# A Unitarity and perturbativity constrains on couplings in QFT

1. May 26, 2016

### 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 any one has an idea ..

2. May 31, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Jun 1, 2016

### Dr.AbeNikIanEdL

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

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.