A theorem on the Higgs sector of the Standard Model

TL;DR

This paper derives the exact Green function for the Higgs sector in the Standard Model, confirming the classical spectrum at the quantum level and predicting the existence of higher excited Higgs states with suppressed production.

Contribution

It provides an exact solution to the Higgs sector's Green function and proves triviality, revealing an internal spectrum of higher excited states for the Higgs particle.

Findings

Exact Green function for the Higgs sector obtained

Spectrum of higher excited Higgs states confirmed

Production rates of excited states are exponentially suppressed

Abstract

We provide the solution of the classical theory for the Higgs sector of the Standard Model obtaining the exact Green function for the broken phase. Solving the Dyson-Schwinger equations for the Higgs field we show that the propagator coincides with that of the classical theory confirming the spectrum also at the quantum level. In this way we obtain a proof of triviality using the K\"allen-Lehman representation. This has as a consequence that higher excited states must exist for the Higgs particle, representing an internal spectrum for it. Higher excited states have exponentially smaller amplitudes and so, their production rates are significantly depressed.