A quantum of solace (for higher energy physics)
- In this framework indeed the low Higgs mass value of 125 GeV can be calculated from first principles thanks to a ultra-weak mixing with a standard model singlet Higgs scalar charged under the gauged B-L symmetry and leaving canonically at a natural ultraheavy see-saw scale. This
forecastpost-diction relies on i) the spectral action principle, ii) a model of spacetime as the product of an ordinary spin manifold by the most simple finite noncommutative geometry F required to accommodate neutrino mixing and iii) a deeper understanding of the noncommutative "dynamics" that consisted in removing (not adding!) a particular axiom called the first order condition that arises now as a spontaneously broken phase of higher symmetry and is not imposed from outside.
- More importantly this theoretical endeavour leads now without arbitrariness to the Pati–Salam  gauge group SU(4)C⊗SU(2)L⊗SU(2)R, together with the corresponding gauge fields and a scalar sector that can not be chosen freely, in contrast to the early work on grand unification. In fact, there are only a few possibilities for the precise scalar content that could depend physically on hypotheses on the flavour structure of the theory (?*). One important feature that deserves to be underline : it has been checked that the spectral action principle gives the usual Pati–Salam action with unification of its three gauge couplings at a scale of the order of 1015-16 GeV while the intermediate see-saw scale is in the range 1011-13 GeV.
* This is a possibly unsafe interpretation of the blogger. To quote the original paper "there are only a few possibilities for the precise scalar content, depending on the assumptions made on the finite Dirac operator".Considering the fact that this operator encodes the fermions masses and mixing in the spectral point of view I hope my own words are basically correct. The interested reader may find a tentative discussion of flavour mixing in the noncommutative geometric setting here.
//Last edit : 13 August 2016.