On symmetry breaking in the B-L extended spectral Standard Model

TL;DR

This paper investigates the B-L extended Standard Model within a noncommutative geometry framework, revealing constraints on scalar couplings, incompatibilities with observed particle masses, and a mass-splitting problem similar to GUT issues.

Contribution

It applies the spectral action to the B-L extended Standard Model, deriving conditions for symmetry breaking and analyzing the model's renormalization flow and mass issues.

Findings

Scalar potential minimum requires specific coupling constraints

Constraints conflict with observed top quark and Higgs masses

Identifies a mass-splitting problem analogous to GUT doublet-triplet splitting

Abstract

We apply Connes-Chamseddine spectral action to the $U(1)_{\rm B-L}$- extension of the Standard Model. We show that in order for the scalar potential to reach its minimum for a non-zero value of the new complex scalar field, thus triggering the breaking of B-L symmetry, a constraint on the quartic coupling constants must be satisfied at unification scale. We then explore the renormalization flow of this model in two opposite scenarios for the neutrino sector, and show that this constraint is not compatible with the pole masses of the top quark and SM Higgs boson. We also show that the model suffers from a mass-splitting problem similar to the doublet-triplet splitting problem of Grand Unified Theories. We discuss potential implications for the Noncommutative Geometry program.