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I was surprised to read that NCG model à la Connes still may suffers from the Hierarchy problem.

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

**Supersymmetric QCD in the Noncommutative Geometry**

http://arxiv.org/abs/1201.3448AFAIK, 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.[...] there is the infamous "hierarchy problem", which is that the Higgs squared mass parameter m_{H}^{2}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.

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

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