Five years after the "fifth" boson discovery ...

... a step further in building the quantum "naturalness" for the 125 GeV Higgs scalar?

The major appeal of the more traditional approaches to beyond the standard model building such as supersymmetry (as well as technicolor, extra dimensions, etc.) is that they address the hierarchy problem, and that they shed light on the apparent unification of couplings, both within the context of local effective field theory (EFT). However, this apparent theoretical appeal of supersymmetry does not exclude approaches that do not necessarily follow the local EFT paradigm. For example, in the Spectral Standard Model approach of Connes et al. [147, 148, 149, 152156, 189] the hierarchy problem can be addressed in a completely different fashion [154]. The crucial noncommutative geometric (and thus in some sense non-local) aspect of the SM is found in the Higgs sector, which in principle comes with an extra (second) scale, to be distinguished from the usual UV scale of local EFT. The hierarchy between the Higgs and the UV (Planck) scale can be associated (as shown by Chamseddine and Connes in Ref. [154]) with the natural exponential factor that comes from the dynamical discrete geometry of the Higgs sector. Similarly, the apparent gauge unification (in the guise of an effective SO(10) relation between the gauge couplings) is also incorporated into the Spectral SM. These aspects of the NCG approach to the SM are almost completely unknown in the particle physics community, and at the moment, almost completely undeveloped from a phenomenological viewpoint. One of our aims in our upcoming review of the Spectral SM [162] is to clarify these interesting features of the NCG approach to the SM and make them palatable to the wider phenomenological community. We are also motivated by a deeper need to understand the limitations of the local EFT paradigm from the point of view of the physics of quantum gravity, which is usually, rather naively, ignored at the currently interesting particle physics scales, by invoking the concept of decoupling, which represents another central feature of the local EFT and which is also challenged by the NCG approach to the SM. Finally, as we discuss in the next concluding subsection of this paper, the usual RG analysis of the local EFT should be re-examined in the new light of the non-commutative/non-local structure of the SM, and the apparent existence of two natural (and naturally related) physics scales.

One of the most interesting aspects of the NCG of the SM and its Pati-Salam-like completion is the existence of the GUT scale which can be found in the close proximity to the Planck scale, i.e., the scale of quantum gravity. Given this fact as well as the presence of a hidden fundamental noncommutative structure in this approach, this suggests that the hierarchy problem should get a quantum gravitational rather than an effective field theory treatment. The more convincing physical meaning of this GUT scale also comes after one realizes that Connes’ approach also produces a gravity sector in parallel with the standard model (and its Pati-Salam completion) and thus the GUT scale should be viewed as being close to the natural scale of gravity, i.e., the Planck scale, and indeed the two scales are not that far apart in the non-commutative approach... 
The Higgs scale also naturally appears as a geometric scale in Connes’ non-commutative geometry approach, in complete analogy with the geometric meaning of the Planck and the Hubble scales. Actually, because of the appearance of gravity and the standard model Lagrangians in the Connes’s spectral action, and because of the discrete nature of the Higgs dimension, there is a natural Higgs-like degree of freedom on the gravity side – a Brans-Dicke-Jordan-like scalar – which can be argued to contribute to the geometric warping of the Higgs discrete dimension. This is similar to the infinite extra dimensional scenarios, however, without infinite extra dimensions [152, 154]. In our view, the approach based on NCG (and its related proposal based on the superconnection approach [159, 163]) offers a new and, phenomenologically, almost completely unexplored view on the rationale for the SM and also for its natural completion. This approach also offers a possibly exciting relation with the fundamental physics of quantum gravity, thus relating the infrared physics of the current exciting experimental searches conducted at the LHC to the hidden ultraviolet physics of quantum theory of space and time.
May 12, 2017