in differential form. This proves essentially useful when exact solutions to the local equations are known. We show that all the formalism of the local theory involving the Dyson-Schwinger approach extends quite naturally to the non-local case. Using these methods, the spectrum of non-local theories become accessible and predictable in the non-perturbative regimes. We calculate the N-point correlation functions and predict the mass-gap in the spectrum arising purely from the self-interaction and the non-local scale M. The mass gap generated gets damped in the UV and it reaches conformal limit. We discuss some implications of our result in particle physics and cosmology.