Does Connes spectral model solves the Hierarchy problem?

[nicoo]

I was surprised to read that NCG model à la Connes still may suffers from the Hierarchy problem.
Supersymmetric QCD in the Noncommutative Geometry
http://arxiv.org/abs/1201.3448

[...] there is the infamous "hierarchy problem", which is that the Higgs squared mass parameter m_H² receives enormous quantum corrections from the virtual effects of every particle that couples to the Higgs field. These diffculties also exist in the NCG standard model.
It is known that these shortcomings are remedied by introducing supersymmetry into the standard model. In order for the NCG standard model to be phenomenologically viable, it is quite desirable to incorporate supersymmetry into the model.

AFAIK, in the Spectal Model the Higgs and top quark masses are computed. So they are direct consequences of the few hypothesis of the model and are in line with experimental values.
I would say there is no Hierarchy problem anymore, since the low mass of the Higgs (with respect to the GUT scale) is not unnatural and fined-tune anymore but "logical" because it comes from direct computation.

So, does NCG solves the Hierarchy problem?

BTW, a very nice introduction to NCG by Andrzej Sitarz

 

[AndyW]

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Hello,

Thank you for bringing up this interesting topic. As you mentioned, the hierarchy problem is a longstanding issue in particle physics and it is not unique to the standard model. It is indeed surprising that the NCG model à la Connes still may suffer from this problem, even though it is a more advanced and elegant approach to describing the fundamental particles and their interactions.

One possible explanation for this is that the NCG model, while incorporating many aspects of the standard model, still has some differences that could lead to different quantum corrections and ultimately, the hierarchy problem. As you also noted, the introduction of supersymmetry has been a successful solution to this problem in the standard model, and it is possible that incorporating supersymmetry into the NCG model could also help alleviate this issue.

I agree with you that the direct computation of the Higgs and top quark masses in the NCG model is a promising step towards a more complete understanding of these particles. However, it is important to continue exploring and testing the model in order to fully understand its strengths and limitations.

Thank you for sharing the link to Andrzej Sitarz's introduction to NCG. I will definitely check it out. Overall, it seems that the NCG model is a fascinating and promising approach to particle physics, but more research and experimentation is needed to fully understand its capabilities and limitations.