New Scalar Fields in Noncommutative Geometry

TL;DR

This paper extends the Standard Model using noncommutative geometry, introducing new scalar fields, fermions, and gauge groups, and analyzes their implications for particle masses and couplings.

Contribution

It presents a novel extension of the Standard Model within noncommutative geometry, including new particles and scalar fields, and studies their renormalization group flow.

Findings

Constraints on Higgs and scalar masses derived from the model

Relations among gauge, scalar, and Yukawa couplings at high energy

Predictions for scalar mixing and particle phenomenology

Abstract

In this publication we present an extension of the Standard Model within the framework of Connes' noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] which contains the Standard Model particles, new vectorlike fermions and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions and the standard Higgs particle. The bosonic part of the action is given by the spectral action [1] which also determines relations among the gauge couplings, the quartic scalar couplings and the Yukawa couplings at a cut-off energy of ca. 10^(17) GeV. We investigate the renormalisation group flow of these relations. The low energy behaviour allows to constrain the Higgs mass, the mass of the new scalar and the mixing between these two scalar fields.