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I'm little confused about the maximal appropriate value for the SM Higgs quartic coupling and the Higgs mass = 125 GeV. that as ## \lambda =m_h^2 / 2 v^2 \simeq 0.1 ## for ##v = 246 ~ GeV##.

But according to the perturbation theory, ##\lambda ## enters into higher order corrections as ##\lambda/(4 \pi)##. So that the very generic limit from perturbativity constraint is ## \lambda/(4 \pi) < 1 ## or ## \lambda < 4 \pi ##.

Now after loop correction, say ## \lambda = 10 ##, it won't any more account for the SM Higgs mass !

Best.