Noncommutative geometry, the Lorentzian Standard Model and its B-L extension

Abstract

We explore the 1-loop renormalization group flow of two models coming from a generalization of the Connes-Lott version of Noncommutative Geometry in Lorentzian signature: the Noncommutative Standard Model and its B-L extension. Both make predictions on coupling constants at high energy, but only the latter is found to be compatible with the top quark and Higgs boson masses at the electroweak scale. We took into account corrections introduced by threshold effects and the relative positions of the Dirac and Majorana neutrino mass matrices and found them to be important. Some effects of 2-loop corrections are briefly discussed. The model is consistent with experiments only for a very small part of its parameter space and is thus predictive. The masses of the $Z^{\prime }$ and B-L breaking scalar are found to be of the order $10^{14}$ GeV.

arXiv commentSection VII.D has been entirely rewritten. A new section (VII.E) briefly discusses the 2-loop corrections

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• Particle models from special Jordan backgrounds and spectral triples
• A critical survey of twisted spectral triples beyond the Standard Model
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes