Unitarity and perturbativity constrains on couplings in QFT

[Safinaz]

Hi all,

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 anyone has an idea ..

 

[Dr.AbeNikIanEdL]

I might not be the best experts, but here are some random thoughts:

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 ?

Being perturbative just means that you can study your theory using, well, perturbation theory. Which is basically the standard way to look at a theory, apart from brute force numerics. So if you actually want to study a theory, you might have to restrict yourself to a parameter space where it is perturbative. But I am not aware of any physical reasons why a theory should be perturbative.
Unitarity on the other hand is essential for a theory to make sense in the first place. I don't think there is a way to interpret scattering otherwise in a sensible way.