Hi,
I'm confused about the definition of a perturbative coupling for QFT that it should be less than 4 π, because the higher order corrections comes of order λ/(4π)..
See for instance this discussion
https://www.researchgate.net/post/What_is_the_maximum_appropriate_value_of_the_Yukawa_coupling_can_be_taken
Now why QCD is not perturvative at low energy as the coupling constant approaches just 1 at this region ?
Links
http://physics.stackexchange.com/questions/288251/perturbative-coupling-for-qft
https://www.physicsforums.com/threads/perturbative-coupling-for-qft.890369/
http://bolvan.ph.utexas.edu/~vadim/Classes/2011f/diman.pdf
http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/Chapter-9-pertthqf.pdf
https://www.quora.com/What-do-physicists-mean-by-non-perturbative
The 4\pi there is just a mathematical convenience and bears no physical meaning whatsoever.
The criteria to have a meaningful perturbative expansion is that successive terms must be significantly smaller than previous ones otherwise the expansion series is not convergent and perturbation methods collapse. I would say that beyond 25% corrections the perturbation scheme is flawed.
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