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

TL;DR

This paper investigates the renormalization group flow of noncommutative geometric models of particle physics, finding that only the B-L extended model aligns with experimental particle masses and predicts very high mass scales for new particles.

Contribution

It extends the noncommutative geometric Standard Model to include B-L symmetry and analyzes its high-energy behavior and experimental viability.

Findings

Only the B-L extension matches observed top quark and Higgs masses.

The B-L breaking scale is around 10^{14} GeV.

The model is highly constrained and predictive.

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.