Resilience of the spectral standard model

Ali H Chamseddine,Alain Connes

doi:10.1007/jhep09(2012)104

Abstract

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.

Highlights

JHEP09(2012)104 adding a new scalar field strongly coupled to the Higgs
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
That the Brout-Englert-Higgs [17,18,19,20] field has been discovered experimentally, it begs for a conceptual explanation of the Lagrangian of the Standard Model coupled to gravity, which would unify its juxtaposed fragmented pieces

Summary

Higgs-singlet scalar potential

The spectral action for Standard Model was calculated for a cutoff function starting with the Dirac operator of the corresponding noncommutative space, using heat kernel methods. We shall work in the rough approximation where the Yukawa couplings of the top quark ku and the neutrino (both Dirac kν and Majorana kνR ) are dominant and in addition we introduce the dimensionless constant n defined by the relation kν. In this approximation we have a = |ku|2 (n + 3) b = |ku|4 (n2 + 3) c = |kνR |2 d = |kνR |4 e = n |kνR |2 |ku|2. 0 to 1 and increases again to 4g2 for n → ∞

Running the initial conditions for the model with cutoff function

Conclusions

Findings

ΛhΣ 0 2 Λh 0 ΛΣ 0