New Scalar Fields in Noncommutative Geometry

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.

Missing left-hand side of eq. (21) added. Some typos and normalisations in section 3 and 5.2 corrected

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• On a Classification of Irreducible Almost-Commutative Geometries V
• Quantum Gravity and Cosmology: an intimate interplay
• Unification of Coupling Constants, Dimension six Operators and the Spectral Action
• A Dark Sector Extension of the Almost-Commutative Standard Model
• Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
• The Inverse Seesaw Mechanism in Noncommutative Geometry
• Can Spectral Action be a Window to Very High Energies?
• A critical survey of twisted spectral triples beyond the Standard Model
• Type-II two-Higgs-doublet model in noncommutative geometry
• Spectral action and the electroweak $\theta$-terms for the Standard Model without fermion doubling