Spectral action and big desert

The values of the Higgs mass are obtained for two possibilities of extending the standard model in a way compatible with the existence of a noncommutative structure at high energies. We assume the existence of a big desert between the low energy electroweak scale and the high energy scale $Λ= 1.1\times 10^{17}$ GeV, where noncommutative features become relevant. We conclude that it is extremely difficult to depart from the Higgs mass value $m_H= 175.1^{+5.8}_{-9.8}$ GeV obtained from noncommutative geometry for the standard model with three generations only.

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