Mass gap in strongly coupled infinite derivative non-local Higgs: Dyson–Schwinger approach

Abstract

We investigate the non-perturbative degrees of freedom (d.o.f.) in the class of non-local Higgs theories that have been proposed as an ultraviolet completion 4D quantum field theory generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by string field theory and ghost-free non-local approaches to quantum gravity. At the perturbative level, the d.o.f. of non-local Higgs are the same of the local theory. We prove that, at the non-perturbative level, the physical spectrum of the strongly-coupled 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 the strongly-coupled non-local theories become accessible 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 proper weak perturbation limit is correctly recovered from the strong coupling regime in the limit of the coupling of the theory goes to zero. Our results show the mass gap generated in the non-local theories gets damped in the UV and it reaches conformal limit. We discuss the implications of our result in particle physics and cosmology.