A $U(1{)}_{B-L}$-extension of the Standard Model from Noncommutative Geometry

Abstract

We derive a $U(1{)}_{B-L}$-extension of the Standard Model from a generalized Connes-Lott model with algebra $\mathbb{C}\oplus \mathbb{C}\oplus \mathbb{H}\oplus M_3(\mathbb{C})$. This generalization includes the Lorentzian signature, the presence of a real structure, and a weakening of the order $1$ condition. In addition to the SM fields, the model contains a $Z_{B-L}^{\prime }$ boson and a complex scalar field $\sigma$ which spontaneously breaks the new symmetry. This model is the smallest one which contains the SM fields and is compatible with both the Connes-Lott theory and the algebraic background framework.

References in corpus (7)

• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Noncommutative Geometry and the standard model with neutrino mixing
• Resilience of the Spectral Standard Model
• Equivariant Lorentzian Spectral Triples
• Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
• The Standard Model as an extension of the noncommutative algebra of forms
• On the definition of spacetimes in Noncommutative Geometry, part II

Cited by in corpus (4)

• On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
• Twisted Standard Model in noncommutative geometry I: the field content
• Particle models from special Jordan backgrounds and spectral triples
• Search for noncommutative interactions in $\gamma \gamma \to \gamma \gamma$ process at the LHC