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More generally, since QCD is asymptotically free (α -> 0 as E -> inf), it may be the only physical QFT we know of that is well-defined at ALL energy scales!
1/4 true .. I strongly disagree with the statement that QCD is well defined at all scales .. namely, below the confinement scale ..
You can write an EFT.. but that’s a *different* lagrangian and hence different theory
Correct, but I am not talking about EFTs. The d.o.f. in the lattice action are *quarks and gluons* - it is not a different theory.
Perhaps we are using “well-defined” to refer to different things. By “well-defined” I meant renormalizable - lattice QCD is an example of a theory that is renormalizable at all scales (including below the confinement scale). What do you mean by the term?
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as E
•There is an E where out denominator will become 0 and hence our series will diverge!
This is called a "Landau Pole" and is exactly the source of our troubles
