Conformal Window: Understanding the Basics

[diegzumillo]

I'm reading about extensions of standard model and this pops up frequently but it's not very clear. I understand it's a region in parameters space so renormalization group naturally becomes relevant and that's about it for my understanding. I can't connect any of this to the beta function of the theory. I also don't really understand what is the 'goal', what is good or bad, what is QCD and what is experimental result. Do we want conformality? why? because QCD is or because the experiment suggests it? Neither?

If anyone cares to clarify or link to some basic overview I would really appreciate. I have a lot of sources but it's an overwhelming subject.

 

[diegzumillo]

Upon reading some more I'm beginning to suspect my problem connecting these dots is the beta function. What we usually see is the one-loop beta function, which shows asymptotic freedom (for number of fermions smaller than 16), however it's calculated using perturbation theory which is not reliable in lower energy regime. So what I'm thinking is that we know the beta function looks like for high values of the coupling constant, but for low values it could have other shapes, including negative values.

Am I close to making sense of this?