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 $Z'$ and B-L breaking scalar are found to be of the order $10^{14}$ GeV.
Highlights
Noncommutative geometry (NCG) is a remarkably elegant mathematical framework which allows to derive the field content and Lagrangian of the Standard Model of particle physics [1,2]
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
Running down the renormalization group equations (RGE) from some unification energy scale μunif, we confirm in this new context the result already obtained with the spectral action [12]: the predicted Higgs mass is at least 30% too large
Summary
Noncommutative geometry (NCG) is a remarkably elegant mathematical framework which allows to derive the field content and Lagrangian of the Standard Model of particle physics [1,2]. It must be said that in order to promote Connes-Chamseddine theory to a fullfledged noncommutative Kaluza-Klein theory, one has to define a structure in which the Dirac operator may vary, and would be to spectral triples what bare differentiable manifolds are to Riemannian manifolds Such a structure has been recently proposed [9] in the form of algebraic backgrounds. Running down the renormalization group equations (RGE) from some unification energy scale μunif (which is a free parameter), we confirm in this new context the result already obtained with the spectral action [12]: the predicted Higgs mass is at least 30% too large
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