Resilience of the spectral standard model

Abstract

We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in the spectral model and we wrongly neglected it in our previous computations. It was shown recently by several authors, independently of the spectral approach, that such a strongly coupled scalar field stabilizes the Standard Model up to unification scale in spite of the low value of the Higgs mass. In this letter we show that the noncommutative neutral singlet modifies substantially the RG analysis, invalidates our previous prediction of Higgs mass in the range 160-180 Gev, and restores the consistency of the noncommutative geometric model with the low Higgs mass.

On globally non-trivial almost-commutative manifolds

“…the Yukawa couplings and the Majorana terms) of the theory are not restricted to be constant, but they are allowed to vary on spacetime. Such variation of the Majorana mass then naturally leads to a new scalar field σ, which was used in [CC12] to restore the consistency of the noncommutative Standard Model with the experimental value of the Higgs mass. In addition however, the variation of the Yukawa couplings will also have its effect on the physical theory.…”

Spectral action with zeta function regularization

“…A nonzero element in that position in the Dirac operator is also necessary to obtain the correct mass of the Higgs [9]. In this case the entry is a field a i ψ c σðxÞψ; i¼ 1; 2; 3 ð5:1Þ…”

“…It is nevertheless remarkable that a theory based on mathematical first principles quantitatively predicts a number which is not too far from the experimental one. Taking the input from experiment, the models can be improved with the introduction of a scalar field which alters the running of the quartic coupling and makes it compatible with the actual mass of 126 GeV [9][10][11]22]. This scalar, usually called σ in this context, had appeared before within noncommutative geometry [8] as well as in general; see e.g.…”

“…Although in Ref. [9] it was inserted ad hoc in the spectral action principle, there are approaches [10] where it comes naturally via the formalism based on introduction of the so-called grand symmetry. Alternatively, it is possible a violation of some of the noncommutativity conditions, as done in Refs.…”

“…It turns out, and this is one of the most interesting aspects of the paper, that these terms are generated by the presence, in the Dirac operator, of a term corresponding to the right-handed neutrino Majorana mass. It is already known [8][9][10][11][12][13] that the presence of a term (or a field) of this kind is crucial in order to obtain the experimental Higgs mass. For the current study, this term must contain dimensionful constants, and this leads to the introduction of the needed lower-dimensional operators in the spectral action.…”