Scalar field theory in the strong self-interaction limit

TL;DR

This paper explores a massless quartic scalar field theory with strong self-interaction, revealing an infinite set of infrared trivial theories with a mass gap and potential implications for the Standard Model Higgs sector.

Contribution

It provides a mathematical treatment of strongly self-interacting scalar fields, including classical solutions and quantum corrections, with implications for Higgs physics.

Findings

Existence of an infinite set of infrared trivial scalar theories with a mass gap

Classical solutions expressed via a current expansion

Quantum corrections suggest higher excited Higgs states and altered decay rates

Abstract

Standard Model with a classical conformal invariance holds the promise to give a better understanding of the hierarchy problem and could pave the way for beyond the standard model physics. So, we give here a mathematical treatment of a massless quartic scalar field theory with a strong self-coupling both classically and for quantum field theory. We use a set of classical solutions recently found and show that there exists an infinite set of infrared trivial scalar theories with a mass gap. Free particles have superimposed a harmonic oscillator set of states. The classical solution is displayed through a current expansion and the next-to-leading order quantum correction is provided. Application to the Standard Model would entail the existence of higher excited states of the Higgs particle and reduced decay rates to WW and ZZ that could be already measured.