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I'm little confused about the unitarity and perturbativity constrains which imposed on a potential's parameters, like 2HD potential. Look for example: [arXiv:1507.03618v3 [hep-ph]]

First, I'd like to know what is most essential ? I mean if unitarity constraind ## \lambda##

to say less than 20 and as it's well known perturbativity constraind ## \lambda## to < 4 pi, so what's the most restricted value for ## \lambda## ?

I think being the coupling perturbative is essential so that the theory be finite at higher order correction , so the coupling value in general can't exceed 4 pi .. is it right ?

But for instance in [arXiv:1303.2426v2 [hep-ph]], subsection (III, A), they consider only the unitarity constrain, reaching for ## \lambda## values to ~ 35 ! and say the unitarity constrain is more important than perturbation .. this looks little bit strange for me ..

Does any one has an idea ..