# Exact solutions to the sector of the Standard Model Higgs

## TL;DR

This paper finds exact solutions to the Dyson-Schwinger equations in the Higgs sector of the Standard Model, revealing a Kaluza-Klein-like mass spectrum that suggests possible extra dimensions.

## Contribution

It extends previous work by identifying an exact solution corresponding to the experimentally observed Higgs, with a novel Kaluza-Klein mass spectrum indicating extra dimensions.

## Key findings

- Exact solutions to Dyson-Schwinger equations for the Higgs sector.
- Discovery of a Kaluza-Klein-like mass spectrum.
- Derivation of gap and running coupling equations.

## Abstract

Recently, we have found an exact solution to the full set of Dyson-Schwinger equations of the non-interacting part of the Higgs sector of the Standard Model obtained by solving the 1-point correlation function equation. In this work we extend this analysis considering also the other possible solution that is the one experimentally observed in the Standard Model. Indeed, the same set of Dyson-Schwinger equations can be exactly solved for the Standard Model with a constant as a solution for the 1-point correlation function. Differently from the Standard Model solution, the one we have found has a mass spectrum of a Kaluza-Klein particle. This could be a clue toward the identification of a further space dimension. Gap equations are obtained in both cases as also the running self-coupling equations.