Unitarity and perturbativity constrains on couplings in QFT

In summary, the conversation discusses the unitarity and perturbativity constraints on a potential's parameters, specifically the 2HD potential. The question is raised about which constraint is more essential and what is the most restricted value for the coupling parameter, Lambda. The expert provides some thoughts, stating that being perturbative is important for studying a theory, but unitarity is crucial for the theory to make sense. They also mention that there may not be a physical reason for a theory to be perturbative.
  • #1
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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 ..
 
  • #3
I might not be the best experts, but here are some random thoughts:

Safinaz said:
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.
 
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1. What is unitarity in QFT?

Unitarity in QFT refers to the principle that the total probability of all possible outcomes of a physical process must equal 1. This ensures that the theory is consistent with the laws of probability.

2. How do unitarity constraints affect couplings in QFT?

Unitarity constraints restrict the allowed values of couplings in a QFT. These constraints are typically represented as bounds on the magnitude of the couplings, and can be used to rule out theories that violate unitarity.

3. What is perturbativity in QFT?

Perturbativity in QFT is the requirement that the coupling constants in a theory must be small compared to the energy scale at which the theory is being probed. This ensures that the theory can be accurately calculated using perturbation theory.

4. How do perturbativity constraints affect the validity of a QFT?

If a theory violates the perturbativity constraint, it means that the coupling constants are too large and the theory cannot be accurately calculated using perturbation theory. This may indicate the need for a more fundamental theory or the breakdown of the QFT at high energies.

5. Are there any theories that satisfy both unitarity and perturbativity constraints?

Yes, there are many theories that satisfy both unitarity and perturbativity constraints. In fact, the Standard Model of particle physics is one such theory. However, these constraints are important in ruling out theories that do not satisfy them, leading to the search for more fundamental theories.

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